The materials to prepare students for practical lessons of inorganic chemistry

The materials to prepare students for practical lessons of inorganic chemistry

LESSON № 8.

Theme:  THE THEORY OF STRONG AND WEAK ELECTROLYTES. THE EQUILIBRIUM IN SOLUTIONS OF SLIGHTLY SOLUBLE ELECTROLYTES.

 

Plan

1. Solutions of electrolytes.

2. The Arheniuse electrolytic dissociation theory. Concept about strong and weak electrolytes.

3. Electrolytes in the human bodies.

4. Properties of strong electrolyte solutions. Activity and coefficient of activity. Ionic force of solution. Constant of ionization. Degree of ionization and it dependence on the concentration (Ostwald law).

5. Solutions of weak electrolytes. Degree and constant of weak electrolyte dissociation. Water-electrolyte balance as bases of homoeostasis. Solubility of salts. Solubility product. Influence of ions on solubility salts.

 

1. Solutions of electrolytes.

Ectrolytic solutions are those that are capable of conducting an electric current. A substance that, when added to water, renders it conductive, is known as an electrolyte. A common example of an electrolyte is ordinary salt, sodium chloride. Solid NaCl and pure water are both non-conductive, but a solution of salt in water is readily conductive. A solution of sugar in water, by contrast, is incapable of conducting a current; sugar is therefore a non-electrolyte.

These facts have been known since 1800 when it was discovered that an electric current can decompose the water in an electrolytic solution into its elements (a process known as electrolysis). By mid-century, Michael Faraday had made the first systematic study of electrolytic solutions.

Faraday recognized that in order for a sample of matter to conduct electricity, two requirements must be met:

The matter must be composed of, or contain, electrically charged particles.

These particles must be mobile; that is, they must be free to move under the influence of an external applied electric field.

In the case of electrolytic solutions, Faraday called the charge carriersions (after the Greek word for “wanderer”). His most important finding was that each kind of ion (which he regarded as an electrically-charged atom) carries a definite amount of charge, most commonly in the range of ±1-3 units.

The fact that the smallest charges observed had magnitudes of ±1 unit suggested an “atomic” nature for electricity itself, and led in 1891 to the concept of the “electron” as the unit of electric charge — although the identification of this unit charge with the particle we now know as the electron was not made until 1897.

An ionic solid such as NaCl is composed of charged particles, but these are held so tightly in the crystal lattice that they are unable to move about, so the second requirement mentioned above is not met and solid salt is not a conductor. If the salt is melted or dissolved in water, the ions can move freely and the molten liquid or the solution becomes a conductor.

Since positively-charged ions are attracted to a negative electrode that is traditionally known as the cathode, these are often referred to as cations. Similarly, negatively-charged ions, being attracted to the positive electrode, or anode, are called anions. (These terms were all coined by Faraday.)

The role of the solvent: what’s special about water

Although we tend to think of the solvent (usually water) as a purely passive medium within which ions drift around, it is important to understand that

·  Electrolytic solutions would not exist without the active involvement of the solvent in reducing the strong attractive forces that hold solid salts and molecules such as HCl together;

·  Once the ions are released, they are stabilized by interactions with the solvent molecules.

Water is not the only liquid capable of forming electrolytic solutions, but it is by far the most important. It is therefore essential to understand those properties of water that influence the stability of ions in aqueous solution.

 

A. properties of solutions of electrolytes

1. Electrolysis

reduction: addition of electrons to a chemical species.

oxidation: removal of electrons from a chemical species.

cation: positive ions

anion: negative ions

cathode: reduction of cation

anode: oxidation of anion

current in a solution: flow of positive and negative ions toward the electrodes.

current in a metallic conductor: flow of free electrons migrating through a crystal lattice of fixed positive ions.

2. Transference Numbers

total current carried by the cations or by the anions. function of hydration, ion size, charge, etc.

(6-1)

(6-2)

() (6-3)

2. Electrical Units

(Ohm’s Law) (6-4)

I: electric current (ampere)

E: electric potential (voltage)

R: resistance (ohm)

(6-5)

Q: quantity of electric charge (Coulomb, 1 Coulomb = 3 x 109 esu)

Electric energy = EQ (6-6)

3. Faraday’s Law

96500 Coulomb – chemical change of 1g equivalent weight of any substance (transport of 6.02 x 1023 ions).

/electron

4. Electrolytic Conductance

(6-7)

r : specific resistance (resistance of 1 cm cube)

(6-8)

conductance (mhos) k : specific conductance

5. Measuring the Conductance of Solutions

(6-9)

(6-10)

6. Equivalent Conductance

equivalent conductance (L ): conductance of a solution containing 1g equivalence of the solute when the electrodes are spaced 1 cm apart. measures current carrying capacity of giveumber of ions.

specific conductance: current carrying capacity of all ions.

(6-11)

7. Equivalent Conductance of Strong and Weak Electrolytes

Upon dilution

specific conductance: decreases due to decrease in the number of ions per unit volume.

equivalent conductance: increases due to less hindrance from other ions.

 (6-12)

: equivalent conductance at infinite dilution

HAc: weak electrolyte, extent of dissociation increases on dilution.

In dilute solution

(6-13)

8. Colligative Properties

For electrolytic solution, Van’t Hoff equation

i: correction factor (extent of deviation from ideal solution)

number of ions into which the molecules dissociated.

deviation of concentrated solutions of nonelectrolytes (internal pressure, polarity,  complexation, etc)

B. Arrhenius theory of electrolytic dissociation

(6-14)

Considering Van’t Hoff factor, i

(6-15)

v: number of ions produced from a molecule.

(6-16)

i can be determined from colligative properties.

C. theory of strong electrolytes

Arrhenius theory: applies only to weak electrolytes.

1. Activity and Activity Coefficients

interionic attractive forces: moderate concentration of strong electrolytes. negligible in dilute solutions and weak electrolyte solutions.

ion pairs: association of ions.

Due to interionic attractive forces and ion pairs, strong electrolyte may be completely ionized, yet incompletely dissociated into free ions.

Activity: effective concentration

At infinite dilution, a = m.

Activity coefficient (g , function of concentration)

mean ionic activity,

(6-17)

m, n: stoichiometric number

(6-18)

mean ionic activity coefficient

(6-19)

(6-20)

(6-21)

 

initial decrease: due to interionic attractions.

rise in activity: due to solvation which reduces interionic attractions.

2. Activity of the Solvent

infinitely dilute solution

for more concentrated solution

for a volatile solvent

3. Reference State

extent of departure from ideal solution. activity = concentration or g = 1.

for solvent: pure solvent

for solute: pure solute (completely miscible liquids)

infinitely dilute solution (limited solubility)

4. Standard State

·                   state of the component at unit activity (a = 1)

·                   for solvent or miscible liquids: pure liquid at 1 atm and at a definite temperature.

·                   for solute with limited solubility: hypothetic solution of unit concentration having the characteristics of an infinitely dilute or ideal solution.

5. Ionic Strength

needed to know activity or activity coefficient.

(6-22)

c: concentration z: valence

Activity coefficient of strong electrolyte

roughly constant in all dilute solutions of the same ionic strength

approximately same for a single class at a definite ionic strength in dilute solutions.

6. The Debye-Huckel Theory relationship between activity coefficient and valence of the ions, ionic strength of the solution, and characteristics ot the solvent.

For ionic strength of up to 0.02

(6-23)

(6-24)

A: function of temperature and dielectric constant of the medium.

: rational activity coefficient (» practical activity coefficient in dilute solutions)

For ionic strength of up to 0.1

(6-25)

: mean effective ionic diameter (ion size parameter). analogous to b in van der Waals equation.

B: function of temperature and characteristics of solvent.

For water at 25 oC

(6-26)

For ionic strength of greater than 0.1

(6-27)

Cm : empirical correction term

D. coefficients for expressing colligative properties activity: inconvenient for calculation the colligative properties of weak electrolyte.

1. The L Value

(6-28)

Liso: at a concentration of drug that is isotonic with body fluids.

