The materials to prepare students for practical lessons of inorganic chemistry

LESSON № 9.

Theme: Theories of acids and bases. Dissociation water.

Plan

1. Acid-base theories. Amphoteric electrolytes (ampholytes). Quantitative descriptions of force of acids and bases.

2. Dissociation of water. Water product. pH. pH-value (рН) of weak and strong acids and bases solutions. рН value for human body liquids iorm and pathology.

 

 

1. ACIDS AND BASES. ACID-BASE THEORIES. AMPHOTERIC ELECTROLYTES (AMPHOLYTES). QUANTITATIVE DESCRIPTIONS OF FORCE OF ACIDS AND BASES.

Early Acid Base Theories: Lavoisier and Davy

The entry Acidity and Basicity explains what acids and bases are. In essence, acids and bases are a way of classifying substances according to a very special form of reaction, namely the exchange of protons ebetween chemical compounds. For more information please consult that entry. The historic evolution of the concepts ‘acid’ and ‘base’ is another topic altogether. That’s what this entry is about.

In a first attempt to characterise substances, the concepts of acids and bases were loosely defined as substances that change some properties of water. Much later (in the 19th Century) the composition of acids and bases was elucidated, bringing a very narrow definition of acids and bases. These concepts evolved even further to become broader again, yet still very fuzzily defined. These concepts are a very useful tool in chemical reasoning. Nowadays, virtually anything can be seen as an acid or a base.

 

In the Beginning

The starting point for most of the scientific historical evolutions is, as usual, the Mediterranean region in BC-times, Greece in particular. There, some smart people were trying to unravel nature’s secrets. One first step in that direction was to sort all kinds of substances in an attempt to characterise nature.

One of the criteria used, which everyone thought was good, was the taste of stuff. According to this criterion the first categories were: salty-tasting stuff, sour-tasting stuff, sweet-tasting stuff, and bitter-tasting stuff. Sour-tasting stuff would give rise to the word ‘acid’, which comes from the Greek word oxein, which mutated into the Latin verb acere, which means ‘to make sour'(thus the term ‘acetic acid’, which is the sour tasting component in vinegar, is a redundancy).

With the passing of time, people found out that the sour-tasting stuff had some other properties in common, apart from just tasting sour; for example, it changes the colour of litmus1 and corrodes some metals. It is for this reason that the classification term ‘acid’ is the only category originally based on taste still in use today. The reasons for the taste of the other stuff were found to be of a more complicated nature, which is the reason why the rest of the categories are no longer in use.

 

Acids

It was not until modern times, that the fundamental working mechanisms and the chemistry of acids was elucidated. One first attempt was delivered by a famous French maamed Antoine Laurent Lavoisier (1743-1796). He used to perform chemistry shows for the wealthy noblesse in Paris, making a good extra buck in that way.

Lavoisier was a remarkable and well-funded scientist, the so-called father of modern chemistry, who eventually lost his head to the French Revolution. Before he did that, however, he was one of the first people to try out a chemical classification of substances. By 1776, he had come up with the idea that a certain compound, element, or essence in the acid would be responsible for its acidity. For that reason he called the substance oxy-gene2, or ‘oxygen’ as we know it today. Eventually, this idea turned out to be wrong. Nevertheless, it was a good beginning.

The British scientist Humphry Davy (1778-1829), who among other things discovered the medicinal uses of nitrous oxide (laughing-gas) by self-experimentations, continued these investigations; and by 1810, he found out that the oxygen was not responsible for the acidity, since certain acids would be acid without containing any oxygen.

In Munich, by the 1840s, Justus Freiherr von Liebig (1803-1873), one of the big chemistry hot-shots in Germany and the founder of agro-chemistry, proposed that the acidity was generated by hydrogen, because it is the component all acids have in common. Now this idea was a very good one, as one will see later… Before starting on that, let us not forget the bases.

 

Bases

Bases were identified and categorised as the substances which are neutralising acids. For that reason, the progress in the characterisation of bases was always connected to the more popular characterisation of acids. As a consequence, the theories for bases were always overshadowed by the theories for acids. Nevertheless, bases have also been known for a long time.

The associated word ‘alkaline’ (which is used to describe the properties of a base-solution, like its soapy taste) has Arabic roots. The term originally meant ‘roasting’, because the first alkaline substances were obtained by roasting ashes then treating them with water and slaked lime (calcium hydroxide). The substances obtained are sodium and potassium hydroxide, two of the most classic bases, which were used to make soap.

The use of the word ‘base’ to describe these substances was introduced a lot later; the original rationale remains obscure. One possibility is that the ‘bases’ were the basic (in the sense of ‘fundamental’) compounds used to form salts with acids. Another possibility is that it’s called that just to add confusion. The second theory has many adherents among chemistry students.

 

I. Before Lavoisier

The words acid and alkaline (i.e. bases) are derived from direct sensory experience.

The word acid comes from the Latin word acere, which means “sour.” All acids taste sour. Well known from ancient times were vinegar, sour milk and lemon juice.

Early in the 1200s, the strong mineral acids were first isolated. Sulfuric acid was made by heating green vitriol [iron(II) sulfate] and condensing the vapor into water. Other vitriols gave the same product. Mixing a vitriol with nitre (postassium nitrate) and heating produced vapors which gave nitric acid. Adding sal ammoniac (ammonium chloride) to nitric acid gave aqua regia, so named for its ability to dissolve gold. Hydrochloric acid (“spirit(s) of salt” – a name still used in commerce/pharmacy as late as the early 1970s) also was known to the middle ages; certainly it was known to Paracelsus (early 1500s).

The word alkaline comes from the Arabic al-qily, which means “to roast in a pan” or “the calcinated ashes of plants.” By leaching the ashes with water, one can obtain a solution of sodium or potassium carbonate (to use the modern terms). This is then mixed with slaked lime (calcium hydroxide) and you get a solution of NaOH or KOH. This technique was described in writing in the 900s, but may have existed for many years prior.

However, it was not until more modern times that the chemical nature of acids and bases began to be explored.

II. Antoine Lavoisier

His basic idea was that acidity was caused by the presence of oxygen in the compound. In fact, Lavoisier (in September 1777) created the word oxygen. From the Latin, it means “acid maker.” This idea turned out to be wrong, but it is historically important since it is the first systematic attempt to chemically characterize acids and bases.

In early 1776, Lavoisier was able to write this:

“It appeared proven . . . that the air we respire contains only a quarter of true air; that this true air is mixed, in our atmosphere, with three or four parts of an injurious air, a sphesis of mophette, which causes most animals to perish, if the quantity of it is a little greater.”

The “true air” is, of course, oxygen and the “species of mophette” is nitrogen. The more complex nature of the atmosphere, with carbon dioxide and the noble gases became apparent later. However, it was Lavoisier that was the first to show the atmosphere was composed of more than one substance.

At this time in scientific history, it was a common belief that the properties of acids could be traced back to a single substance. Lavoisier had studied the combustion of phosphorus and sulfur in 1772-73 and had proven that they combine with something in the atmosphere. He also knew that, when dissolved in water, phosphorus and sulfur oxides made acidic solutions.

Also, the test Lavoisier used to demonstrate the presence of “true air” was the nitrous air test, devised by Joseph Priestley. Lavoisier knew that nitrous air combined with oxygen and the resulting compound made nitric acid in water.

Hence, his conclusion (published about April 1776) was that oxygen was the component in a compound that was responsible for the generic property of acid. The other portion of the compound combined with the oxygen was called an ‘acidifiable base” and was responsible for the specific properties of the compound.

III. Humphry Davy

Joseph Priestley discovered HCl (a gas) in 1772 when he reacted concentrated sulfuric acid on NaCl. When HCl was dissolved in water, a typical acidic solution was formed and it was named muriatic acid. This is from the Latin word muria, meaning brine.

In 1774, Carl Scheele heated HCl with manganese dioxide (MnO₂) and got a yellowish, choking gas. In sunlight, a water solution of this gas evolved oxygen and left muriatic acid in solution. This led Claude Berthollet, in 1785, to name this new substance oxymuriatic acid, even though it did not show acidic properties.

(In 1810, Davy recognized oxymuriatic acid as an element and give it its modern name – chlorine.)

In 1779, Lavoisier concluded that oxygen was present in muriatic acid and that this was making it an acid.

Events remained unchanged until about 1809-1810, when Davy enters the scene. He reacted many metals and non-metals with oxymuriatic acid and never obtained oxygeor did he obtain any oxygen compounds. He heated charcol to white-hot temperatures in the presence of oxymuriatic gas and did not get a reaction, much less any oxygen evolved.

Here is some of what he wrote in 1810:

“One of the singular facts I have observed on this subject, and which I have before referred to, is, that charcol, even when ignited to whiteness in oxymuriatic or muriatic acid gases, by the Voltaic battery, effects no change in them; if it has been preveiously freed from hydogen and moisture by intense ignition in vacuo. This experiment, which I have several times repeated, led me to doubt the existence of oxygen in that substance.”

On September 23, 1809, Davy had written in a letter to a friend:

“. . . the substance we took for Sulphuretted Hydrogene is telluretted Hydrogene, . . . , a substance affording another proof that Hydrogene is an oxide.”

Davy was reasoning that, since H₂S and H₂Te are acids, their common component (hydrogen) must contain oxygen, the principle of acidity according to Lavoisier.

Finally, in the 1810 article, Davy writes:

“Few substances, perhaps have less claim to be considered a acid, than oxymuriatic acid… May it not in fact be a peculiar acidifying and dissolving principle, forming compounds, with combustible bodies, analogous to acids containing oxygen, or oxides? On this idea, muriatic acid may be considered as having hydrogen for its base and oxymuriatic acid for its acidifying principle.”

What Davy means by base in the last sentence is that hydrogen confers the generic proper of acid, he does not mean a base in the modern sense of the word.

 

Lavoisier’s oxygen theory of acids

The first scientific concept of acids and bases was provided by Lavoisier circa 1776. Since Lavoisier’s knowledge of strong acids was mainly restricted to oxoacids, such as HNO₃ (nitric acid) and H₂SO₄ (sulfuric acid), which tend to contain central atoms in high oxidation states surrounded by oxygen, and since he was not aware of the true composition of the hydrohalic acids (HF, HCl, HBr, and HI), he defined acids in terms of their containing oxygen, which in fact he named from Greek words meaning “acid-former” (from the Greek οξυς (oxys) meaning “acid” or “sharp” and γεινομαι (geinomai) meaning “engender”). The Lavoisier definition was held as absolute truth for over 30 years, until the 1810 article and subsequent lectures by Sir Humphry Davy in which he proved the lack of oxygen in H2S, H2Te, and the hydrohalic acids. However, Davy failed to develop a new theory, concluding that “acidity does not depend upon any particular elementary substance, but upon peculiar arrangement of various substances”. One notable modification of oxygen theory was provided by Berzelius, who stated that acids are oxides of nonmetals while bases are oxides of metals.

Liebig’s hydrogen theory of acids

Circa 1838 Justus von Liebig proposed that an acid is a hydrogen-containing substance in which the hydrogen could be replaced by a metal This redefinition was based on his extensive work on the chemical composition of organic acids, finishing the doctrinal shift from oxygen-based acids to hydrogen-based acids started by Davy. Liebig’s definition, while completely empirical, remained in use for almost 50 years until the adoption of the Arrhenius definition.

Common acid–base theories

Arrhenius definition

The first modern definition of acids and bases was devised by Svante Arrhenius. A hydrogen theory of acids, it followed from his 1884 work with Friedrich Wilhelm Ostwald in establishing the presence of ions in aqueous solution and led to Arrhenius receiving the Nobel Prize in Chemistry in 1903.