1.86 for nonelectrolyte

2.0 for weak electrolyte

3.4 for univalent electrolyte

(See Fig. 6-7)

2. Osmotic Coefficient (g)

at infinite dilution

for more concentrated solution (practical osmotic coefficient)

in a dilute solution

(6-29)

3. Osmolality

1 osmolal solution: 1 mole of a nonionizable substance in 1 Kg of water.

in dilute solution

milliosmolality (mOsm/Kg) = i mm

i: number of ions formed per molecule

mm: millimolal concentration

Osmolarity = Osmolality x d (1 – 0.001 )

d: solution density

: partial molar volume

·                    Electrical Conductivity: A useful property of solutions is their electrical conductivity. Pure water does not conduct electricity, but many aqueous solutions do.

o        Strong Electrolytes: Strong electrolytes are solutions whose electrical conductivity is high. They are good conductors of electricity.

o        Weak Electrolytes: Weak electrolytes are solutions that conduct electricity, but not very well. They are still called conductors, but only poor conductors.

o        Non Electrolytes: Non electrolytes do not conduct electricity.

A device for detecting electrical conductivity in solutions is shown in Figure 4.4 in the text:

·                    Arrhenius’ Theory of Electrical Conductivity: The first modern theory to explain electrical conductivity in solutions was advanced by Svante Arrhenius, at the time a doctoral student in physics at the University of Uppsala, Sweden. He deduced the presence of charged particles in an electrically conductive solution, and he postulated that the extent of the conductivity depended on the number of ions present. Hence the solute in a strong electrolyte would produce many ions and conduct electricity well, while the solute in a weak electrolyte would produce relatively few ions and not conduct electricity very well. In a non electrolyte, the solute would produce no ions, hence no electrical conductivity for these solutions.

·                    Strong Electrolytes: The conductivity of a strong electrolyte is high, as illustrated in Figure 4.4a. This conductivity is produced by solutes that are completely ionized in solution. Three classes of strong electrolytes are:

·         Soluble Salts

·         Strong Acids

·         Strong Bases

·                    Soluble Salts: Any salt that readily dissolves in water produces a strong electrolyte when it is so dissolved. A good example is sodium chloride (NaCl). See Figure 4.5.

·                    Strong Acids: According to Arrhenius, an acid is a substance that ionizes in aqueous solution to generate H⁺ ions (hydrogen ions or protons). If the ionization is complete or nearly complete, the acid solution is a good conductor of electricity, and the acid is regarded as a strong acid. Some examples of strong acids in aqueous solution are:

Sulfuric acid (H₂SO₄) deserves a closer look. When sulfuric acid dissolves in water, the first hydrogen dissociates completely to form protons in aqueous solution, but the second hydrogen remains bonded to the sulfate. Thus aqueous sulfuric acid contains mostly protons (H⁺(aq)) and hydrogen sulfate (HSO₄^–(aq)) ions.

·                    Strong Bases: According to Arrhenius, a base is a substance that ionizes in aqueous solution to produce hydroxide ions (OH^–). Bases that ionize completely are regarded as strong bases. The two most common strong bases are sodium hydroxide and potassium hydroxide:

 

·                    Weak Electrolytes: Many substances will form ions in aqueous solution, but the extent of ionization is slight. For example, acetic acid (the essence of vinegar), will readily dissolve in water, but only around 1% of acetic acid molecules will ionize to form hydrogen ions and acetate ions. The remaining acetic acid molecules will remain as electrically neutral acetic acid molecules, even though they are totally dissolved in the solution. The result is a solution that is electrically conductive, but much less so than a comparative solution containing a strong electrolyte. The most common weak electrolytes are:

·         Weak acids

·         Weak bases

·                    Weak Acids: A weak acid is an acid that is only partially ionized in aqueous solution. Thus an aqueous solution of acetic acid (HC₂H₃O₂) contains some hydrogen ions (H⁺(aq)) and some acetate ions (C₂H₃O₂^–(aq)), but most of the solute particles are undissociated acetic acid molecules (HC₂H₃O₂(aq)).

 

·                    Weak Bases: Ammonia (NH₃) is the most common of the weak bases. It is a base because its aqueous solutions contain hydroxide ions (OH^–(aq)). It is a weak electrolyte because only a small fraction of ammonia molecules form ions. Most of the ammonia remains as neutral ammonia molecules.

 

·                    Nonelectrolytes: Nonelectrolytes are substances that dissolve in water, but do not generate any ions. Their solutions do not conduct electricity because of their total lack of ions. Common examples are:

·         Ethanol (C₂H₅OH)

·         Sucrose (C₁₂H₂₂O₁₁), also known as cane sugar.

4.3 The Composition of Solutions: Many important chemical reactions occur in solution. We need to be able to perform stoichiometric calculations on these reactions.

·                    Stoichiometry in Solutions: We need to know:

o        The forms that the reactants and products take in solution, and

o        The amounts of chemicals present in the solutions.

In the previous chapter, we learned to count the molecules in a reaction by weighing them, but when we deal with solutions, we need a different way of counting. The most convenient way to measure a liquid is to measure its volume. Thus, for example, if we had prepared a 1.000 liter solution containing 1.000 mol of sodium nitrate and then drew out a 50.00 mL portion of that solution, we would know that the 50.00 mL portion contains 0.05000 mol of sodium nitrate.

·                    Molarity: We can say that the above solution of sodium nitrate contains 1.000 moles of sodium nitrate in each 1.000 liters. Does this not look like a useful way to characterize a solution? So we define molarity as:

We can quantitatively describe our example solution as a 1.000 molar aqueous solution of sodium nitrate, and we can abbreviate that to 1.000 M NaNO₃.

·                    Sample Exercise: What is the molarity of a solution prepared by dissolving 11.5 g of solid NaOH in enough water to make up 1.5 L of solution? (The molar mass of NaOH is 40.00 g/mol.) We define some familiar symbols: m represents mass, MM represents molar mass, and n represents number of moles. And we need a new one: V for volume.

 

·                    Sample Exercise: Calculate the molarity of a solution prepared by dissolving 1.56 g of gaseous HCl in enough water to make 26.8 mL of solution. (The molar mass of HCl is 36.46 g/mol.)

·                    Ion Concentrations: The above definition of molarity is based upon how the solution was prepared. What is the volume of the solution? How much solute did you weigh? It does not necessarily describe what is actually in the solution. For example, our 0.192 M solution of NaOH in Sample Exercise 4.1 does not contain NaOH molecules. The actual species and their molarities are:

o        0.192 M sodium ions.

o        0.192 M hydroxide ions.

·                    Suppose we had a 0.192 M solution of sodium sulfate (Na₂SO₄). The species in solution would be:

o        0.192 M sulfate ions.

o        0.384 M sodium ions (because each mole of sodium sulfate generates 2 moles of sodium ions).

·                    Sample Exercise: What are the concentrations of each type of ion in the following solutions:

o        0.50 M Co(NO₃)₂

o        1 M Fe(ClO₄)₃

Moles of Solute in a Given Volume: If we know the molarity of a solution, we can calculate how many moles of each of its components there are in a given volume. We need simply to determine the molarities of each component and multiply them by the volume. Remember that the units of the answer will be moles.

Sample Exercise: How many moles of Cl^– ions are there in 1.75 L of 1.0 x 10^-3 M ZnCl₂?

·                    Standard Solutions: A standard solution is a solution whose concentration is accurately known. The procedure for preparing a standard solution is illustrated in Figure 4.10 form the text:

Sample Exercise: A chemist needs 1.00 L of an aqueous solution of K₂Cr₂O₇ (potassium dichromate) to analyze the alcohol contents of some samples of wine. How much K₂Cr₂O₇ must be weighed out to prepare the solution?

o        The number of moles of K₂Cr₂O₇ required is:

o        Then the mass of K₂Cr₂O₇ (molar mass = 294.20 g/mol) that must be weighed out is:

Dilution: Instead of preparing large volumes of solutions with relatively low concentrations of solute, chemists will often instead prepare a smaller volume of a much more concentrated solution and dilute portions of it as needed. For example: Suppose the chemist in Sample Exercise 4.6 had needed 20 L of 0.200 M K₂Cr₂O₇. Rather than perform the steps in Figure 4.10 twenty times over, she might instead have prepared 1.00 L of a 4.00 M solution. Then each time she needed some 0.200 M solution for an analysis, she could accurately measure (by pipette) 50.00 mL of the 4.00 M solution into another 1 liter volumetric flask and add water to the 1.00 L mark. The key to dilution calculations is that:

Moles of solute before dilution = Moles of solute after dilution

In a dilution problem, you will know or be given information to calculate 3 of the 4 quantities in the line above.

Example: We need 500. mL of 1.00 M acetic acid (HC₂H₃O₂) from a 17.4 M stock solution. What volume of stock solution do we need? (Work out on whiteboard.)