As defined by Arrhenius:

·        an Arrhenius acid is a substance that dissociates in water to form hydrogen ions (H+); that is, an acid increases the concentration of H+ ions in an aqueous solution.

This causes the protonation of water, or the creation of the hydronium (H₃O+) ion. Thus, in modern times, the use of H+ is regarded as a shorthand for H₃O+, because it is now known that a bare proton does not exist as a free species in aqueous solution.

·        an Arrhenius base is a substance that dissociates in water to form hydroxide (OH−) ions; that is, a base increases the concentration of OH− ions in an aqueous solution.

The Arrhenius definitions of acidity and alkalinity are restricted to aqueous solutions, and refer to the concentration of the solvent ions. Under this definition, pure H₂SO₄ and HCl dissolved in toluene are not acidic, and molten NaOH and solutions of calcium amide in liquid ammonia are not alkaline.

Overall, to qualify as an Arrhenius acid, upon the introduction to water, the chemical must either cause, directly or otherwise:

·        an increase in the aqueous oxonium concentration, or

·        a decrease in the aqueous hydroxide concentration.

Conversely, to qualify as an Arrhenius base, upon the introduction to water, the chemical must either cause, directly or otherwise:

·        a decrease in the aqueous oxonium concentration, or

·        an increase in the aqueous hydroxide concentration.

The universal aqueous acid–base definition of the Arrhenius concept is described as the formation of a water molecule from a proton and hydroxide ion. This leads to the definition that in Arrhenius acid–base reactions, a salt and water are formed from the reaction between an acid and a base.[6] This is a neutralization reaction – the acid and base properties of H+ and OH− are neutralized, for they combine to form H2O, the water molecule. The acid-base neutralization reaction can be put into a word equation:

acid + base → salt + water

The positive ion from a base and the negative ion from an acid form a salt together – in other words, an acid-base neutralization reaction is a double-replacement reaction. For example, when a neutralization reaction takes place between hydrochloric acid (HCl) and sodium hydroxide (NaOH), the products are sodium chloride (common table salt) and water.

HCl(aq) + NaOH(aq) → NaCl + H2O

Notice how the cations and the anions merely switched places: the Na+ from the NaOH combined with the Cl- from the HCl to form NaCl, while the OH− from the NaOH combined with the H+ from the HCl to form H₂O.

Solvent system definition

One of the limitations of the Arrhenius definition is its reliance on water solutions. Edward C. Franklin studied the acid–base reactions in liquid ammonia in 1905 and pointed out the similarities to the water-based Arrhenius theory. Albert F. O. Germann, working with liquid COCl₂, formulated the solvent-based theory in 1925, thereby generalizing the Arrhenius definition to cover aprotic solvents.

Germann pointed out that in many solutions, there are ions in equilibrium with the neutral solvent molecules:

Ø solvonium: A generic name for a positive ion.

Ø solvate:  A generic name for a negative ion.

For example, water and ammonia undergo such dissociation into hydronium and hydroxide, and ammonium and amide, respectively:

2 H₂O is in equilibrium with H₃O+ + OH−

2 NH₃ is in equilibrium with NH₄⁺ + NH₂−

Some aprotic systems also undergo such dissociation, such as dinitrogen tetroxide into nitrosonium and nitrate, antimony trichloride into dichloroantimonium and tetrachloroantimonate, and phosgene into chlorocarboxonium and chloride:

N₂O₄ is in equilibrium with NO+ + NO₃−

2 SbCl₃ is in equilibrium with SbCl₂+ + SbCl₄−

COCl2 is in equilibrium with COCl+ + Cl−

A solute that causes an increase in the concentration of the solvonium ions and a decrease in the concentration of solvate ions is defined as an acid. A solute that causes an increase in the concentration of the solvate ions and a decrease in the concentration of the solvonium ions is defined as a base.

Thus, in liquid ammonia, KNH₂ (supplying NH₂−) is a strong base, and NH₄NO₃ (supplying NH₄+) is a strong acid. In liquid sulfur dioxide (SO₂), thionyl compounds (supplying SO₂+) behave as acids, and sulfites (supplying SO₃²⁻) behave as bases.

The non-aqueous acid–base reactions in liquid ammonia are similar to the reactions in water:

2 NaNH₂ (base) + Zn(NH₂)₂ (amphiphilic amide) → Na₂[Zn(NH₂)₄]

2 NH₄I (acid) + Zn(NH₂)₂ (amphiphilic amide) → [Zn(NH₃)₄)]I₂

Nitric acid can be a base in liquid sulfuric acid:

HNO₃ (base) + 2 H₂SO₄ → NO₂+ + H₃O+ + 2 HSO₄−

The unique strength of this definition shows in describing the reactions in aprotic solvents; for example, in liquid N2O4:

AgNO₃ (base) + NOCl (acid) → N₂O₄ (solvent) + AgCl (salt)

Because the solvent system definition depends on the solute as well as on the solvent itself, a particular solute can be either an acid or a base depending on the choice of the solvent: HClO₄ is a strong acid in water, a weak acid in acetic acid, and a weak base in fluorosulfonic acid; this characteristic of the theory has been seen as both a strength and a weakness, because some substances (such as SO₃ and NH₃) have been seen to be acidic or basic on their own right. On the other hand, solvent system theory has been criticized as being too general to be useful. Also, it has been thought that there is something intrinsically acidic about hydrogen compounds, a property not shared by non-hydrogenic solvonium salts.

PROTON DONORS AND ACCEPTORS

The older Arrhenius theory of acids and bases viewed them as substances which produce hydrogen ions or hydroxide ions on dissociation. As useful a concept as this has been, it was unable to explain why NH₃, which contains no OH^– ions, is a base and not an acid, why a solution of FeCl₃ is acidic, or why a solution of Na₂S is alkaline.

A more general theory of acids and bases was developed by Franklin in 1905, who suggested that the solvent plays a central role. According to this view, an acid is a solute that gives rise to a cation (positive ion) characteristic of the solvent, and a base is a solute that yields aanion (negative ion) which is also characteristic of the solvent. The most important of these solvents is of course H₂O, but Franklin’s insight extended the realm of acid-base chemistry into non-aqueous systems as we shall see in a later lesson.

 

THE BRØNSTED-LOWRY THEORY OF ACIDS AND BASES

The Brønsted-Lowry theory was developed to eliminate some of the limitations of the Arrhenius concept of acids and bases.

Although the theory states that the acid must still contain hydrogen, it does not require an aqueous medium. E.g. liquid ammonia is a base in aqueous solution but it can act as an acid in the absence of water by transferring a proton to a base and forming the amide anion, NH₂⁻:

NH₃ + base ↔ NH₂⁻ + base + H⁺

In the Brønsted-Lowry theory, acid-base reactions are regarded as proton transfer reactions. This definition enabled the Arrhenius list to include gases such as HCl and NH₃ among many others.

A broader theory of acids and bases was later proposed by the Lewis theory. According to this theory, an acid is any species that acts as an electron pair acceptor (electrophile) and a base is any species that acts as an electron pair donor (nucleophile). Therefore an acid-base reaction is the sharing of an electron pair provided by the base to the acid.

This definition expanded the list to include metal ions and other electron pair acceptors as acids and provides a handy framework for non-aqueous reactions.

A number of points about the Brønsted–Lowry definition should be emphasized:

1. As mentioned above, this definition is independent of the solvent. The ions derived from the solvent (H₃O⁺ and OH⁻ in water and NH₄⁺ and NH₂⁻ in liquid ammonia) are not accorded any special status but appear as examples of acids or bases in terms of the general definition. On the other hand, of course, they will be particularly important species for reactions in the solvent to which they relate.

2. Definition. The first comprises anions derived from acids containing more than one acidic hydrogen—e.g., the bisulfate ion (HSO₄⁻) and primary and secondary phosphate ions (H₂PO₄⁻ and HPO₄²⁻) derived from phosphoric acid (H₃PO₄). The second and more interesting class consists of positively charged ions (cations), such as the ammonium ion (NH₄⁺), which can be derived by the addition of a proton to a molecular base, in this case ammonia (NH₃). The hydronium ion (H₃O⁺), which is the hydrogen ion in aqueous solution, also belongs to this class. The charge of these ionic acids, of course, always must be balanced by ions of opposite charges, but these oppositely charged ions usually are irrelevant to the acid–base properties of the system. For example, if sodium bisulfate (Na⁺HSO₄⁻) or ammonium chloride (NH₄⁺Cl⁻) is used as an acid, the sodium ion (Na⁺) and the chloride ion (Cl⁻) contribute nothing to the acidic properties and could equally well be replaced by other ions, such as potassium (K⁺) and perchlorate (ClO₄⁻), respectively.

3. Molecules such as ammonia and organic amines are bases by virtue of their tendency to accept a proton. With metallic hydroxides such as sodium hydroxide, on the other hand, the basic properties are due to the hydroxide ion itself, the sodium ion serving merely to preserve electrical neutrality. Moreover, not only the hydroxide ion but also the anions of other weak acids (for example, the acetate ion) must be classed as bases because of their tendency to reform the acid by accepting a proton. Formally, the anion of any acid might be regarded as a base, but for the anion of a very strong acid (the chloride ion, for example) the tendency to accept a proton is so weak that its basic properties are insignificant and it is inappropriate to describe it as a base. Similarly, all hydrogen compounds could formally be defined as acids, but in many of them (for example, most hydrocarbons, such as methane, CH₄) the tendency to lose a proton is so small that the term acid would not normally be applied to them.

4. Some species, including molecules as well as ions, possess both acidic and basic properties; such materials are said to be amphoteric. Both water and ammonia are amphoteric, a situation that can be represented by the schemes H₃O⁺–H₂O–OH⁻ and NH₄⁺–NH₃–NH₂⁻. Another example is the secondary phosphate ion, HPO₄²⁻, which can either lose or accept a proton, according to the following equations: HPO₄²⁻ ⇄ PO₄³⁻ + H⁺ and HPO₄²⁻ + H⁺ ⇄ H₂PO₄⁻. The amphoteric properties of water are particularly important in determining its properties as a solvent for acid–base reactions.

5. The equation A ⇄ B + H⁺, used in the Brønsted–Lowry definition, does not represent a reaction that can be observed in practice, since the free proton, H⁺, can be observed only in gaseous systems at low pressures. In solution, the proton always is attached to some other species, commonly a solvent molecule. Thus in water the ion H₃O⁺ consists of a proton bound to a water molecule. For this reason all observable acid–base reactions in solution are combined in pairs, with the result that they are of the form A₁ + B₂ ⇄ B₁ + A₂. The fact that the process A ⇄ B + H⁺ cannot be observed does not imply any serious inadequacy of the definition. A similar situation exists with the definitions of oxidizing andreducing agents, which are defined respectively as species having a tendency to gain or lose electrons, even though one of these reactions never occurs alone and free electrons are never detected in solution (any more than free protons are).

 

Alternative definitions

Although the Brønsted–Lowry concept of acids and bases as donors and acceptors of protons is still the most generally accepted one, other definitions are often encountered. Certain of these are adapted for special situations only, but the most important of these other definitions is in some respects more general than the Brønsted–Lowry definition. This definition was first proposed by the American chemist Gilbert N. Lewis in 1923.

According to Lewis, an acid is a species that can accept an electron pair from a base with the formation of a chemical bond composed of a shared electron pair (covalent bond). This classification includes as bases the same species covered by the Brønsted–Lowry definition, since a molecule or ion that can accept a proton does so because it has one or more unshared pairs of electrons, and therefore it also can combine with electron acceptors other than the proton. On the other hand, the typical Lewis acids need not (and usually do not) contain protons, being species with outer electron shells that are capable of expansion, such as boron trifluoride (BF₃), sulfur trioxide (SO₃), and silver ion (Ag+). Lewis originally based his ideas on the experimental fact that these nonprotonic acids often exhibit the properties regarded as typical of acids, such as neutralization of bases, action on indicators, and catalysis. Such substances often are electron acceptors, but this is not always the case; carbon dioxide (CO₂) and nitrogen pentoxide (N₂O₅), for example, contain completed octets of electrons and, according to usual valence theory, cannot accept any more. In addition, hydrogen-containing substances that have always been regarded as acids (acetic acid, for example) are not obviously electron acceptors, being rather adducts of the proton (a true Lewis acid) and a base such as the acetate ion. They can only be brought logically into the Lewis scheme by appealing to the fact that the reaction between a proton acid, which may be designated as XH, and a base, denoted by B, passes through an intermediate hydrogen-bonded state, X-H…B (in which the dotted line indicates a hydrogen bond, a relatively weak secondary attractive force).

Numerous lengthy polemical exchanges have taken place regarding the relative merits of the Brønsted–Lowry and Lewis definitions. The difference is essentially one of nomenclature and has little scientific content. In the remainder of this article the term acid is used to denote a proton donor (following the Brønsted–Lowry terminology), whereas the term Lewis acid is employed exclusively to refer to electron-pair acceptors. This choice is based partly on the logical difficulties mentioned in the last paragraph and partly on the fact (see below Acid–base equilibria) that the quantitative description of acid–base reactions is much simpler when it is confined to proton acids. It also represents the commonest usage of the terms.

The definition of Lewis acids and bases in terms of the gain or loss of electrons should not be confused with the definition of oxidizing and reducing agents in similar terms. In oxidation–reduction reactions one or more electrons are transferred completely from the reducing agent to the oxidizing agent, whereas in a Lewis acid–base reaction an electron pair on the base is used to form a covalent link with the acid.

Certain other acid–base definitions have been based upon reactions occurring in specific solvent systems. For proton acids in amphoteric solvents these are equivalent to the Brønsted–Lowry definition. It is sometimes convenient to have general terms for the cation and anion derived from the solvent molecule by the addition and removal of a proton, respectively. The terms lyonium and lyate ions are occasionally used in this way. In water, the lyonium and lyate ions are H₃O+ and OH−; in ethanol, C₂H₅OH₂+ and C₂H₅O−; and in liquid ammonia, NH₄+ and NH₂−. For a given solvent, an acid can then be defined as a substance that increases the lyonium ion concentration (and correspondingly decreases the lyate ion concentration), whereas a base increases the lyate ion concentration (and decreases the lyonium ion concentration). This kind of definition, to be sure, really does not add anything to the concept of acids and bases as proton donors and proton acceptors.

 

The idea that an acid is a solute that gives rise to cations characteristic of the solvent and that a base is a solute that gives rise to anions characteristic of the solvent has sometimes been extended to solvents where no protons are involved at all—for example, liquid sulfur dioxide, SO₂. In this example, the solvent is supposed to ionize according to the equation 2SO₂ ⇄ SO²⁺ + SO₃²⁻. Thionyl chloride, regarded as SO²⁺ + 2Cl⁻, then can be considered an acid, and potassium sulfite, 2K⁺ + SO₃²⁻, can be considered a base. The species SO²⁺ and SO₃²⁻ can certainly be regarded as Lewis acids and bases, but it is doubtful that they exist to any appreciable extent in liquid sulfur dioxide, a situation that makes the discussion somewhat artificial. Although this view of acids and bases has been useful in stimulating work in unusual types of solvent (for example, in carbonyl chloride, selenium oxychloride, antimony trichloride, and hydrogen cyanide), it has not met with general acceptance.

The Brønsted–Lowry model of proton donors and proton acceptors in acid–base reactions is an improvement over the Arrhenius theory, which was limited for it stated that bases had to contain the hydroxyl group. The main effect of the Brønsted–Lowry definition is to identify the proton (H+) transfer occurring in the acid–base reaction.

 

Acid–base reactions

Proton-transfers

As already mentioned (The Brønsted–Lowry definition), the reaction expressed by the Brønsted–Lowry definition, A ⇄ B + H⁺, does not actually occur in any solution processes. This is because H⁺, the bare proton, has an enormous tendency to add to almost all chemical species and cannot exist in any detectable concentrations except in a high vacuum. Apart from any specific chemical interaction, the very small size of the proton (about 10⁻¹⁵ metre) means that it exerts an extremely powerful electric field, which will polarize and therefore attract any molecule or ion it comes into contact with. It has been estimated that the dissociation of 19 grams of the hydronium ion H₃O⁺ to give 1 gram of protons and 18 grams of water would require the expenditure of about 1,200,000 joules (290,000 calories) of energy, and thus it is an extremely unlikely process indeed.

Typical acid–base reactions may be thought of as the combination of two reaction schemes, A₁ ⇄ B₁ + H⁺ and H⁺ + B₂ ⇄ A₂, leading to the combined form A₁ + B₂ ⇄ B₁ + A₂. This represents a proton-transfer reaction from A₁ to B₂, producing B₁ and A₂. A large number of reactions in solution, often referred to under a variety of names, can be represented in this way. This is illustrated by the following examples, in each of which the species are written in the order A₁, B₂, B₁, A₂.

DISSOCIATION OF MOLECULAR ACIDS IN WATER

In this instance, water acts as a base. The equation for the dissociation of acetic acid, for example, is CH₃CO₂H + H₂O ⇄ CH₃CO₂⁻ + H₃O⁺.

DISSOCIATION OF BASES IN WATER

In this case, the water molecule acts as an acid and adds a proton to the base. An example, using ammonia as the base, is H₂O + NH₃ ⇄ OH⁻ + NH₄⁺. Older formulations would have written the left-hand side of the equation as ammonium hydroxide, NH₄OH, but it is not now believed that this species exists, except as a weak, hydrogen-bonded complex.

DISSOCIATION OF ACIDS AND BASES IN NONAQUEOUS SOLVENTS

These situations are entirely analogous to the comparable reactions in water. For example, the dissociation of acetic acid in methanol may be written as CH₃CO₂H + CH₃OH ⇄ CH₃CO₂⁻ + CH₃OH and the dissociation of ammonia in the same solvent as CH₃OH + NH₃ ⇄ CH₃O⁻ + NH₄⁺.

SELF-DISSOCIATION OF AMPHOTERIC SOLVENTS

In this case, one solvent molecule acts as an acid and another as a base. Self-dissociation of water and liquid ammonia may be given as examples:

NEUTRALIZATION

For a strong acid and a strong base in water, the neutralization reaction is between hydrogen and hydroxide ions—i.e., H₃O⁺ + OH⁻ ⇄ 2H₂O. For a weak acid and a weak base, neutralization is more appropriately considered to involve direct proton transfer from the acid to the base. For example, the neutralization of acetic acid by ammonia may be written as CH₃CO₂H + NH₃ → CH₃CO₂⁻ + NH₄⁺. This equation does not involve the solvent; it therefore also represents the process of neutralization in an inert solvent, such as benzene, or in the complete absence of a solvent. (If one of the reactants is present in large excess, the reaction is more appropriately described as the dissociation of acetic acid in liquid ammonia or of ammonia in glacial acetic acid.)

HYDROLYSIS OF SALTS

Many salts give aqueous solutions with acidic or basic properties. This is termed hydrolysis, and the explanation of hydrolysis reactions in classical acid–base terms was somewhat involved. In terms of the Brønsted–Lowry concept, however, hydrolysis appears to be a natural consequence of the acidic properties of cations derived from weak bases and the basic properties of anions derived from weak acids. For example, hydrolysis of aqueous solutions of ammonium chloride and of sodium acetate is represented by the following equations:

The sodium and chloride ions take no part in the reaction and could equally well be omitted from the equations.

The acidity of the solution represented by the first equation is due to the presence of the hydronium ion (H₃O⁺), and the basicity of the second comes from the hydroxide ion (OH⁻). The reverse reactions simply represent, respectively, the neutralization of aqueous ammonia by a strong acid and of aqueous acetic acid by a strong base.

A superficially different type of hydrolysis occurs in aqueous solutions of salts of some metals, especially those giving multiply charged cations. For example, aluminum, ferric, and chromic salts all give aqueous solutions that are acidic. This behaviour also can be interpreted in terms of proton-transfer reactions if it is remembered that the ions involved are strongly hydrated in solution. In a solution of an aluminum salt, for instance, a proton is transferred from one of the water molecules in the hydration shell to a molecule of solvent water. The resulting hydronium ion (H₃O⁺) accounts for the acidity of the solution:

In the Brønsted–Lowry theory, an acid donates a proton and the base accepts it. The ion or molecule remaining after the acid has lost a proton is known as that acid’s conjugate base, and the species created when the base accepts the proton is known as the conjugate acid. This is expressed in the following reaction:

acid + base is in equilibrium with conjugate base + conjugate acid.

Notice how this reaction can proceed in either forward or backward direction; in each case, the acid donates a proton to the base.

With letters, the above equation can be written as:

HA + B is in equilibrium with A− + HB+

The acid, HA, donates a H+ ion to become A−, its conjugate base. The base, B, accepts the proton to become HB+, its conjugate acid. In the reverse reaction, A− it accepts a H+ from HB+ to recreate HA in order to remain in equilibrium. In the reverse reaction, as HB+ has donated a H+ to A−, it therefore recreates B and remains in equilibrium.

In 1923 the Danish chemist J.N. Brønsted, building on Franklin’s theory, proposed that

An acid is a proton donor; a base is a proton acceptor.

In the same year the English chemist T.M. Lowry published a paper setting forth some similar ideas without producing a definition; in a later paper Lowry himself points out that Brønsted deserves the major credit, but the concept is still widely known as the Brønsted-Lowry theory.

These definitions carry a very important implication: a substance cannot act as an acid without the presence of a base to accept the proton, and vice versa. As a very simple example, consider the equation that Arrhenius wrote to describe the behavior of hydrochloric acid:

HCl → H⁺ + A^–

This is fine as far as it goes, and chemists still write such an equation as a shortcut. But in order to represent this more realistically as a proton donor-acceptor reaction, we now depict the behavior of HCl in water by in which the acid HCl donates its proton to the acceptor (base) H₂O.

 

“Nothing new here”, you might say, noting that we are simply replacing a shorter equation by a longer one. But consider how we might explain the alkaline solution that is created when ammonia gas NH₃ dissolves in water. An alkaline solution contains an excess of hydroxide ions, so ammonia is clearly a base, but because there are no OH^– ions in NH₃, it is clearly not an Arrhenius base. It is, however, a Brønsted base:

In this case, the water molecule acts as the acid, donating a proton to the base NH₃ to create the ammonium ion NH₄⁺.

The foregoing examples illustrate several important aspects of the Brønsted-Lowry concept of acids and bases:

·        A substance cannot act as an acid unless a proton acceptor (base) is present to receive the proton;

·        A substance cannot act as a base unless a proton donor (acid) is present to supply the proton;

Water plays a dual role in many acid-base reactions; H₂O can act as a proton acceptor (base) for an acid, or it can serve as a proton donor (acid) for a base (as we saw for ammonia.

The hydronium ion H₃O⁺ plays a central role in the acid-base chemistry of aqueous solutions.