Sample Exercise What volume 16 M sulfuric acid (H₂SO₄) must be used to prepare 1.5 L of a 0.10 M H₂SO₄ solution? (The solution in the text is a bit convoluted. We’ll work it out directly on the whiteboard.)

Early concepts of acids and bases

Arrhenius defined an acid as a hydrogen-containing compound that when dissolved in water produces a concentration of hydrogen ions (or protons) greater than that of pure water. A base is defined as a substance that when dissolved in water produces an excess of hydroxyl ions, OH⁻. The neutralization reaction can be described as such:

H⁺ (aq) + OH⁻ (aq) →H₂O (l)

However, the Arrhenius theory of acids and bases had limitations.

1.                The theory restricts acids to hydrogen-containing species and bases to hydroxyl-containing species

2.                The theory applies to aqueous solutions only, while we know that many acid-base reactions can take place in the absence of water

3.                The theory is inadequate for gas and solid phase reactions in which H⁺ and OH⁻ may not exist

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.

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.

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.

 

2. THE ARHENIUSE ELECTROLYTIC DISSOCIATION THEORY. CONCEPT ABOUT STRONG AND WEAK ELECTROLYTES.

The Arrhenius theory

Two of the most important ions are the hydrogen cation (H⁺)and the hydroxide anion (OH^–). Since a hydrogen atom contains one proton and one electron, a hydrogen cation is simply a proton. A hydroxide ion, by contrast, is a polyatomic anion in which an oxygen atom is covalently bonded to a hydrogen atom.

The relation between acidic behavior and the presence of hydrogen in a compound was clarified in 1887 by the Swedish chemist Svante Arrhenius (1859–1927). Arrhenius proposed that acids are substances that dissociate in water to produce hydrogen ions (H⁺) and that bases are substances that dissociate in water to yield hydroxide ions (OH^–).

ACID A substance that provides H⁺ ions in water

BASE A substance that provides OH^– ions in water

Depending on their structure, different acids can provide different numbers of H⁺ ions. Hydrochloric acid and nitric acid provide one H+ ion each per molecule, etc.

Sodium hydroxide (NaOH; also known as lye or caustic soda), potassium hydroxide (KOH; also known as caustic potash), and barium hydroxide [Ba(OH)₂] are examples of bases. When any of these compounds dissolves in water, anions OH^– go into solution along with the corresponding metal cation.

Although convenient to use in equations, the symbol H⁺ does not really represent the structure of the ion present in aqueous solution. As a bare hydrogeucleus (proton) with no electroearby, H⁺ is much too reactive to exist by itself. Rather, the attaches to a water molecule, giving the more stable hydronium ion, H₃O⁺ We’ll sometimes write H⁺ for convenience, particularly when balancing equations, but will more often write to represent an aqueous acid solution. Hydrogen chloride, for instance, gives Cl^– and H₃O⁺ when it dissolves in water

Sulfuric acid, for instance, can dissociate twice, and phosphoric acid can dissociate three times. In the case of sulfuric acid, the first dissociation of an H⁺ is complete—all H₂SO₄ (because it’s strong acid) molecules lose one H⁺—but the second dissociation is incomplete, as indicated by the double arrow below. In the case of phosphoric acid, none of the three dissociations is complete.

Limitations:

(i)  For the acidic or basic properties, the presence of water is absolutely necessary. Dry HCl shall not act as an acid. HCl is regarded as an acid only when dissolved in water and not in any other solvent.

(ii)  The concept does not explain acidic and basic character of substances in non-aqueous solvents.

(iii) The neutralization process is limited to those reactions which can occur in aqueous solutions only, although reactions involving salt formation do occur in the absence of solvent.

(iv) It cannot explain the acidic character of certain salts such as AlCl₃ in aqueous solution.

(v) An artificial explanation is required to explain the basic nature of NH₃ and metallic oxides and acidic nature of non-metal oxides.

Limitations of the theory

Hydrochloric acid is neutralised by both sodium hydroxide solution and ammonia solution. In both cases, you get a colourless solution which you can crystallise to get a white salt – either sodium chloride or ammonium chloride.

These are clearly very similar reactions. The full equations are:

In the sodium hydroxide case, hydrogen ions from the acid are reacting with hydroxide ions from the sodium hydroxide – in line with the Arrhenius theory.

However, in the ammonia case, there don’t appear to be any hydroxide ions!

You can get around this by saying that the ammonia reacts with the water it is dissolved in to produce ammonium ions and hydroxide ions:

This is a reversible reaction, and in a typical dilute ammonia solution, about 99% of the ammonia remains as ammonia molecules. Nevertheless, there are hydroxide ions there, and we can squeeze this into the Arrhenius theory.

However, this same reaction also happens between ammonia gas and hydrogen chloride gas.

In this case, there aren’t any hydrogen ions or hydroxide ions in solution – because there isn’t any solution. The Arrhenius theory wouldn’t count this as an acid-base reaction, despite the fact that it is producing the same product as when the two substances were in solution. That’s silly!

In the sodium hydroxide case, hydrogen ions from the acid are reacting with hydroxide ions from the sodium hydroxide – in line with the Arrhenius theory.

However, in the ammonia case, there don’t appear to be any hydroxide ions!

You can get around this by saying that the ammonia reacts with the water it is dissolved in to produce ammonium ions and hydroxide ions.

This is a reversible reaction, and in a typical dilute ammonia solution, about 99% of the ammonia remains as ammonia molecules. Nevertheless, there are hydroxide ions there, and we can squeeze this into the Arrhenius theory.

However, this same reaction also happens between ammonia gas and hydrogen chloride gas.

In this case, there aren’t any hydrogen ions or hydroxide ions in solution – because there isn’t any solution. The Arrhenius theory wouldn’t count this as an acid-base reaction, despite the fact that it is producing the same product as when the two substances were in solution. That’s silly!

 

 

3. ELECTROLYTES IN THE HUMAN BODIES.

 

Within the human body, electrolytes are most commonly found in the form of potassium, sodium, magnesium, calcium, phosphate, chloride and bicarbonate. These electrolytes found in the human body are critical for the proper functioning and maintenance of the body. Electrolytes are essential for the proper functioning of the nerves and muscles. If electrolytes are not in proper balance, hydration as well as the pH of the blood can be adversely affected. Electrolytes play a crucial role in the chemical reactions that occur within the human body.

In humans, electrolytes are introduced into the body when the person takes electrolyte containing fluids by mouth. The electrolyte balance within the body is maintained and controlled by hormones secreted within the person’s body, and the kidneys will expel excess electrolytes from the body through the urinary tract. If electrolytes are severely imbalanced, serious life-threatening cardiac and neurological complications may ensue, which require emergency medical intervention to treat.

Specialty electrolyte drinks can be used to restore the balance of electrolytes in a person’s body after becoming sick, dehydrated or ill. Water is usually not a first choice due to the possibility that introducing plain water may further dilute already present electrolytes and cause serious complications to the person’s health. Electrolyte drinks do however, contain high amounts of sugar, and are not generally recommended for regular consumption, especially to children. There are specialty electrolyte drinks available on the market for children which contain less sugars than sports drinks.

 

 

Figure. Electrolyte composition of extracellular and intracellular fluid compartments of humans (Modified from Guyton 1986)  

 

4. PROPERTIES OF STRONG ELECTROLYTE SOLUTIONS. ACTIVITY AND COEFFICIENT OF ACTIVITY. IONIC FORCE OF SOLUTION. CONSTANT OF IONIZATION. DEGREE OF IONIZATION AND IT DEPENDENCE ON THE CONCENTRATION (OSTWALD LAW).

We all know from experience that both sugar (sucrose) and table salt (NaCl) dissolve in water. The solutions that result, though, are quite different. When sucrose, a molecular substance, dissolves in water, the solution that results contains neutral sucrose molecules surrounded by water. When NaCl, an ionic substance, dissolves in water, the solution contains separate Na⁺ and Cl^– ions surrounded by water. Because of the presence of the ions, the NaCl solution conducts electricity, but the sucrose solution does not.

I        In chemistry, an electrolyte is any substance containing free ions that make the substance electrically conductive. The most typical electrolyte is an ionic solution, but molten electrolytes and solid electrolytes are also possible.

Electrolytes commonly exist as solutions of acids, bases or salts. Furthermore, some gases may act as electrolytes under conditions of high temperature or low pressure. Electrolyte solutions can also result from the dissolution of some biological (e.g., DNA, polypeptides) and synthetic polymers (e.g., polystyrene sulfonate), termed polyelectrolytes, which contain charged functional groups.