Hydrogen ions cannot exist in water

There is another serious problem with the Arrhenius view of an acid as a substance that dissociates in water to produce a hydrogen ion. The hydrogen ion is no more than a proton, a bare nucleus. Although it carries only a single unit of positive charge, this charge is concentrated into a volume of space that is only about a hundred-millionth as large as the volume occupied by the smallest atom. (Think of a pebble sitting in the middle of a sports stadium!) The resulting extraordinarily high charge density of the proton strongly attracts it to any part of a nearby atom or molecule in which there is an exess of negative charge. In the case of water, this will be the lone pair (unshared) electrons of the oxygen atom; the tiny proton will be buried within the lone pair and will form a shared-electron (coordinate) bond with it, creating a hydronium ion, H₃O+. In a sense, H₂O is acting as a base here, and the product H₃O+ is the conjugate acid of water:

Atoms can gain or lose electrons in order to form ions in a process called ionization (compounds formed in this way are called ionic compounds).  When ionic compounds dissolve in water, their ions separate from one another in a process called dissociation.  One interesting feature of water and many other covalent compounds is that they too can dissociate into ions.  Unlike ionic compounds, such as sodium chloride, they are not ionized before they dissociate; they accomplish ionization and dissociation at the same time.

Acid-base reactions à la Brønsted

According to the Brønsted concept, the process that was previously written as a simple dissociation of a generic acid HA (“HA → H+ + A–)” is now an acid-base reaction in its own right:

HA + H₂O → A–+ H₃O⁺

The idea, again, is that the proton, once it leaves the acid, must end up somewhere; it cannot simply float around as a free hydrogen ion.

 

Conjugate pairs

 

A reaction of an acid with a base is thus a proton exchange reaction; if the acid is denoted by AH and the base by B, then we can write a generalized acid-base reaction as

AH + B → A^– + BH⁺

Notice that the reverse of this reaction,

BH⁺ + A^– → B + AH⁺

is also an acid-base reaction. Because all simple reactions can take place in both directions to some extent, it follows that transfer of a proton from an acid to a base must necessarily create a new pair of species that can, at least in principle, constitute an acid-base pair of their own.

Strong acids and weak acids

We can look upon the generalized acid-base reaction

 

as a competition of two bases for a proton:

Definition of a “strong” acid

If the base H₂O overwhelmingly wins this tug-of-war, then the acid HA is said to be a strong acid. This is what happens with hydrochloric acid and the other common strong “mineral acids” H₂SO₄, HNO₃, and HClO₄:

Solutions of these acids in water are really solutions of the ionic species shown in heavy type on the right. This being the case, it follows that what we call a 1 M solution of “hydrochloric acid” in water, for example, does not really contain a significant concentration of HCl at all; the only real a acid present in such a solution is H₃O⁺!

These considerations give rise to two important rules:

H₃O⁺ is the strongest acid that can exist in water;

All strong acids appear to be equally strong in water.

The leveling effect

The second of these statements is called the leveling effect. It means that although the inherent proton-donor strengths of the strong acids differ, they are all completely dissociated in water. Chemists say that their strengths are “leveled” by the solvent water.

A comparable effect would be seen if one attempted to judge the strengths of several adults by conducting a series of tug-of-war contests with a young child. One would expect the adults to win overwhelmingly on each trial; their strengths would have been “leveled” by that of the child.

Weak acids

Most acids, however, are able to hold on to their protons more tightly, so only a small fraction of the acid is dissociated. Thus hydrocyanic acid, HCN, is a weak acid in water because the proton is able to share the lone pair electrons of the cyanide ion CN^– more effectively than it can with those of H₂O, so the reaction

HCN + H₂O → H₃O⁺ + CN^–

proceeds to only a very small extent.

Since a strong acid binds its proton only weakly, while a weak acid binds it tightly, we can say that

Strong acids are “weak”; Weak acids are “strong”

If you are able to explain this apparent paradox, you understand one of the most important ideas in acid-base chemistry!

Strong acids have weak conjugate bases

This is just a re-statement of what is implicit in what has been said above about the distinction between strong acids and weak acids. The fact that HCl is a strong acid implies that its conjugate base Cl^– is too weak a base to hold onto the proton in competition with either H₂O or H₃O⁺. Similarly, the CN^– ion binds strongly to a proton, making HCN a weak acid.

Salts of weak acids give alkaline solutions

The fact that HCN is a weak acid implies that the cyanide ion CN^– reacts readily with protons, and is thus is a relatively good base. As evidence of this, a salt such as KCN, when dissolved in water, yields a slightly alkaline solution:

CN^– + H₂O → HCN + OH^–

This reaction is still sometimes referred to by its old namehydrolysis (“water splitting”), which is literally correct but tends to obscure its identity as just another acid-base reaction. Reactions of this type take place only to a small extent; a 0.1M solution of KCN is still, for all practical purposes, 0.1M in cyanide ion.

In general, the weaker the acid, the more alkaline will be a solution of its salt. However, it would be going to far to say that “ordinary weak acids have strong conjugate bases.” The only really strong base is hydroxide ion, OH^–, so the above statement would be true only for the very weak acid H₂O.

Strong bases and weak bases

The only really strong bases you are likely to encounter in day-to-day chemistry are alkali-metal hydroxides such as NaOH and KOH, which are essentially solutions of the hydroxide ion.

Most other compounds containing hydroxide ions such as Fe(OH)₃and Ca(OH)₂ are not sufficiently soluble in water to give highly alkaline solutions, so they are not usually thought of as strong bases.

There are actually a number of bases that are stronger than the hydroxide ion ‑ best known are the oxide ion O^2– and theamide ion NH₂^–, but these are so strong that they can rob water of a proton:

O^2– + H₂O → 2 OH^–

NH₂^– + H₂O → NH₃ + OH^–

This gives rise to the same kind of leveling effect we described for acids, with the consequence that

Hydroxide ion is the strongest base that can exist in aqueous solution.

Salts of weak bases give acidic solutions

The most common example of this is ammonium chloride, NH₄Cl, whose aqueous solutions are distinctly acidic:

NH₄⁺ + H₂O → NH₃ + H₃O⁺

Because this (and similar) reactions take place only to a small extent, a solution of ammonium chloride will only be slightly acidic.

Autoprotolysis

From some of the examples given above, we see that water can act as an acid

CN^– + H₂O → HCN + OH^–

and as a base

NH₄⁺ + H₂O → NH₃ + H₃O⁺

If this is so, then there is no reason why “water-the-acid” cannot donate a proton to “water-the-base”:

This reaction is known as the autoprotolysis of water.

Chemists still often refer to this reaction as the “dissociation” of water and use the Arrhenius-style equation H₂O → H⁺ + OH^– as a kind of shorthand.

As discussed in the previous lesson, this process occurs to only a tiny extent. It does mean, however, that hydronium and hydroxide ions are present in any aqueous solution.

Can other liquids exhibit autoprotolysis? The answer is yes. The most well-known example is liquid ammonia:

2 NH₃ → NH₄⁺ + NH₂^–

Even pure liquid sulfuric acid can play the game:

2 H₂SO₄→ H₃SO₄⁺ + HSO₄^–

Each of these solvents can be the basis of its own acid-base “system”, parallel to the familiar “water system”.

Ampholytes

Water, which can act as either an acid or a base, is said to beamphiprotic: it can “swing both ways”. A substance such as water that is amphiprotic is called an ampholyte.

 

It is of course the amphiprotic nature of water that allows it to play its special role in ordinary aquatic acid-base chemistry. But many other amphiprotic substances can also exist in aqueous solutons. Any such substance will always have a conjugate acid and a conjugate base, so if you can recognize these two conjugates of a substance, you will know it is amphiprotic.

The carbonate system

For example, the triplet set {carbonic acid, bicarbonate ion, carbonate ion} constitutes an amphiprotric series in which the bicarbonate ion is the ampholyte, differing from either of its neighbors by the addition or removal of one proton:

If the bicarbonate ion is both an acid and a base, it should be able to exchange a proton with itself in an autoprotolysis reaction:

HCO₃^– + HCO₃^– → H₂CO₃ + CO₃^2–

Your very life depends on the above reaction! CO₂, a metabolic by-product of every cell in your body, reacts with water to form carbonic acid H₂CO₃ which, if it were allowed to accumulate, would make your blood fatally acidic. However, the blood also contains carbonate ion, which reacts according to the reverse of the above equation to produce bicarbonate which can be safely carried by the blood to the lungs. At this location the autoprotolysis reaction runs in the forward direction, producing H₂CO₃ which loses water to form CO₂ which gets expelled in the breath. The carbonate ion is recycled back into the blood to eventually pick up another CO₂molecule.

If you can write an autoprotolysis reaction for a substance, then that substance is amphiprotic.

Dissociation of Water

When water dissociates, one of the hydrogeuclei leaves its electron behind with the oxygen atom to become a hydrogen ion, while the oxygen and other hydrogen atoms become a hydroxide ion.  Since the hydrogen ion has no electron to neutralize the positive charge on its proton, it has a full unit of positive charge and is symbolized as H+.  The hydroxide ion retains the electron left behind and thus has a full unit of negative charge, symbolized by OH-.  The hydrogen ion (proton) does not wander long by itself before it attaches to the oxygen atom of a second un-ionized water molecule to form a hydronium ion (H3O +)

In any sample of water, very few of the molecules are dissociated at any one time:  in fact, only about one in 550 million.  There is, however, a constant change; as one hydrogen ion reattaches to a hydroxide ion to form a water molecule, another water molecule dissociates to replace the hydrogen ion and the hydroxide ion in solution.

Hydrochloric Acid

Certain molecules, ionic and covalent, dissociate in such a way that they release a hydrogen ion without releasing a hydroxide ion.  These substances are called acids.  Since a hydrogen ion is really just a single proton in most cases, the chemist’s definition of an acid is a “proton donor.” If very many protons (hydrogen ions) are “donated” the effect can be very profound, such as burning your skin or dissolving metal.  The acid illustrated is hydrochloric acid.  Pure hydrochloric acid is a gas, but it dissolves easily in water to produce a solution of hydrogen ion and chloride ion.  Since nearly all of it is dissociated in water, it is called a strong acid.  Acids that do not dissociate completely are called weak acids.

Sodium Hydroxide

The opposite of an acid is a base, also known as an alkali.  A typical strong base is sodium hydroxide, the principal component of lye.  Sodium hydroxide dissociates to form a sodium ion and a hydroxide ion.  A base is defined as a “proton acceptor.”  The most common bases produce hydroxide ion when they dissociate, and it is the hydroxide ion that accepts the proton.  A strong base can give your skin a much worse burn than an acid.

Neutralization

When a base and an acid are mixed, the hydroxide ion and the base combines with the hydrogen ion from the acid to form water.   This process is called neutralization.

The ionic product, K_w

Water ionization occurs endothermically due to electric field fluctuations betweeeighboring molecules. Dipole librations, resulting from thermal effects and favorable localized hydrogen bonding, cause these fluctuations. The process may be facilitated by exciting the O-H stretch overtone vibration.Once formed, the ions may separate by means of the Grotthuss mechanism but normally (>99.9%) recombine within a few femtoseconds. Rarely (about once every eleven hours per molecule at 25 °C, or less than once a week at 0 °C) the localized hydrogen bonding arrangement breaks before allowing the separated ions to return. The pair of ions (H⁺, OH^–) hydrate independently and continue their separate existence for about 70 μs (this lifetime also dependent on the extent of hydrogen bonding, being shorter at lower temperatures). They tend to recombine when separated by only one or two water molecules.

H₂O   H⁺ + OH^–

K_w = [H⁺][OH^–]

Although the extent of ionization is tiny ([H⁺]/[H₂O] = 2.8 x 10^-9 at 37 °C), the ionization and consequential changes in the tiny concentrations of hydrogen ions have absolute importance to living processes. Hydrogen ions are produced already hydrated (that is, as oxonium ions, H₃O⁺; also called oxonium or hydroxonium ions) and have negligible existence as naked protons in liquid or solid water, where they interact extremely strongly with electron clouds. All three hydrogen atoms in the oxonium ion are held by strong covalent bonds and are equivalent (that is, C_3v symmetry). The thermodynamic properties of the dissociation at 25 °C and 100,000 Pa are ΔU = 59.5 kJ mol^-1, ΔV =21.4 cm³ mol^-1, ΔH = kJ mol^-1, ΔG = 79.9 kJ mol^-1, ΔS = -77.2 J K^-1 mol^-1.

 

The above equations are better written as:

2 H₂O   H₃O⁺ + OH^–

K_w = [H₃O⁺][OH^–]

 

Both ions are ionic kosmotropes, creating order and form stronger hydrogen bonds with surrounding water molecules. The concentrations of H₃O⁺ and OH^– are normally taken as the total concentrations of all the small clusters including these species. As other water molecules are required to promote the hydrolysis, the equation below includes the most important. 

 

4 H₂O   H₅O₂⁺ + H₃O₂^–

The concentration of oxonium and hydroxide ions produced is therefore equal to the square root of the ionization constant (K_w).

Aqueous OH^– does not ionize further as (O^2- + H₂O 2OH^–, K > 10²²). = pH

The oxonium ion concentration (commonly called ‘hydrogen ion concentration’) is often given in terms of the pH, where pH = Log₁₀(1/[H₃O⁺]) = -Log₁₀([H₃O⁺]) (that is, [H₃O⁺] = 10^-pH)  with the concentration of H₃O⁺ in mol l^-1. More precisely pH = -Log₁₀(a_H) = -Log₁₀(m_Hλ_H/m°) where a_H, m_H, λ_H and m° are the relative (molality based) activity, molality, molal activity coefficient and standard molality (1 mol kg^-1) of the hydrogen ions. At the low concentrations normally found, the hydrogen ion concentration is close enough to the relative (molality based) activity for its use for most purposes. The molal activity of hydrogen ions cannot be determined directly but may be determined using a glass electrode relative to the response of standard buffer solutions of suitable ionic strength. Glass electrode-determined pH values are error-prone and calculated hydrogen ion concentrations should be treated with caution, particularly at the extremes of pH. For more information and a list of primary pH standards see. Proof that the use of the equation pH = -Log₁₀(H⁺) may give misleading results (and pH = -Log₁₀(a_H) is preferred) is easily shown as the pH of 0.1 M HCl decreases when it is diluted with 5% M LiCl. The pH scale was first introduced by Sørensen (as p_H·) in 1909 using colorimetric measurements and the hydrogen electrode, which gives an electrode potential proportional to pH. The pH scale extends to negative numbers (for example, concentrated HCl has a pH of about -1.1) and to greater than 14 (for example, saturated NaOH has a pH of about 15.0). There is a recent review of the pH of natural water.

In a similar manner pK_w is defined by pK_w = Log₁₀(1/K_w) = -Log₁₀(K_w), utilizing concentrations in mol l^-1 

 

pK_w = -log₁₀(K_w )

Variation in K_w with T and P

K_w is very temperature dependent, increasing with temperature (that is, from 0.001 x 10^-14 mol² l^-2 at -35 °C (pH 8.5), 0.112 x 10^-14 mol² l^-2 at 0 °C (pH 7.5), to 0.991 x 10^-14 mol² l^-2 at 25 °C (pH 7.0), to 9.311 x 10^-14 mol² l^-2 at 60 °C (pH 6.5), to 10^-12 mol² l^-2 at 300 °C (pH 6.0, ~50 MPa) in agreement with the high positive standard free energy There is a minimum at about 249 °C along the saturated pressure line for H₂O and at about 257 °C for D₂O). The pK_w H₂O minimum is about 0.74 lower than that for D₂O.

A theoretical treatment of this temperature dependence is available.

 

Temperature and density dependence of ionization has been examined. Ionization depends on the pressure, with K_w doubling at about 100 MPa; unsurprising in view of the negative ΔV associated with the ionization, -18.1 cm³ mol^-1 .

Ionization also varies with solute concentration and ionic strength; for example, K_w goes through a maximum of about 2 x 10^-14 mol² l^-2 at about 0.25 M ionic strength (using tetramethylammonium chloride, where possibly the change in hydrogen bonding caused by clathrate formation encourages ionization) before dropping to a value of about 1 x 10^-16 mol² l^-2at 5 M (with higher concentrations disrupting the hydrogen bonding). Ionization will also be different at interfaces; for example, it is greater at lipid membrane surfaces.

In ice, where the local hydrogen bonding rarely breaks to separate the constantly forming and re-associating ions, the ionization constant is much lower (for example at -4 °C, K_w = 2 x 10^-20 mol² l^-2 ).

Footnotes

This low occurrence means that at neutrality (pH 7 at 25 °C)^c, similarly charged ions are, on average, separated by vast distances (~0.255 μm) in molecular terms and (for example) bacteria contain only a few tens of free hydrogen ions. Contributing to this effect are the high dielectric constant (encouraging charge separation) and high concentration of H₂O (~55.5 M; increasing the absolute amount dissociated). The mean lifetime of a oxonium ion (1 ps; about the same as that of a hydrogen bond) is such that the charge could be associated with over 10⁷ molecules of water before neutralization.

Note that acid-base neutrality only occurs when the concentration of hydrogen ions equals the concentration of hydroxyl ions (whatever the pH). This only occurs at pH 7 in pure water when at 25 °C. A solution is acidic when the hydrogen ion concentration is greater than the hydroxide ion concentration, whatever the pH.

In a vacuum the reaction H₂O  H⁺ + OH^– requires over three times more energy (1.66 MJ mol^-1) than dissociation H₂O   H· + ·OH (531 kJ mol^-1). In water the hydration of the ions (H⁺ ΔG° hydration -1112.5 kJ mol^-1, this includes H₃O⁺ ΔG° hydration -461.1 kJ mol^-1; OH^– ΔG° hydration -437.6 kJ mol^-1 reduces the ΔG° of the reaction 2 H₂O   H₃O⁺ + OH^– to +99.78 kJ mol^-1 (These calculations assumes that the standard state of the solvent water is taken as 1.0 M. If the standard state of the solvent water is its mole fraction (= 1.0), the ΔG° is +79.907 kJ mol^-1). The dissociated radicals (H·, ·OH) are also somewhat stabilized in liquid water, as shown by the occasional dissociation of water.

The acidity constant (K_a) of H₂O is defined (as other acids) by the equation H₂O(+H₂O) H⁺(aq)+OH^–. Therefore K_a= [H⁺][OH^–]/[H₂O] = K_w/[H₂O] = K_w/55.345 (at 25 °C) and pK_a = pK_w +1.743 (= 15.739 at 25 °C; compare pK_as of H₂Te, H₂Se and H₂S are 2.6, 3.89 and 7.04 respectively). There is a difficulty that has been ignored in this definition as the K_a should be expressed in terms of activities rather than concentrations and the activity of pure H₂O is defined as unity whereas that of solutes is defined relative to their standard state (1 mol kg^-1).

As Logarithms may only be taken of dimensionless numbers, all the concentrations (activities, partial pressures, etc.) in any Logarithmic expression are actually divided by unit values in the same units of that concentration (activity, partial pressure, etc.); thus, for example here [H₃O⁺] (concentration of of H₃O⁺ in mol l^-1) is actually [H₃O⁺]/(1.0 mol l^-1).

The p in pH originated as the arbitrary choice for the naming of the electrode solutions ‘p’ and ‘q’ by Sørensen , but is now taken to mean the ‘logarithm to the base 10 of the reciprocal of’ (cologarithm).

It is generally thought that protons and hydroxide ions rapidly diffuse in liquid water, with protons diffusing almost twice as fast as hydroxide ions (and seven times as fast as Na⁺ ions). However, it should be recognized that these diffusivities are determined from movement in an electric field (at 100 v m^-1 ; H⁺ and OH^– have mobilities of 36.23 and 20.64 μm s^-1 respectively at 298 K), where the special mechanisms described below are operational, and the true diffusive movements of the ions may be somewhat less (particularly as they are attached to their attendant hydrogen-bonded water and accompanied by thier counter ions), as can be recognized by the proton diffusional limitations that take place at the surface of some immobilized enzymes

Diffusion of hydrogen ions

The Grotthuss mechanism, whereby protons tunnel from one water molecule to the next via hydrogen bonding, is the usual mechanism given for facilitated proton mobility. The process is similar to that of autoionization; the mechanism causing the ions (H⁺, OH^–) to initially separate. Both processes increase with increasing temperature

 

 

It is noteworthy that this process, although faster than translational diffusion, proves to be much slower than might be expected from its mechanism. This relative sluggishness may be due to the rotation of molecules required for trains of sequential proton movement (see below) and the consequential necessity for the breakage of hydrogen bonds. The strange effect of degassing increasing proton diffusion over ten-fold, however, indicates that the non-polar dissolved gas molecules, naturally present, disrupt the linear chains of water molecules necessary for the Grotthuss mechanism and so slow the proton movement. After a proton has moved along a chain of water molecules, it is clear that further proton movement requires a reorientation of the hydrogen bonding, if continued proton tunneling through the same molecules and in the same direction is to proceed.

In order to migrate, the ions must be associated with hydrogen bonded clusters; the stronger and more extensive the cluster, the faster the migration. Stronger hydrogen bonding causes the O···O distance to be shorter, so easing the close approach required for transfer. A limiting factor in the mobility for both ions is the breakage of an outer shell hydrogen bonds. This enables the proton to transfer from H₃O⁺ and involves the additional energy requirements of stretching the outer hydrogen bonds due to the contraction of the O···O distance.

 

Oxonium ion transport mechanism

 

The triangular arrangement of water molecules formed during proton transfer, has also been found in the protonated trimer (H₇O₃⁺),and necessarily involves a rotation around the hydrogen bond as the ‘Zundel’ dihydronium (H₅O₂⁺) ion flattens from its normal tetrahedral structure. The presence of the fourth water molecule associated with the H₉O₄⁺ cluster is seen in a neutron diffraction study as oriented but distant (3.2 Å,). Proton transport may also occur using ‘Zundel’ dihydronium (H₅O₂⁺) ions only, as below, which involves the concerted movement of two molecules. Such proton jumps may be short (shown on left) or long (shown on right). An ab initio simulation favored this mechanism, where H₅O₂⁺ mobility was induced by thermal movement in the second solvation shell. An external electrical field was found to ease the process by suitably orienting the water in this direction. It has been suggested that proton mobility above 149 °C decreases due to the decreasing amounts of H₅O₂⁺ present.

 

 

An additional and alternative mechanism has been proposed, using ab initio simulations but in agreement with the Zundel’ dihydronium (H₅O₂⁺) ions concentrations, by which the rapid diffusion of hydrogen ions, at temperatures below about 400 °C, is due to the high diffusion of these H₅O₂⁺ ions, allowed by the weaker surrounding hydrogen-bonded water network.

Proton transport in water, protein channels and bioenergetic proteins has recently been reviewed]. It is interesting that aquaporin water channels deliberately re-orient water molecules to preclude sequential hydrogen bonding so preventing proton transfer by the Grotthuss mechanism.

Diffusion of hydroxyl ions

 

A similar process to that for hydrogen ions was initially proposed for hydroxide mobility:

 

However it is now thought that hydroxide ions make use of an entirely different mechanism  for diffusion in an electric field. It has been proposed that the movement of the hydroxyl ion is accompanied by a hyper-coordinating (that is, a fourth hydrogen bond donor) water molecule. The hydrated hydroxide ion is coordinated to four electron-accepting water molecules such that when an incoming electron-donating hydrogen bond forms (necessitating the breakage of one of the original hydrogen bonds) a fully tetrahedrally coordinated water molecule may be easily formed by the hydrogen ion transfer. The structure below left, HO^–(··HOH)₄, together with the more distant oriented water molecule below it, has been seen using neutron diffraction, with empirical structure refinement, of concentrated NaOH solutions. The different mechanism, involving extra hydrogen bond rearrangements plus re-orientations, is the reason for the reduced mobility of the hydroxide ion compared with the oxonium ion. Interestingly, the transfer involves an anionic trimer (H₅O₃^–), whereas hydrogen ion movement involved the cationic trimer (H₇O₃⁺) (note that neither of these trimers are stable by themselves).