Electrolyte solutions are normally formed when a salt is placed into a solvent such as water and the individual components dissociate due to the thermodynamic interactions between solvent and solute molecules, in a process called solvation. For example, when table salt, NaCl, is placed in water, the salt (a solid) dissolves into its component ions, according to the dissociation reaction

NaCl_(s) → Na⁺_(aeq) + Cl⁻_(aq)

It is also possible for substances to react with water when they are added to it, producing ions, e.g., carbon dioxide gas dissolves in water to produce a solution which contains hydronium, carbonate, and hydrogen carbonate ions.

Note that molten salts can be electrolytes as well. For instance, when sodium chloride is molten, the liquid conducts electricity.

An electrolyte in a solution may be described as concentrated if it has a high concentration of ions, or dilute if it has a low concentration. If a high proportion of the solute dissociates to form free ions, the electrolyte is strong; if most of the solute does not dissociate, the electrolyte is weak. The properties of electrolytes may be exploited using electrolysis to extract constituent elements and compounds contained within the solution.

Electrolytes are substances such as NaCl or KBr, which dissolve in water to produce conducting solutions of ions.

Nonelectrolytes are substances such as sucrose or ethyl alcohol, which do not produce ions in aqueous solution.

In physiology, the primary ions of electrolytes are sodium(Na⁺), potassium (K⁺), calcium (Ca²⁺), magnesium (Mg²⁺), chloride (Cl⁻), hydrogen phosphate (HPO₄²⁻), and hydrogen carbonate (HCO₃⁻). The electric charge symbols of plus (+) and minus (−) indicate that the substance in question is ionic iature and has an imbalanced distribution of electrons, which is the result of chemical dissociation.

All known higher life forms require a subtle and complex electrolyte balance between the intracellular and extracellular milieu. In particular, the maintenance of precise osmotic gradients of electrolytes is important. Such gradients affect and regulate the hydration of the body as well as blood pH, and are critical for nerve and muscle function. Various mechanisms exist in living species that keep the concentrations of different electrolytes under tight control.

Both muscle tissue and neurons are considered electric tissues of the body. Muscles and neurons are activated by electrolyte activity between the extracellular fluid or interstitial fluid, and intracellular fluid. Electrolytes may enter or leave the cell membrane through specialized protein structures embedded in the plasma membrane called ion channels. For example, muscle contraction is dependent upon the presence of calcium (Ca²⁺), sodium (Na⁺), and potassium (K⁺). Without sufficient levels of these key electrolytes, muscle weakness or severe muscle contractions may occur.

Electrolyte balance is maintained by oral, or in emergencies, intravenous (IV) intake of electrolyte-containing substances, and is regulated by hormones, generally with the kidneys flushing out excess levels. In humans, electrolyte homeostasis is regulated by hormones such as antidiuretic hormone, aldosterone and parathyroid hormone. Serious electrolyte disturbances, such as dehydration and overhydration, may lead to cardiac and neurological complications and, unless they are rapidly resolved, will result in a medical emergency.

Measurement of electrolytes is a commonly performed diagnostic procedure, performed via blood testing with ion selective electrodes or urinalysis by medical technologists. The interpretation of these values is somewhat meaningless without analysis of the clinical history and is often impossible without parallel measurement of renal function. Electrolytes measured most often are sodium and potassium. Chloride levels are rarely measured except for arterial blood gas interpretation since they are inherently linked to sodium levels. One important test conducted on urine is the specific gravity test to determine the occurrence of electrolyte imbalance.

In oral rehydration therapy, electrolyte drinks containing sodium and potassium salts replenish the body’s water and electrolyte levels after dehydration caused by exercise, excessive drinking, diaphoresis, diarrhea, vomiting, intoxication or starvation. Athletes exercising in extreme conditions (for three or more hours continuously e.g. marathon or triathlon) who do not consume electrolytes risk dehydration (or hyponatremia).

A simple electrolyte drink can be home-made by using the correct proportions of water, sugar, salt, salt substitute for potassium, and baking soda. However, effective electrolyte replacements should include all electrolytes required by the body, including sodium chloride, potassium, magnesium, and calcium that can be either obtained in a sports drink or a solid electrolyte capsule.

Electrolytes are commonly found in fruit juices, sports drinks, tomato soup and many fruits and vegetables (e.g. potatoes, avocados).

When electrodes are placed in an electrolyte and a voltage is applied, the electrolyte will conduct electricity. Lone electrons normally cannot pass through the electrolyte; instead, a chemical reaction occurs at the cathode consuming electrons from the anode, and another reaction occurs at the anode producing electrons to be taken up by the cathode. As a result, a negative charge cloud develops in the electrolyte around the cathode, and a positive charge develops around the anode. The ions in the electrolyte neutralize these charges, enabling the electrons to keep flowing and the reactions to continue.

For example, in a solution of ordinary table salt (sodium chloride, NaCl) in water, the cathode reaction will be

2H₂O + 2e⁻ → 2OH⁻ + H₂

and hydrogen gas will bubble up; the anode reaction is

2NaCl → 2 Na⁺ + Cl₂ + 2e⁻

and chlorine gas will be liberated. The positively charged sodium ions Na⁺ will react towards the cathode neutralizing the negative charge of OH⁻ there, and the negatively charged oxide ions OH⁻ will react towards the anode neutralizing the positive charge of H⁺ there. Without the ions from the electrolyte, the charges around the electrode would slow down continued electron flow; diffusion of H⁺ and OH⁻ through water to the other electrode takes longer than movement of the much more prevalent salt ions.

Also: Electrolytes dissociate in water because water molecules are dipoles and the dipoles orient in an energetically favorable manner to solvate the ions.

In other systems, the electrode reactions can involve the metals of the electrodes as well as the ions of the electrolyte.

Electrolytic conductors are used in electronic devices where the chemical reaction at a metal/electrolyte interface yields useful effects.

·                    In batteries, two metals with different electron affinities are used as electrodes; electrons flow from one electrode to the other outside of the battery, while inside the battery the circuit is closed by the electrolyte’s ions. Here the electrode reactions convert chemical energy to electrical energy.

·                    In some fuel cells, a solid electrolyte or proton conductor connects the plates electrically while keeping the hydrogen and oxygen fuel gases separated.

·                    In electroplating tanks, the electrolyte simultaneously deposits metal onto the object to be plated, and electrically connects that object in the circuit.

·                    In operation-hours gauges, two thin columns of mercury are separated by a small electrolyte-filled gap, and, as charge is passed through the device, the metal dissolves on one side and plates out on the other, causing the visible gap to slowly move along.

·                    In electrolytic capacitors the chemical effect is used to produce an extremely thin ‘dielectric’ or insulating coating, while the electrolyte layer behaves as one capacitor plate.

·                    In some hygrometers the humidity of air is sensed by measuring the conductivity of a nearly dry electrolyte.

·                    Hot, softened glass is an electrolytic conductor, and some glass manufacturers keep the glass molten by passing a large current through it.

 

       Anode          (positive electrode)              Cathode (negative electrode)

 (a) A solution of NaCl conducts electricity because of the movement of charged particles (ions), thereby completing the circuit and allowing the bulb to light.

(b) A solution of sucrose does not conduct electricity or complete the circuit because it has no charged particles. The bulb therefore remains dark.

 According to the Degree of dissociation (α) electrolytes can be classified into the following:

·strong electrolytes are compounds that dissociate to a large extent ( α> 30%) into ions when dissolved in water. For example, HCl, H₂SO₄, HNO₃, HJ, NaOH, KOH, KCl.

medium  strong electrolytes α = 2 – 30%. For istance, H₃PO ₄, H₃PO _3.

weak electrolytes are compounds that dissociate to only a small extent α<2%. For example, NH₄OH, H₂S, HCN, H₂CO₃.

nonelectrolytes α = 0 are compounds that don’t dissociate when dissolved in water.

Note that when we write a dissociation, we use a forward-and-backward double arrow to indicate that the reaction takes place simultaneously in both directions. That is, a dissociation is a dynamic process in which an equilibrium is established between the forward and reverse reactions. The balance between the two opposing reactions defines the exact concentrations of the various species in solution.

In chemistry, biochemistry, and pharmacology, a dissociation constant is a specific type of equilibrium constant that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as when a complex falls apart into its component molecules, or when a salt splits up into its component ions. The dissociation constant is usually denoted K_d and is the inverse of the association constant. In the special case of salts, the dissociation constant can also be called an ionization constant.