 

 

The bare hydrogen ion (a proton) readily hydrates and cannot exist freely in solution. Initial hydration forms the oxonium ion (H₃O⁺) (sometimes called the hydrogen ion). This has a flattened trigonal pyramidal structure (calculated gas phase values O-H bond length 0.961 Å, H-O-H angle 114.7°; compare with the significantly different calculated liquid values of O-H bond length 1.002 Å, H-O-H angle 106.7° with C_3v symmetry and equivalent protons. H₃O⁺ has an effective ionic radius of 0.100 nm somewhat less than that of the H₂O molecular radius (0.138 nm). Its molar volume is -5.4 cm³ mol^-1 due to electrostriction It forms the core of the ‘Eigen’ cation, described later. The structure can invert (like a wind-blown umbrella) with an activation energy less than that of a hydrogen bond and this may occur as an alternative, or even preferred, pathway to rotation within a dynamic hydrogen bonded clusters. H₃O⁺ is also found in the monohydrates of HCl, H₂SO₄and HClO₄, for example, [H₃O⁺]₂[SO₄^2-]. All the occupied molecular orbitals of H₃O⁺are on another page.

It has been shown that H₃O⁺ can donate three hydrogen bonds (but accepts almost none); the strength of these donated hydrogen bonds being over twice as strong as those between H₂O molecules in bulk water.  This effectively means that the H₃O⁺ cation can be considered as H₉O₄⁺ in solution. The polarization causes these first shell water molecules to also each donate two further hydrogen bonds (but also accept little) with strengths still somewhat higher than bulk water. Second shell water molecules also donate two hydrogen bonds (but also accept only one with a rather weak hydrogen bond) with strengths still fractionally higher than bulk water. The bias towards donated hydrogen bonds, within the two-shell H₂₁O₁₀⁺ ion cluster, requires that it must be surrounded by a zone of broken hydrogen bonds. This is confirmed by infrared spectra that show that the presence of an H₃O⁺ ion extends to affect the hydrogen bonding of at least 100 surrounding water molecules.

The oxonium ion binds strongly to another water molecule in two possible manners. Opposite are shown the two H₅O₂⁺ dihydronium ions with closely matched energies, where the proton is asymmetrically (top) or symmetrically (bottom) centered between the O-atoms. The asymmetric structure (top) of H₅O₂⁺ is found to be more stable using the 6-31G** basis set. However, other more thorough ab initio treatments have found the symmetric hydrogen-bonded structure (bottom), with a slightly shorter hydrogen bond, to be the global minimum of by about 0.6 kJ mol^-1

In this symmetric form (the ‘Zundel’ cation, shown bottom opposite), all O-H bonds are the same length (0.95 Å) except the two involved in the hydrogen bond, which are covalent and equally-spaced (1.18 Å; similar to that in ice-ten, and as found by neutron diffraction in some crystals mid way between the oxygen atoms such as the dihydrates of HCl and HClO₄, for example, [H₅O₂⁺][ClO₄^–]). There is localized but low electron density around the central hydrogen atom. The vibrational spectrum of H₅O₂⁺ shows a strong sharp peak (at 1090 cm^-1) for its shared proton, similar to H₃O₂^–. As expected, these spectra are much broadened, shifted and poorly resolved in bulk liquid water.

All the occupied molecular orbitals, found using the 6-31G** basis set, of H₅O₂⁺

H₅O₂⁺ may be fully hydrated, also with an equally spaced central hydrogen bond, with one water molecule hydrogen bonded to the four free hydrogen atoms as H₁₃O₆⁺. The presence of these three similar energy minima for the proton lying so close between the two oxygen atoms is surely the major reason for the ease of transfer of protons between water molecules; the proton moving very quickly (< 100 fs) between the extremes of triply-hydrogen bonded H₃O⁺ (H₉O₄⁺, ‘Eigen cation’) ions through symmetrical H₅O₂⁺ ions (‘Zundel cation’), with the low potential energy barriers washed out by the zero-point motion of the proton . Note that the small movement of the proton gives rise to a much greater movement of the center of positive charge. Preference for the Zundel cation structure occurs when its outer hydrogen bonding is approximately symmetrical as in H₁₃O₆⁺ (right), although the O····O separation may be greater than expected for the lone H₅O₂⁺ Zundel ion.

When the extra proton is shared equally between more than one water molecule the approximate structure can be deduced from a consideration of the resonance structures; for example, the two shared protons in H₇O₃⁺ give rise to bond lengths half way between those in (H₂O)₂ and H₅O₂⁺ (the calculated minimum energy structure is shown.

and the three shared protons in H₉O₄⁺ giving rise to bond lengths a third of the way between those in (H₂O)₂ and H₅O₂⁺ (below; the calculated minimum energy structure is shown). Once correctly oriented, the potential energy barrier to proton transfer is believed to be very small.

 

However, the hydrated oxonium ion (opposite; the ‘Eigen’ cation) may be the most stable hydrated proton species in liquid water, being slightly more stable than the symmetrical dihydronium ion, due to electronic delocalization over several water molecules being preferred over the nuclear delocalization.

In acid solutions, there will be many contributing structures giving rise to particularly broad stretching vibrations associated with the excess protons (for example, magic number ions). It has been determined from studies of freezing point depression that H₃O⁺(H₂O)₆ (that is, H₁₅O₇⁺) is the mean structural ion in cold water. H₇O₃⁺ and H₉O₄⁺ are both also found in HBr.4H₂O, i.e. [H₉O₄⁺][H₇O₃⁺][Br^–]₂.H₂O.

The central (positively charged) hydrated proton interacts very much more strongly with the oxygen of neighboring water molecukes rather than any weakly forming hydrogen bonds; H₂O···OH₃⁺(H₂O)₃ being a much stronger link than the hydrogen bond HO-H···OH₃⁺(H₂O)₃. This causes rotations in the neighboring water molecules as a hydrogen ion moves through the solution so disrupting the hydrogen bonded network. This O···O attraction even exists between H₃O⁺ species as in more concentrated acid solutions (~0.5 – ~3 M) with the hydrated protons appearing to form contact ion pairs, with the oxonium lone-pair sides pointing toward one another and the oxygen atoms only about 0.34 nm apart.. This unusual “amphiphilic” behavior minimises the disruption to the water’s hydrogen bond network caused by the strong hydration of the protons. A similar effect may occur at the surface of concentrated acid solutions, causing the lone pairs to point towards the (hydrophobic) gas phase.

As hydrogen ions can be readily stripped from aqueous surfaces, by themselves, as constituents of small clusters or as aerosol, there may be a build -up of positive charge within clouds and negative charge on Earth that leads to thunder and lightning.

Footnotes

The hydration of ‘Eigen’ (H₉O₄⁺) and ‘Zundel’ (H₅O₂⁺) ions has been investigated

H₂O accepts protons from stronger acids to form H₃O⁺ and H₃O⁺ donates protons to the bases of weaker acids. The acidity constant (K_a) of H₃O⁺ is defined (as other acids) by the equation H₃O⁺(+H₂O) H⁺(aq)+H₂O. Therefore K_a= [H⁺][H₂O]/[H₃O⁺] and as [H⁺] is the same as [H₃O⁺], K_a = [H₂O] = 55.345 M (at 25 °C), and pK_a = -1.743 (at 25 °C). There is a difficulty that has been ignored in this definition as the K_a should be expressed in terms of activities rather than concentrations and the activity of pure H₂O is defined as unity whereas that of solutes is defined relative to their standard state (1 mol kg^-1).

Note that acid-base neutrality only occurs when the concentration of hydrogen ions equals the concentration of hydroxyl ions (whatever the pH). Neutrality is at pH 7 only in pure water when at 25 °C. A solution is acidic when the hydrogen ion concentration is greater than the hydroxide ion concentration, whatever the pH.

The term ‘oxonium ion’ should be reserved for the H₃O⁺ ion with the term ‘hydronium ion’ now obsolete. The term ‘hydrogen ion’ may refer to any of the group of protonated water clusters including H₃O⁺.

The oxonium ion and small hydrated hydrogen ion clusters shown on this page were drawn using ab initio calculations using the 6-31G** basis set. Where not otherwise referenced, bond distances, angles and atomic charges are derived from these calculations.

^f H⁺ + H₂O H₃O⁺ (ΔG° = -651.4 kJ mol^-1) , this is followed by H₃O⁺ + aq H₃O⁺(aq) (ΔG° = 461.1 kJ mol^-1; ~260 nm) giving an overall H⁺ + aq H₃O⁺(aq) (ΔG° = -1112.5 kJ mol^-1). These calculations assume that the standard state of the solvent water is taken as 1.0 M.

The hydration of the hydroxide ion (OH^–) is very important for biological and non-biological processes. Unfortunately, it is neither well-knowor simply described. Most experimental structural work on this hydrated ion involves concentrated or very concentrated solutions, containing structure-disruptive cations. Within such experimental environments, the basic tetrahedral structuring of water is destroyed and the specific effects of solvent separated and contact ion pairs are introduced and confuse any results. It is clear, however, that the hydroxide ion is strongly hydrated but the extent of this hydration is less clear.

The hydroxide ion, shown right,^a strongly interacts with other water molecules to give clusters and is essentially absent (as such) in aqueous solution. All the occupied molecular orbitals of OH^– are on another page.

Although many recent studies have attempted to determine the preferred hydration of the hydroxide ion in solution, there is no consensus. In particular, the hydrogen bonding capacity utilizing the donated OH^– proton, remains in doubt. Studies indicate that any such bond must be very weak, if formed, and may be essentially absent.

OH^– has an effective ionic radius of 0.110 nm, somewhat less than that of the H₂O molecular radius (0.138 nm). Its molar volume is 1.2 cm³ mol^-1 due to electrostriction The nearest aqueous oxygen atom to the hydroxide proton appears to average about 0.25 nm, almost twice the distance as in the hydroxide ions accepting hydrogen bonds (~0.14 nm), well outside the normal hydrogen-bond signature distance of  0.15-0.21 nm and at a distance often considered. [The O-H stretch vibration behaves as the free hydroxyl group in small gas-phase clusters and both concentrated and more dilute hydroxide solutions.

In solution, the hydroxide ion must be surrounded by water with orientations governed by the local polarity and the presence of counter ions. Clearly water molecules (rather than cationic counter ions) will reside relatively close to the hydroxide proton and it is not surprising that this can form the fleeting hydrogen bonds described, perhaps encouraged by solvent separated counter ions and contact ion-pairing when in concentrated solution. Such bonds are, however, far weaker than the hydrogen bonds between water molecules, as judged from their bond length and longer wavelength (i.e. blue-shifted rather than the usual red-shift noted generally for hydrogen bonds , and not readily formed. Even in ab initio calculations no local minima is found for a water hydrogen-bonded  to the OH^– proton unless held by an extensive  (and somewhat unlikely) network of bridging hydrogen bonds from 16 other water molecules and the free hydroxide O-H stretch was found at higher frequency indicative of very weak or absent  true hydrogen bonding, by Fourier transform infrared (FTIR) spectroscopy of HDO isotopically diluted in H₂O. It is probable, however, that a fleeting very weak hydrogen bond may facilitate the OH^– transport mechanism.

The hydroxide ion (OH^–) is a very good acceptor of hydrogen bonds, with the first water molecule binding strongly to form H₃O₂^– (right, where the proton is off-center, giving rise to a low-barrier hydrogen bond) hydrated ions. A centrally-positioned proton within the hydrogen bond (similar to that in the H₅O₂⁺ ion, ‘Zundel cation’) does not appear to be stable, however. Although evidence for this H₃O₂^– ion has been difficult to find in aqueous solution, it is expected to possess a particularly strong hydrogen bond ] and infrared spectroscopy indicates that it may last for 2-3 vibration periods (~110 fs)  

The hydrogen atom lies significantly asymmetrically in H₃O₂^– where the energy barrier for proton transfer has been calculated (~0.9 kJ mol^-1) to be much lower than the available vibrational energy, so allowing easy equilibration of the proton’s position as occurs with H₅O₂⁺. The vibrational spectrum of H₃O₂^– indicates that it behaves as a single (vibrationally-averaged) species with no bend vibration (v₂), both free O-H stretch vibrations being equivalent and a very strong and sharp band at 697 cm^-1, corresponding to the vibration of the shared proton; thus the shared proton hops between the two minimum energy sites giving a quantum-averaged structure, similar to what may happen with H₅O₂⁺, which also shows a strong sharp peak (at 1090 cm^-1) for its shared proton. As expected, these spectra will be very much broadened, shifted and poorly resolved in bulk liquid water.

In crystal structures, H₃O₂^– with a symmetrical hydrogen bond may be found (for example, O···O 2.41 Å; O···H 1.205 Å; O-H 0.733 Å ).

All the occupied molecular orbitals, found using the 6-31G** basis set, of H₃O₂^– Ab initio studies shows that up to four further water molecules may hydrogen bond around the oxygen atom of the OH^–, as it charge density is spread out and not tetrahedrally situated. As the hydration increases, the hydroxide O-H bond becomes shorter, its hydrogen atom more positive and its oxygen atom less negative. The hydrogen bonds become longer and individually weaker whereas the hydrogen bonded water molecules become less polarized.

The O···O distance in H₇O₄^– and H₃O₂^– are slightly greater (~2.67 Å and ~2.50 (2.467 Å respectively) and the O-H slightly shorter (~0.98 Å and ~1.05 (1.125 Å) respectively) than in H₅O₂⁺. The hydration of these ions reduce their chemical activity, which may be a factor in their increased reactivity when subjected to hydrogen-bond disrupting electromagnetic effects.

The tetrahedral ion H₇O₄^–, see HO^–··(HOH)₃ above opposite, is probably the most stable hydrated  hydroxide ion being slightly energetically favored over  H₃O₂^–. It hydrogen bonds well at the surface of small clusters and even in the gas phase. It is also possible that four water molecules may coordinate to the hydroxide ion as HO^–(··HOH)₄, (all donating their hydrogen atoms, see below opposite) because the electron distribution around the hydroxide ion is not directional.. Such an arrangement has been recently reported using neutron diffraction, with empirical structure refinement, and is consistent with X-ray absorption spectroscopy of concentrated solutions, with both studies utilizing concentrated hydroxide solutions. It should be noted, however, that at such high concentrations most, if not all, water molecules must be within the first shell of at least one ion and the normal tetrahedral clustering of water, as found in more dilute solutions, has been destroyed. Certainly the Raman spectra of hydroxide solutions changes when the solution is diluted below OH^–:H2O 1:20. Also, HO^–(··HOH)₄ was found to be energetically unfavorable using quasi-chemical theory and spectroscopic studies indicate the 4^th H₂O in HO^–(··HOH)₄ to be preferably hydrogen bonded to the other three forming a second shell.

The strong hydrogen bonding between the hydroxide ion (OH^–) and its first shell water molecules is thought responsible for the very large temperature dependence of the hydroxide reorientation, with three-fold increase in activation energy at low temperatures (<290 K). Although thought possibly due to the presence of hyper-coordinated HO^–··(HOH)₄ clusters, such an effect could equally well be due to dominant tetrahedral HO^–··(HOH)₃ clusters at low temperatures, fitting better into the more extensive tetrahedral network of water molecules then present. Certainly, this reorientation effect seems to indicate a changing hydration structuring around the hydroxide ion with temperature. It is clearly not proven that the planar HO^–(··HOH)₄ ion (bottom opposite) has importance in dilute solutions beyond its, perhaps transient, formation during diffusion.

 

2. DISSOCIATION OF WATER. WATER PRODUCT. PH. PH-VALUE (РН) OF WEAK AND STRONG ACIDS AND BASES SOLUTIONS. РН VALUE FOR HUMAN BODY LIQUIDS IN NORM AND PATHOLOGY.

Dissociation in chemistry and biochemistry is a general process in which ionic compounds (complexes, or salts) separate or split into smaller particles, ions, or radicals, usually in a reversible manner. For instance, when a Brønsted-Lowry acid is put in water, a covalent bond between an electronegative atom and a hydrogen atom is broken by heterolytic fission, which gives a proton and a negative ion. Dissociation is the opposite of association and recombination. The process is frequently confused with ionization.

In chemistry, pH (/piː eɪtʃ/ or /piː heɪtʃ/) is a measure of the acidity or basicity of an aqueous solution. Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic or alkaline. Pure water has a pH very close to 7.

The pH scale is traceable to a set of standard solutions whose pH is established by international agreement. Primary pH standard values are determined using a concentration cell with transference, by measuring the potential difference between a hydrogen electrode and a standard electrode such as the silver chloride electrode. Measurement of pH for aqueous solutions can be done with a glass electrode and a pH meter, or using indicators.

pH measurements are important in medicine, biology, chemistry, agriculture, forestry, food science, environmental science, oceanography, civil engineering, chemical engineering, nutrition, water treatment & water purification, and many other applications.

Mathematically, pH is the negative logarithm of the activity of the (solvated) hydronium ion, more often expressed as the measure of the hydronium ion concentration.

pOH

 

Relation between p[OH] and p[H] (red = acid region, blue = basic region)

pOH is sometimes used as a measure of the concentration of hydroxide ions, OH−, or alkalinity. pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by

where KW is the self-ionisation constant of water. Taking logarithms

So, at room temperature pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of soil alkalinity.

Extremes of pH

Measurement of pH below about 2.5 (ca. 0.003 mol dm−3 acid) and above about 10.5 (ca. 0.0003 mol dm−3 alkali) requires special procedures because, when using the glass electrode, the Nernst law breaks down under those conditions. Various factors contribute to this. It cannot be assumed that liquid junction potentials are independent of pH.[10] Also, extreme pH implies that the solution is concentrated, so electrode potentials are affected by ionic strength variation. At high pH the glass electrode may be affected by “alkaline error”, because the electrode becomes sensitive to the concentration of cations such as Na+ and K+ in the solution. Specially constructed electrodes are available which partly overcome these problems.

Runoff from mines or mine tailings can produce some very low pH values.

pH indicators

Chart showing the variation of color of universal indicator paper with pH

Indicators may be used to measure pH, by making use of the fact that their color changes with pH. Visual comparison of the color of a test solution with a standard color chart provides a means to measure pH accurate to the nearest whole number. More precise measurements are possible if the color is measured spectrophotometrically, using a colorimeter of spectrophotometer. Universal indicatorconsists of a mixture of indicators such that there is a continuous color change from about pH 2 to pH 10. Universal indicator paper is made from absorbent paper that has been impregnated with universal indicator.

Universal indicator components
Indicator	Low pH color	Transition pH range	High pH color
Thymol blue (first transition)	Red	1.2 – 2.8	Yellow
Methyl red	Red	4.4 – 6.2	Yellow
Bromothymol blue	Yellow	6.0 – 7.6	Blue
Thymol blue (second transition)	Yellow	8.0 – 9.6	Blue
Phenolphthalein	Colorless	8.3 – 10.0	Fuchsia

 

pH values of some common substances

Water has a pH of pKw/2, so the pH of pure water is about 7 at 25 °C; this value varies with temperature. When an acid is dissolved in water, the pH will be less than that of pure water. When a base, or alkali, is dissolved in water, the pH will be greater than that of pure water. A solution of a strong acid, such as hydrochloric acid, at concentration 1 mol dm−3 has a pH of 0. A solution of a strong alkali, such as sodium hydroxide, at concentration 1 mol dm−3, has a pH of 14. Thus, measured pH values will lie mostly in the range 0 to 14. Since pH is a logarithmic scale, a difference of one pH unit is equivalent to a tenfold difference in hydrogen ion concentration. The pH of an aqueous solution of a salt such as sodium chloride is slightly different from that of pure water, even though the salt is neither acidic nor basic. This is because the hydrogen and hydroxide ions’ activity is dependent on ionic strength, so Kw varies with ionic strength.

The pH of pure water decreases with increasing temperatures. For example, the pH of pure water at 50 °C is 6.55. Note, however, that water that has been exposed to air is mildly acidic. This is because water absorbs carbon dioxide from the air, which is then slowly converted into bicarbonate and hydrogen ions:

pH iature

pH-dependent plant pigments that can be used as pH indicators occur in many plants, including hibiscus, red cabbage (anthocyanin) and red wine. The juice of citrus fruits is acidic mainly because it contains citric acid. Other carboxylic acids occur in many living systems. For example, lactic acid is produced by muscle activity. The state of protonation of phosphate derivatives, such as ATP, is pH-dependent. The functioning of the oxygen-transport enzyme hemoglobin is affected by pH in a process known as the Root effect.Seawater

The pH of seawater plays an important role in the ocean’s carbon cycle, and there is evidence of ongoing ocean acidification caused by carbon dioxide emissions.  However, pH measurement is complicated by the chemical properties of seawater, and several distinct pH scales exist in chemical oceanography.

As part of its operational definition of the pH scale, the IUPAC defines a series of buffer solutions across a range of pH values (often denoted with NBSor NIST designation). These solutions have a relatively low ionic strength (~0.1) compared to that of seawater (~0.7), and, as a consequence, are not recommended for use in characterizing the pH of seawater, since the ionic strength differences cause changes in electrode potential. To resolve this problem, an alternative series of buffers based on artificial seawater was developed.  This new series resolves the problem of ionic strength differences between samples and the buffers, and the new pH scale is referred to as the total scale, often denoted as pHT.

The total scale was defined using a medium containing sulfate ions. These ions experience protonation, H⁺ + SO₄²⁻   HSO₄⁻, such that the total scale includes the effect of both protons (free hydrogen ions) and hydrogen sulfate ions:

[H⁺]_T = [H⁺]_F + [HSO₄⁻]

An alternative scale, the free scale, often denoted pH_F, omits this consideration and focuses solely on [H⁺]_F, in principle making it a simpler representation of hydrogen ion concentration. Only [H⁺]_T can be determined,therefore [H⁺]_F must be estimated using the [SO₄²⁻] and the stability constant of HSO₄⁻, K_S^*:

[H⁺]_F = [H⁺]_T − [HSO₄⁻] = [H⁺]_T ( 1 + [SO₄²⁻] / K_S^* )⁻¹

However, it is difficult to estimate K_S^* in seawater, limiting the utility of the otherwise more straightforward free scale.

Another scale, known as the seawater scale, often denoted pH_SWS, takes account of a further protonation relationship between hydrogen ions and fluoride ions, H⁺ + F⁻ ⇌ HF. Resulting in the following expression for [H⁺]_SWS:

[H⁺]_SWS = [H⁺]_F + [HSO₄⁻] + [HF]

However, the advantage of considering this additional complexity is dependent upon the abundance of fluoride in the medium. In seawater, for instance, sulfate ions occur at much greater concentrations (> 400 times) than those of fluoride. As a consequence, for most practical purposes, the difference between the total and seawater scales is very small.