For a general reaction

AxBy = xA + yB

in which a complex A_xB_y breaks down into x A subunits and y B subunits, the dissociation constant is defined

K_d = [A]^x * [B]^y / [A_xB_y]

where [A], [B], and [A_xB_y] are the concentrations of A, B, and the complex A_xB_y, respectively.

The dissociation constant is commonly used to describe the affinity between a ligand (L) (such as a drug) and a protein (P) i.e. how tightly a ligand binds to a particular protein. Ligand-protein affinities are influenced by non-covalent intermolecular interactions between the two molecules such as hydrogen bonding, electrostatic interactions, hydrophobic and Van der Waals forces. They can also be affected by high concentrations of other macromolecules, which causes macromolecular crowding.

The formation of a ligand-protein complex (C) can be described by a two-state process

C = P + L

the corresponding dissociation constant is defined

where [P], [L] and [C] represent molar concentrations of the protein, ligand and complex, respectively.

The dissociation constant has molar units (M), which correspond to the concentration of ligand [L] at which the binding site on a particular protein is half occupied, i.e. the concentration of ligand, at which the concentration of protein with ligand bound [C], equals the concentration of protein with no ligand bound [P]. The smaller the dissociation constant, the more tightly bound the ligand is, or the higher the affinity between ligand and protein. For example, a ligand with a nanomolar (nM) dissociation constant binds more tightly to a particular protein than a ligand with a micromolar (μM) dissociation constant.

Sub-nanomolar dissociation constants as a result of non-covalent binding interactions between two molecules are rare. Nevertheless, there are some important exceptions. Biotin and avidin bind with a dissociation constant of roughly 10 ^{− 15} M = 1 fM = 0.000001 nM. Ribonuclease inhibitor proteins may also bind to ribonuclease with a similar 10 ^{− 15} M affinity. The dissociation constant for a particular ligand-protein interaction can change significantly with solution conditions (e.g. temperature, pH and salt concentration). The effect of different solution conditions is to effectively modify the strength of any intermolecular interactions holding a particular ligand-protein complex together.

Drugs can produce harmful side effects through interactions with proteins for which they were not meant to or designed to interact. Therefore much pharmaceutical research is aimed at designing drugs that bind to only their target proteins with high affinity (typically 0.1-10 nM) or at improving the affinity between a particular drug and its in-vivo protein target.

In the specific case of antibodies (Ab) binding to antigen (Ag), usually the affinity constant is used. It is the inverted dissociation constant.

This chemical equilibrium is also the ratio of the on-rate (k_forward) and off-rate (k_back) constants. Two antibodies can have the same affinity, but one may have both a high on- and off-rate constant, while the other may have both a low on- and off-rate constant.

 

The main concepts of the theory of strong electrolytes. Ionic strength of solution, the activity coefficient and activity.

A strong electrolyte is a solute that completely, or almost completely, ionizes or dissociates in a solution. These ions are good conductors of electric current in the solution.

Originally, a “strong electrolyte” was defined as a chemical that, when in aqueous solution, is a good conductor of electricity. With greater understanding of the properties of ions in solution its definition was gradually changed to the present one. A concentrated solution of this strong electrolyte has a lower vapour pressure than that of pure water at the same temperature. Strong acids, strong bases, and soluble ionic salts that are not weak acids or weak bases are strong electrolytes.

For strong electrolytes, a single reaction arrow shows that the reaction occurs completely in one direction, in contrast to the dissociation of weak electrolytes, which both ionize and re-bond in significant quantities .

Strong electrolyte(aq) → Cation⁺(aq) + Anion^–(aq)

Strong electrolytes conduct electricity only when molten or in aqueous solutions. Strong electrolytes break apart into ions completely..

The stronger an electrolyte the greater the voltage produced when used in a galvanic cell.

When the concentration of a solute is greater than about 0.1 mol/dm^-3, or we have strong electrolytes solution (NaCl, HCl, etc.),  interactions between the solute molecules or ions are significant, and the effective and real concentrations are no longer equal. It becomes necessary to define a new quantity called the activity, which is a measure of concentration but takes into account the interactions between the solution species. The relative activity, a_i, of a component i

is dimensionless and is defined by equation 6.6 where μ_i is the chemical potential of component i or ionic strength , μ_i⁰  is the standard chemical potential of i, R is the molar gas constant, and T is the temperature in kelvin.

The relative activity of a solute is related to its molality by equation 6.7 where f_i is the activity coefficient of the solute, and C_M is the molality.

a_i =  f_i C_M

In very dilute solutions of strong electrolytes f   equals to 1. The activity coefficient depends at the ion concentration of solutions, the nature of an electrolyte, a temperature, the ionic strength solution.

μi = 0.5 (C_M1 Z₁² + C_M2 Z₂²+….. C_Mi Z_i²)

where Z is the charge of ions

The ionic strength characterizes the electrostatic interaction of ions in a solution. Experimentally established, that with increasing the ionic strength of a solution the activity coefficient  decreases. For values of the ionic strength of dilute solutions of strong electrolytes calculates the activity coefficient of ions by the  formula

 lg f = -0.5 Z²√ μi

 

Another notation

Often when we are discussing the dissociation of an acid, the symbol K_a is used for the dissociation constant, which can lead to it being confused with the association constant described above. It is sometimes expressed by its pK_a, which is defined as:

pK_a = − log₁₀K_a

These pK_a‘s are mainly used for covalent dissociations (i.e., reactions in which chemical bonds are made or broken) since such dissociation constants can vary greatly.

For the deprotonation of acids, K is known as K_a, the acid dissociation constant. Stronger acids, for example sulfuric or phosphoric acid, have larger dissociation constants; weaker acids, like acetic acid, have smaller dissociation constants. A molecule can have several acid dissociation constants. In this regard, that is depending on the number of the protons they can give up, we define monoprotic, diprotic and triprotic acids. The first (e.g. acetic acid or ammonium) have only one dissociable group, the second (carbonic acid, bicarbonate, glycine) have two dissociable groups and the third (e.g. phosphoric acid) have three dissociable groups. In the case of multiple pK values they are designated by indices: pK₁, pK₂, pK₃ and so on. For amino acids, the pK₁ constant refers to its carboxyl (-COOH) group, pK₂ refers to its amino (-NH₃) group and the pK₃ is the pK value of its side chain.

 

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.

Example.

The ionization constant of HCN is 4 × 10^-10. Calculate the concentration of hydrogen ions in 0.2 M solution of HCN containing 1 mol L^-1 of KCN?

Solution: The dissociation of HCN is represented as

HCN ↔ H⁺ + CN^–

Applying law of mass action,

K_a =   ([H⁺ ][CN^–])/[HCN] or [H⁺ ] (K_a [HCN])/[CN^– ]

In presence of strong electrolyte, the total CN^– concentration comes from KCN which undergoes complete dissociation. It is further assumed that dissociation of HCN is very-very small and the concentration of HCN can be taken as the concentration of undissociated HCN.

Thus, [HCN] = 0.2 M and [CN^–] = 1M

Putting these values in the expression

[H⁺] = (K_a [HCN])/([CN^– ]) = (4×10^-10×0.2)/1 = 8×10^-11 mol L^-1

Note: When KCN is not present, the [H+] concentration is equal to √CK i.e., √(0.2*4*10^-10) = 8.94 *10^-8mol L^-1 . This shows that concentration of H⁺ ions fails considerably when KCN is added to HCN solution.

Example

Determine the concentration of hydroxyl ions in 0.4 M NH₄OH solution having (i) no ammonium chloride, (ii) 5.35 g of NH₄Cl in a litre of the solution. Ionization constant of NH₄OH is 1.8 × 10^-5.

Solution:  

(i)  Let ‘α‘ be the degree of dissociation of NH₄OH is absence of NH₄Cl.

α = √(K_b/c)

So, [OH^–] = C α = √(K_bc) = √(1.8 * 10^-5 * 0.4)  = 2.68 × 10^-3 mol L

(ii)   In presence of NH₄Cl

[NH^–₄] = 5.35/53.5 = 0.1M and [NH₄OH] = 0.4M

So, [OH^–] =(K_b [NK₄OH])/[NH₄^–]=(1.8×10^-3×0.4)/0.1 = 7.2 × 10^-5 mol L^-1

Example

 When 0.100 mole of ammonia, NH₃, is dissolved in sufficient water to make 1.0 L solution, the solution is found to have a hydroxide ion concentration of 1.34 × 10^-3 M. Calculate K_b for ammonia.