The following three equations summaries the three scales of pH:

pH_F = − log [H⁺]_F

pH_T = − log ( [H⁺]_F + [HSO₄⁻] ) = − log [H⁺]_T

pH_SWS = − log ( [H⁺]_F + [HSO₄⁻] + [HF] ) = − log [H⁺]_SWS

In practical terms, the three seawater pH scales differ in their values by up to 0.12 pH units, differences that are much larger than the accuracy of pH measurements typically required, in particular, in relation to the ocean’s carbonate system.Since it omits consideration of sulfate and fluoride ions, the free scale is significantly different from both the total and seawater scales. Because of the relative unimportance of the fluoride ion, the total and seawater scales differ only very slightly.

The pH of different cellular compartments, body fluids, and organs is usually tightly regulated in a process called acid-base homeostasis. The most common disorder in acid-base homeostasis isacidosis, which means an acid overload in the body, generally defined by pH falling below 7.35.* Alkalosis is the opposite condition, with blood pH being excessively high.

The pH of blood is usually slightly basic with a value of pH 7.365. This value is often referred to as physiological pH in biology and medicine. Plaque can create a local acidic environment that can result in tooth decay by demineralization. Enzymes and other proteins have an optimum pH range and can become inactivated or denatured outside this range.

 

Living systems

 

Polyprotic Acids

Acids that contain more than one dissociable proton are called polyprotic acids.

Polyprotic acids dissociate in a stepwise manner, and each dissociation step is characterized by its own acid-dissociation constant K_a1, K_a2 and so forth.

As shown in Table 15.3, the values of stepwise dissociation constants of polyprotic acids decrease in the order . Because of electrostatic forces, it’s more difficult to remove a positively charged proton from a negative ion.

Example 3. Calculate the pH and the concentrations of all species present (H₂CO₃, HCO₃^–,CO₃^2-, H₃O⁺and OH^– ) in a 0.020 M carbonic acid solution.

Use the eight-step procedure summarized in Example 3.

Step 5. Substituting the equilibrium concentrations into the equilibrium equation for the principal reaction gives

Assuming that 0.020 –x = 0.02, we have:

X² = (4.3 * 10^-7) 0.020

X = 9.3 * 10^-5

Step 6. The big concentrations are 

Step 7. The small concentrations are obtained from the subsidiary equilibria—(1) dissociation of HCO₃^– and (2) dissociation of water—and from the big concentrations already determined:

In general, for a solution of a weak diprotic acid  

 

NOTE The second dissociation of H₂CO₃ produces a negligible amount of H₃O⁺ compared with the obtained H₃O⁺ from the first dissociation.

Step 8.  

 

Equilibria in Solutions of Weak Bases

Weak bases, such as ammonia, accept a proton from water to give the conjugate acid of the base and OH^– ions:

The equilibrium constant K_b is called the base-dissociation constant:

 

Relation Between K_a and K_b

For any conjugate acid–base pair, the product of the acid-dissociation constant for the acid and the base-dissociation constant for the base always equals the ionproduct constant for water:

For example,

 

Acid–Base Properties of Salts

When an acid neutralizes a base, an ionic compound called a salt is formed. Salt solutions can be neutral, acidic, or basic, depending on the acid–base properties of the constituent cations and anions. As a general rule, salts formed by reaction of a strong acid with a strong base are neutral, salts formed by reaction of a strong acid with a weak base are acidic, and salts formed by reaction of a weak acid with a strong base are basic. It’s as if the influence of the stronger partner dominates:

Salts That Yield Neutral Solutions

Salts such as NaCl that are derived from a strong base (NaOH) and a strong acid (HCl) yield neutral solutions because neither the catioor the anion reacts appreciably with water to produce H₃O⁺ or OH^– ions.

The following ions do not react appreciably with water to produce either H₃O⁺ or OH^– ions:

Salts that contain only these ions give neutral solutions in pure water pH=7

 

Salts That Yield Acidic Solutions

Salts such as NH₄Cl that are derived from a weak base NH₃ and a strong acid (HCl) produce acidic solutions. In such a case, the anion is neither an acid nor a base, but the cation is a weak acid:

Example 4.

In aqueous solution, the Al³⁺ ion bonds to six water molecules to give the hydrated cation Al(H₂O)₆³⁺

In general, the acidity of hydrated main-group cations increases from left to right in the periodic table as the metal ion charge increases and the metal ion size decreases  Transition metal cations, such as Zn²⁺ Cr³⁺and Fe³⁺ also give acidic solutions hydrated cation are much stronger proton donors than are free solvent water molecules.

 

 

 

Step 5. The value of x is obtained from the equilibrium equation:

Salts That Yield Basic Solutions

Salts such as NaCN that are derived from a strong base (NaOH) and a weak acid (HCN) yield basic solutions. In this case, the cation is neither an acid nor a base, but the anion is a weak base:

Example 5.

Salts That Contain Acidic Cations and Basic Anions

Example 6. Finally, let’s look at a salt such as (NH₄)₂CO₃ in which both the cation and the anion can undergo proton-transfer reactions. Because NH₄⁺ is a weak acid and CO₃^2- is a weak base, the pH of an (NH₄)₂CO₃ solution depends on the relative acid strength of the cation and base strength of the anion:

We can distinguish three possible cases:

Because K_a < K_b the solution is basic (pH > 7).

Buffer Solutions

Solutions , which contain a weak acid and its conjugate base, are called buffer solutions because they resist drastic changes in pH. If a small amount of OH^– is added to a buffer solution, the pH increases, but not by much because the acid component of the buffer solutioeutralizes the added OH^– If a small amount of H₃O⁺ is added to a buffer solution, the pH decreases, but agaiot by much because the base component of the buffer solutioeutralizes the added H₃O⁺

Buffer solutions are very important in biological systems. Blood, for example, is a buffer solution that can soak up the acids and bases produced in biological reactions. The pH of human blood is carefully controlled at a value very close to 7.4 by conjugate acid–base pairs, primarily H₂CO₃ and its conjugate base HCO₃^–. The oxygen-carrying ability of blood depends on control of the pH to within 0.1 pH unit.

Example 7. To see how a buffer solution works, let’s return to the 0.10 M acetic acid–0.10 M sodium acetate solution.

The principal reaction and the equilibrium concentrations for the solution are

Note that in calculating this result we have set the equilibrium concentrations, (10-x) and (10+x) equal to the initial concentrations, 0.10, because x is negligible compared with the initial concentrations, 0.10.

Addition of OH^– to a Buffer

Suppose that we add 0.01 mol of solid NaOH to 1.00 L of the 0.10 M acetic acid–0.10 M sodium acetate solution. Initially, we have (1.00 L) (0.1 mol/L) = 0.1 mol of acetic acid and an equal amount of acetate ion. When we add 0.01 mol of NaOH, the neutralization reaction will alter the numbers of moles:

If we assume that the solution volume remains constant at 1.00 L, the concentrations of the buffer components after neutralization are

Substituting these concentrations into the expression for [H₃O⁺] we can then calculate

the pH:

The corresponding change in pH, from 4.74 to 4.82, is only 0.08 pH unit.

Addition of H₃O⁺ to a Buffer

Now suppose that we add 0.01 mol of HCl to 1.00 L of the 0.10 M acetic acid–0.10 M sodium acetate buffer solution. The added strong acid will convert 0.01 mol of acetate ions to 0.01 mol of acetic acid because of the neutralization reaction.

Again, the change in pH, from 4.74 to 4.66, is small because the concentration ratio [weak acid]/[conjugate base] remains close to its original value.

Buffer Capacity

To appreciate the ability of a buffer solution to maintain a nearly constant pH

We sometimes talk about the buffering ability of a solution using the term buffer capacity as a measure of the amount of acid or base that the solution can absorb without a significant change in pH. Buffer capacity is also a measure of how little the pH changes with the addition of a given amount of acid or base. Buffer capacity depends on how many moles of weak acid and conjugate base are present. For equal volumes of solution, the more concentrated the solution, the greater the buffer capacity. For solutions having the same concentration, the greater the volume, the greater the buffer capacity.

 

Questions:

1. What happens when an atom gains or loses an electron?

2. In your own words, explain why water generally has a neutral pH, even though water molecules dissociate.

3. Why are acids called proton donors?

4. What happens during neutralization?

5. Give an example of a strong base, and a strong acid.

1. Name the following compounds that will form, and identify as an acid or base:

a) Br + H

b) 2H + SO₃

c) K + H

d) 2H + SO₆

e) 3He + P₂

f) H + BrO₁₀₀

g) N + C

ducks everywhere

 

2.justify your answer with equation that sodium acetate gives basic solution while ammonium chloride an acidic solution with water.

 

3. In a conductivity test, 5 different solutions were set up with light bulbs. The following observations were recorded:

Solution A glowed brightly.

Solution B glowed dimly.

Solution C glowed dimly.

Solution D did not glow.

Solution E glowed brightly.

a) Which solution(s) could contain strong bases?

b) Which solution(s) could contain weak acids?

c) Which solution(s) could contain ions?

d) Which solution(s) could contain pure water?

e) Based solely on these observations, would it be possible to distinguish between acidic and basic solutions?

4. Identity the conjugate base and conjugate acid in these following equations:

a) HCl + H₂O → H₃O⁺ + Cl^–

b) HClO + H₂O → ClO^– + H₃O⁺

c) CH₃CH₂NH₂ + H₂O → CH₃CH₂NH₃⁺ + OH^–

5. Identify these bases as Arrhenius, Brønsted-Lowry, or both.

a) strontium hydroxide

b) butyllithium (C₄H₉Li)

c) ammonia

d) potassium hydroxide

e) potassium iodide

6. Based on the Brønsted-Lowry Theory of Acids and Bases, would you expect pure water to have no dissolved ions whatsoever? Explain, using a balanced chemical equation.

 

TRUE OR FALSE: The equivalence point of a weak base-strong acid titration should be less than 7.

A. True

B. False

True or False: The equivalence point of a strong acid-strong base titration is always at a pH of 7.

A. True

B. False

What is the pH of a solution that has a [OH^–] of 0.0500 M?

A. 1.30

B. 12.7

C. 13.0

D. 1.27

In a titration of 50.0 mL HBr of unknown concentration with 0.125 M LiOH, 75.0 mL of LiOH had to be added to the HBr solution to reach the endpoint. The concentration of the initial HBr solution is:

A. 0.00938 M

B. 1.88 M

C. 0.188 M

D. 0.938 M

The pH of the above titration system after only 25 mL of LiOH has been added would be:

A. 1.08

B. 12.6

C. 1.38

B. 1.26

True or False: In a weak acid-strong base titration, the equivalence point is always below 7.

A. True

B. False

Consider a titration between 100 mL of 0.100 M acetic acid and 0.0600 M potassium hydroxide solution. How many mL of KOH needs to be added to this solution to reach the equivalence point?

A. 0.0100 mL

B. 167 mL

C. 100 mL

D. 66.0 mL

True or False: At the moment when the equivalence point is reached, all of the initial acetic acid has now been converted into the conjugate base?

A. True

B. False

 

References:

1. The abstract of the lecture.

2. intranet.tdmu.edu.ua/auth.php

3. Atkins P. W. Physical chemistry / P.W. Atkins. – New York, 1994. – P.299‑307.

4. Cotton F. A. Chemical Applications of Group Theory / F. A. Cotton. ‑ John Wiley & Sons : New York, 1990.

5. Girolami G. S. Synthesis and Technique in Inorganic Chemistry / G. S. Girolami, T. B. Rauchfuss, R. J. Angelici. ‑ University Science Books : Mill Valley, CA, 1999.

6. Russell J. B. General chemistry / J B. Russell. New York.1992. – P. 550‑599.

7. Lawrence D. D. Analytical chemistry / D. D. Lawrence. –New York, 1992. – P. 218–224.

8. http://www.lsbu.ac.uk/water/ionish.html

 

Prepared by PhD Falfushynska H.