Solution

NH₃  +   H₂O  ↔  NH⁺₄

At equilibrium (0.100 -1.34 ×10^-3) M=1.34×10^-3 M = 0.09866 M    +    OH^–   1.34 × 10^-3 M

K_b = [NH₄⁺ ][OH^– ]/[NK₃ ] = (1.34×10^-3 × 1.34×10^-3)/0.09866 =1.8199×10^-5

Example

Ka for HA is 4.9 ×10^-8. After making the necessary approximation, calculate for its decimolar solution

(a)   % dissociation

(b)   H⁺ ion concentration.

Solution:  For a weak electrolyte.

α = √K/C = √((4.9×10^-8)/0.1) = 7 × 10^-4

% dissociation = 100 × α = 100 × 7 × 10^-4 = 7 ×10^-2

HA       ↔         H⁺     +      A^–

C(-1-α)           Cα                    Cα

[H⁺] = C × α = 0.1 ×7 × 10^-4 = 7 × 10^-5 mol L^-1

Wilhelm Ostwald’s dilution law is a relationship between the dissociation constant and the degree of dissociation of a weak electrolyte (acids, bases).

 

Ostwald’s Dilution law:

According to Arrhenius theory of electrolyte dissociation, the molecules of an electrolyte in solution are constantly splitting up into ions and the ions are constantly reuniting to form unionized molecules. Therefore, a dynamic equilibrium exists between ions and unionized molecules of the electrolyte in solution. It was pointed out by Ostwald that like chemical equilibrium, law of mass action van be applied to such systems also.

Consider a binary electrolyte AB which dissociates into A⁺ and B- ions and the equilibrium state is represented by the equation:

AB ↔  A⁺ + B^–

Initially t = o       C         0     0

At equilibrium     C(1-α)   Cα    Cα

So, dissociation constant may be given as

K = [A⁺][B^–]/[AB] = (Cα * Cα)/C(1-α) =   Cα² /(1-α) ……. (i)

For very weak electrolytes,

α <<< 1,  (1 – α ) = 1

K = Cα²

α = √K/C ……. (ii)

Concentration of any ion = Cα = √CK .

From equation (ii) it is a clear that degree of ionization increases on dilution.

Thus, degree of dissociation of a weak electrolyte is proportional to the square root of dilution.

Limitations of Ostwald’s dilution law:

The law holds good only for weak electrolytes and fails completely in the case of strong electrolytes. The value of ‘α‘ is determined by conductivity measurements by applying the formula Λ/Λ_∞. The value of ‘α‘ determined at various dilutions of an electrolyte when substituted in Eq. (i) gives a constant value of K only in the case of weak electrolytes like CH₃COOH, NH₄OH, etc. the cause of failure of Ostwald’s dilution law in the case of strong electrolytes is due to the following factors”

(i)   The law is based on the fact that only a portion of the electrolyte is dissociated into ions at ordinary dilution and completely at infinite dilution. Strong electrolytes are almost completely ionized at all dilutions and Λ/Λ_∞ does not give accurate value of ‘α‘.

(ii)  When concentration of the ions is very high, the presence of charges on the ions appreciably effects the equilibrium. Hence, law of mass action its simple form cannot be strictly applied in the case of string electrolytes.

Ostwald’s Dilution law:

SOME SOLVED EXAMPLES

Example

A 0.01 M solution of acetic is 5% ionized at 25^o C. Calculate its dissociation constant.

Solution: According to Ostwald’s dilution law

K_α = α²/(1-α)V

α = 0.05,    V = 1/0.01 = 100 litres

Hence,                K_a = 0.05 * 0.05/(1-0.05)100 = 2.63 * 10^-5

Example

Calculate the H+ ion concentration of a 0.02 N weak monobasic acid. The value of dissociation constant is 4.0 × 10^-10.

Solution:

HA ↔  H⁺ + A^–

Applying Ostwald’s dilution law of a weak acid,

α = √k_aV

Ka= 4.0 ×10^-10,          V = 1/0.01 = 100 litres

α = √(4 * 10^-10 * 10²) = 2 * 10^-4

Concentration of hydrogen ions

a/√V = (2*10^-4)/100 = 2*10^-6 mol L^-1

or Concentration of hydrogen ions

=  √(CK) = √(0.01 * 4 *10^-10) = 2 * 10^-6mol L^-1

Example

The concentration of H⁺ ions in 0.10 M solution of a weak acid is 1.0 × 10^-5 mol L^-1. Calculate the dissociation constant of the acid.

Solution:

    HA   ↔    H⁺     +      A^–

Initial concentration   0.1          0              0

Equilibrium concentration

(mol L^-1)        0.1-1.0×10^-5    1.0×10^-5    1.0×10^-5

[HA] can be taken as 0.1 M as 1.0 × 10^-5 is very small.

Applying law of mass action.

K_α = [H⁺][A^–]/[HA] = (1.0*10^-5 * 1.0 *10^-5)/0.10 = 1 × 10^-9

Example

What will be the dissociation constant of 0.1 N aqueous ammonia solution in terms of degree of dissociation ‘α‘? What will be the value if the concentration is 0.01 N?

Solution:

NH₄OH ↔ NH^–₄ + OH^–

At equilibrium  (1-α)     α         α

Since the solution is 0.1 N,

V = 1/0.1 = 10litre

 [NH₄OH]=(1-α)/10,  [NH^–₄] = α/10 and [OH^–] = α/10

Applying law of mass action,

For 0.01 N Solution, K_b remains the same at the same temperature but degree of dissociation value becomes different.

Example

A 0.0128 N solution of acetic acid has A = 14 mho equiv^-1 and A_∞ = 391 mho equiv^-1 at 25^oC. Calculate the dissociation constant of the acid.

Solution: Degree of dissociation,

α = Λ/Λ_∞ = 14/391 = 3.58*10^-2

Now applying Ostwald’s dilution law,

K_α = α²/(1-α)V

α = 3.58 * 10^-2 and V = 1/0.0128 litre

So, K_α = 3.58 * 10^-2 * 3.58 * 10^-2 * 0.0128 = 1.64 * 10^-5

 

3. Remove of equilibrium in solution in weak electrolytes. Reactions of neutralization.

A weak acid is not the same thing as a dilute solution of a strong acid. Whereas a strong acid is 100% dissociated in aqueous solution, a weak acid is only partially dissociated. The dissociation of a weak acid in water is characterized by an equilibrium equation. The equilibrium constant for the dissociation reaction, denoted K_a is called the acid-dissociation constant:

 

Values of K_a and pK_a = – log K_a for some typical weak acids are listed in Table 15.2. (Just as the pH is defined as – log [H⁺], so the pK_a of an acid is defined as -log K_a). Also included in Table 15.2 for comparison are values for HCl, a typical strong acid. As indicated by the equilibrium equation, the larger the value of K_a, the stronger the acid.

 For example, The pH of 0.250 M HF is 2.036. What is the value of K_a for hydrofluoric acid?

Calculating Equilibrium Concentrations in Solutions of Weak Acids

Example

Calculate the concentrations of all species present (HCN, H₃O⁺, CN^– and OH^–) and the pH in a 0.15 M HCN solution.

Step 1. Let’s begin by listing the species present initially before any dissociation reactions and by identifying them as acids or bases.

Step 2. Because we have two acids (HCN and H₂O) and just one base H₂O two proton-transfer reactions are possible:

Step 3. The proton-transfer reaction that has the larger equilibrium constant—is called the principal reaction. Any other proton-transfer reactions are called subsidiary reactions. Since K_a for HCN is more than 1000 times greater than Kw, the principal reaction in this case is dissociation of HCN, and dissociation of water is a subsidiary reaction.

We’ll assume that essentially all the H₃O⁺comes from the principal reaction.

Step 4. Next, we express the concentrations of the species involved in the principal reaction in terms of the concentration of HCN that dissociates—say, x mol/L. According to the balanced equation for the dissociation of HCN, if x mol/L of HCN dissociates, then x mol/L of H₃O⁺ and CN^– x mol/L of are formed, and the initial concentration of HCN before dissociation (0.50 mol/L in our example) is reduced (0.15 – x) mol/L at equilibrium. Let’s summarize these considerations in a table under the principal reaction:

If [H⁺] = [CN^–] = 8.6 x 10^-6, then we have lost this amount

Step 5. Substituting the equilibrium concentrations

Because K_a is very small, the principal reaction will not proceed very far to the right, and x will be negligibly small compared to 0.10. Therefore, we can make the approximation that (0.15 – x) = 0.15 which greatly simplifies the solution:

of HCN, so:

[HCN] = 0.15 – (8.6 x 10^-6) = 0.15 M

Step 6. Next, we use the calculated value of x to obtain the equilibrium concentration of all species involved in the principal reaction:

Step 7. The concentrations of the species involved in the principal reaction are the “big” concentrations. The species involved in the subsidiary reaction(s) are present in smaller concentrations that can be calculated from equilibrium equations for the subsidiary reaction(s) and the big concentrations already determined.

[OH^–] determined from the subsidiary equilibrium equation

Note that [OH^–] is 5000 times smaller than [H₃O⁺]

Step 8. Finally, we can calculate the pH:

pH = -log (0.15) = 0.824

pH + pOH = 14

pOH = 14 – .824 = 13.18

conc. OH- = 10^-13.18 = 6.61*10^14 (very small obviously since HCN is a strong acid

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

 

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:

A MOLECULAR EQUATION

In fact, lead nitrate, potassium iodide, and potassium nitrate are strong electrolytes that dissolve in water to yield solutions of ions. Thus, it’s more accurate to write the reaction as an ionic equation, in which all the ions are explicitly shown:

 

AN IONIC EQUATION

A look at this ionic equation shows that the and ions undergo no change during the reaction. Instead, they appear on both sides of the reaction arrow and act merely as spectator ions, whose only role is to balance the charge. The actual reaction, when stripped to its essentials, can be described more simply by writing a net ionic equation

Aqueous reactions can be grouped into three general categories, each with its own kind of driving force: precipitation reactions, acid–base neutralization reactions, and oxidation–reduction reactions.

1) Precipitation reactions are processes in which soluble reactants yield an insoluble solid product that drops out of the solution. Most precipitations take place when the anions and cations of two ionic compounds change partners. For example, an aqueous solution of lead(II) nitrate reacts with an aqueous solution of potassium iodide to yield an aqueous solution of potassium nitrate plus an insoluble yellow precipitate of lead iodide:

Pb(NO₃)₂ (aq)  +  2 KCl (aq)    PbCl₂ (s)  +  2 KNO₃ (aq)

To predict whether a precipitation reaction will occur on mixing aqueous solutions of two substances, you must know the solubility of each potential product—that is, how much of each compound will dissolve in a given amount of solvent at a given temperature. If a substance has a low solubility in water, it is likely to precipitate from an aqueous solution. If a substance has a high solubility in water, no precipitate will form. Solubility is a complex matter, and it’s not always possible to make correct predictions. In addition, solubilities depend on the concentrations of the reactant ions, and the very words “soluble” and “insoluble” are imprecise. As a rule of thumb, though, a compound is probably soluble if it meets either (or both) of the following criteria:

1. A compound is probably soluble if it contains one of the following cations:

Group 1A cation: Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺

Ammonium ion: NH₄⁺

2. A compound is probably soluble if it contains one of the following anions:

Halide Cl^–, Br^–, I^–: except  and  compounds

Nitrate (NO₃^–) perchlorate (ClO₄^–) acetate (CH₃COO^–) sulfate (SO₄^2-) except and sulfates

Note A compound that does not contain one of the ions listed above is probably not soluble. Such as CaCO₃ however, contains neither a group 1A catioor any of the anions on the list and is therefore not soluble

 

2) Acid–base neutralization reactions are processes in which an acid reacts with a base to yield water plus an ionic compound called a salt. Thus, the driving force behind a neutralization reaction is the production of the stable covalent water molecule by removal of H⁺ and OH^– ions from solution. The reaction between hydrochloric acid and aqueous sodium hydroxide to yield water plus aqueous sodium chloride is a typical example:

HCl (aq)  +  NaOH (aq)    NaCl + H₂O

Because salts are generally strong electrolytes in aqueous solution, we can write the neutralization reaction of a strong acid with a strong base as an ionic equation:

H⁺ (aq)  +  Cl¯ (aq)  +  Na⁺ (aq)  +  OH¯ (aq)    Na⁺ (aq)  +  Cl¯ (aq)  +  H₂O (l)

For the reaction of a weak acid with a strong base, a similar neutralization occurs, but we must write the molecular formula of the acid rather than simply H⁺, because the dissociation of the acid in water is incomplete. Instead, the acid exists primarily as the neutral molecule. In the reaction of HF with KOH, for example, we write the net ionic equation as

HF(aq) + KOH(aq) = KF(aq) + H₂O(l).

 

3) Oxidation–reduction reactions, or redox reactions, are processes in which one or more electrons are transferred between reaction partners (atoms, molecules, or ions). As a result of this transfer of electrons, charges on atoms in the various reactants change. When metallic magnesium reacts with iodine vapor, for instance, a magnesium atom gives an electron to each of two iodine atoms, forming an ion and two ions. The charge on the magnesium changes from 0 to +2 and the charge on each iodine changes from 0 to -1

 

The condition of a precipitation and a solubility of an electrolyte’s sediment.

If to a given amount of solvent at a particular temperature, a solute is added gradually in increasing amounts, a stage is reached when some of the solute remains undissolved, no matter how long we wait or how vigorously we stir. The solution is then said to be saturated. A solution which remains in contact with undissolved solute is said to be saturated. At saturated stage, the quantity of the solute dissolved is always constant for the given amount of a particular solvent at a definite temperature.

In case the solute is an electrolyte, its ionisation occurs in solution and degree of dissociation depends on the concentra­tion of dissolved electrolyte at a particular temperature.

Applying the law of action to the ionic equilibrium,

[A⁺][B^–]/[AB]

Since the solution is saturated, the concentration of unionised molecules of the electrolyte is constant at a particular temperature, i.e., [AB] = K’= constant.

Hence, [A⁺] [B^–] = K[AB] = KK = K_s (constant)

K_s is termed as the solubility product. It is defined as the product of the concentration of ions in a saturated solution of an electrolyte at a given temperature.

Consider, in general, the electrolyte of the type A_xB_y which is dissociated as:

A_xB_y ↔ xA^y+ + yB^x-

Applying law of mass action,

[Ay+]x[Bx-]y/[A_xB_y] = K

When the solution is saturated,

[A_xB_y] = K’ (constant)

or     [A^y+]^x[B^x-]^y = K [A_xB_y] = KK’ = K_s (constant)

Thus, solubility product is defined as the product of concentrations of the ions raised to a power equal to the number of times the ions occur in the equation representing the dissociation of the electrolyte at a given temperature when the solution is saturated.

Note:  Solubility product is not the ionic product under all conditions but only when the solution is saturated.

Different Expressions for Solubility Products

(i)   Electrolyte of the type AB:

Its ionisation is represented as:

AB ↔  A⁺ + B^–

Thus,     K_s = [A⁺][B^–]

AgCl ↔  Ag⁺ + Cl^–;               K_s = [Ag⁺][Cl^–]

BaSO₄ ↔ Ba²⁺ + SO^-2₄ ;     K_s = [Ba²⁺][SO^-2₄]

(ii)  Electrolyte of the type AB₂:

Its ionisation is represented as:

AB₂ ↔ A²⁺ + 2B^–

Thus,     K_s = [A²⁺][B^–]²

PbCl₂ ↔ Pb²⁺ + 2Cl^–;          K_s = [Pb²⁺][Cl^–]²

CaF₂ ↔ Ca²⁺ + 2F^–;            K_s = [Ca²⁺][F^–]²

(iii)  Electrolyte of the type A₂B:

Its ionisation is represented as:

A₂B ↔  2A²⁺ + B^2-

Thus,     K_s = [A⁺]²[B^2-]

Ag₂CrO₄ ↔ 2Ag⁺ + CrO^-2₄;    K_s = [Ag⁺]²[CrO^-2₄]

H₂S ↔  2H⁺ + S2^–;                    K_s = [H⁺]²[S^2-]

(iv)   Electrolyte of the type A₂B₃:

Its ionisation is represented as:

A₂B₃ ↔ 2A³⁺ + 3B^2-

Thus,     K_s = [A³⁺]²[B^2-]³

As₂S₃ ↔ 2As³⁺ + 3S^2-;       K_s = [As³⁺]²[S^2-]³

Sb₂S₃ ↔ 2Sb³⁺ + 3S2^–;      K_s = [Sb³⁺]²[S^2-]³

(v)   Electrolyte of the type AB₃:

Its ionisation is represented as:

AB₃ ↔ A³⁺ + 3B^–

Thus,     K_s = [A³⁺][B^2-]³

Fe(OH)₃  ↔  Fe³⁺ + 3OH^–;     K_s = [Fe³⁺][OH^–]³

AH₃  ↔  Al³⁺ + 3l^–;      K_s = [Al³⁺][I^–]³

Solubility product of a weak electrolyte:

Let degree of ionization of weak electrolyte A_mB_n be ‘α‘.

A_mB_n ↔ mAⁿ⁺ + nB^m-

t = 0                  s          0          0

t_eq                    s-sα     msα      nsα

K_sp = [Aⁿ⁺]^m[B^m-]ⁿ= [msα ]^m[nsα]ⁿ

K_sp = m^mnⁿ (sα)^m+n

 

Criteria of precipitation of an electrolyte:

A very useful conclusion is derived from the solubility product concept. No precipitation of the electrolyte occurs if the ionic product is less than the solubility product, i.e., the solution has not reached the saturation stage.

Case I:    When K_ip<K_sp, then solution is unsaturated in which more solute can be dissolved.

Case II:   When K_ip = K_sp, then solution is saturated in which no more solute can be dissolved.

Case III:  When K_ip > K_sp, then solution is supersaturated and precipitation takes place.

When the ionic product exceeds the solubility product, the equilibrium shifts towards left hand side, i.e., increasing the concentration of undissociated molecules of the electrolyte. As the solvent can hold a fixed amount of electrolyte at a definite temperature, the excess of the electrolyte is thrown out from the solution as precipitate.

Thus, for the precipitation of an electrolyte, it is neces­sary that the ionic product must exceed its solubility product For example, if equal volumes of 0.02 M AgN0₃ solution and 0.02 M K₂Cr0₄ solution are mixed, the precipita­tion of Ag₂Cr0₄ occurs as the ionic product exceeds the solubility product of Ag₂Cr0₄ which is 2 × 10^-12

In the resulting solution,

[Ag⁺] = 0.02/2 = 0.01 = 1*10^-2 M

and  [CrO^2-₄ ]= 0.02/2 = 0.01 = 1*10^-2 M

Ionic product of Ag₂CrO₄ = [Ag⁺]² [CrO^2-₄] = (1×10^-2)² (1×10^-2) =  1 × 10^-6

1 × 10^-6 is higher than 2 × 10^-12 and thus precipitation of Ag₂CrO₄ occurs.

If the solubility of an ionic salt is extremely small (i.e. a saturated solution contains very few ions), the salt is said to be sparingly soluble. Such salts may include some that we might loosely refer to as being ‘insoluble’, for example AgCl and BaSO₄. Equation shows the equilibrium that is established in aqueous solution when CaF₂ dissolves. Calcium fluoride is a strong electrolyte in water and exists in the aqueous phase as dissociated hydrated ions, Ca²⁺ and F^–.

Since we are dealing with very dilute solutions, we may express K in terms of concentrations

At equilibrium, the ion concentrations remain constant because the rate at which solid dissolves to give Ca²⁺ and F^– exactly equals the rate at which the ions crystallize to form solid CaF₂:

The equilibrium constant is thereby given in terms of the equilibrium concentrations of the dissolved ions and is referred to as the solubility product, or solubility constant, or solubility product constant Ksp:

The Common-Ion Effect

The molar solubility of MgF₂ in pure water at 25°C is 2,6 * 10^-4 M. Thus,

When MgF₂ dissolves in a solution that contains a common ion from another source—say, F^– from NaF—the position of the solubility equilibrium is shifted to the left by the common-ion effect. If F^– is larger than 5,2 *10^-4 M then Mg²⁺ must be correspondingly smaller than 2,6 *10 ^-4 M to maintain the equilibrium expression [Mg ²⁺][ F^–] at a constant value of K_sp = 7,4 * 10^-11 M. A smaller value of [Mg ²⁺] thus means that MgF₂ is less soluble in a sodium fluoride solution than it is in pure water. Similarly, the presence of Mg ²⁺ from another source—say, MgCl₂ —shifts the solubility equilibrium to the left and decreases the solubility of MgF₂.

In general, the solubility of a slightly soluble ionic compound is decreased by the presence of a common ion in the solution

 

5. Solubility of salts. Solubility product. Influence of ions on solubility salts.

 

1  Solubility: the dissolution of salts in water

Drop some ordinary table salt into a glass of water, and watch it “disappear”. We refer to this as dissolution, and we explain it as a process in which the sodium and chlorine units break away from the crystal surface, get surrounded by H₂O molecules, and become hydrated ions.

NaCl(s) → Na⁺(aq)+ Cl^–(aq)

The designation (aq) means “aqueous” and comes from aqua, the Latin word for water. It is used whenever we want to emphasize that the ions are hydrated — that H₂O molecules are attached to them.

But if you keep adding salt, there will come a point at which it no longer seems to dissolve. If this condition persists, we say that the salt has reached its solubility limit, and the solution is saturated in NaCl. The situation is now described by

NaCl(s) Na⁺(aq)+ Cl^–(aq)

in which the solid and its ions are in equilibrium.

Salt solutions that have reached or exceeded their solubility limits (usually 36-39 g per 100 mL of water) are responsible for prominent features of the earth’s geochemistry. They typically form when NaCl leaches from soils into waters that flow into salt lakes in arid regions that have no natural outlets; subsequent evaporation of these brines force the above equilibrium to the left, forming natural salt deposits. These are often admixed with other salts, but in some cases are almost pure NaCl.

Many parts of the world contain buried deposits of NaCl (known as halite) that formed from the evaporation of ancient seas, and which are now mined.

Expressing solubilities

Solubilities are most fundamentally expressed in molar (mol L–1 of solution) or molal (mol kg–1 of water) units. But for practical use in preparing stock solutions, chemistry handbooks usually express solubilities in terms of grams-per-100 ml of water at a given temperature, frequently noting the latter in a superscript. Thus 6.9 20 means 6.9 g of solute will dissolve in 100 mL of water at 20° C.

When quantitative data are lacking, the designations “soluble”, “insoluble”, “slightly soluble”, and “highly soluble” are used. There is no agreed-on standard for these classifications, but a useful guideline might be that shown below.

What determines solubility?

The solubilities of salts in water span a remarkably large range of values, from almost completely insoluble to highly soluble. Moreover, there is no simple way of predicting these values, or even of explaining the trends that are observed for the solubilities of different anions within a given group of the periodic table.

Dissolution of a salt is conceptually understood as a sequence of the two processes depicted above: breakup of the ionic lattice of the solid, followed by attachment of water molecules to the released ions. The first step consumes a large quantity of energy, something that by itself would strongly discourage solubility. But the second step releases a large amount of energy and thus has the opposite effect.

Thus the net energy change depends on the sum of two large energy terms (often approaching 1000 kJ/mol) having opposite signs. Each of these terms will to some extent be influenced by the size, charge, and polarizability of the particular ions involved, and on the lattice structure of the solid. This large number of variables makes it impossible to predict the solubility of a given salt.

Nevertheless, there are some clear trends for how the solubilities of a series of salts of a given anion (such as hydroxides, sulfates, etc.) change with a periodic table group. And of course, there are a number of general solubility rules — for example, that all nitrates are soluble, while most sulfides are insoluble.

Solubility and temperature

Solubility usually increases with temperature – but not always

This is very apparent from the solubility-vs.-temperature plots shown here. (Some of the plots are colored differently in order to make it easier to distinguish them where they crowd together.)

The temperature dependence of any process depends on its entropy change — that is, on the degree to which thermal kinetic energy can spread throughout the system. When a solid dissolves, its component molecules or ions diffuse into the much greater volume of the solution, carrying their thermal energy along with them. So we would normally expect the entropy to increase — something that makes any process take place to a greater extent at a higher temperature.

So why does the solubility of cerium sulfate (green plot) diminish with temperature? Dispersal of the Ce³⁺ and SO₄^2– ions themselves is still associated with an entropy increase, but in this case the entropy of the waterdecreases even more owing to the ordering of the H₂O molecules that attach to the Ce³⁺ ions as they become hydrated. It’s difficult to predict these effects, or explain why they occur in individual cases — but they do happen.

 

Sparingly soluble solids: why they are important

All solids that dissociate into ions exhibit some limit to their solubilities, but those whose saturated solutions exceed about 0.01 mol L^–1 cannot be treated by simple equilibrium constants owing to ion-pair formation that greatly complicates their behavior. For this reason, most of what follows in this lesson is limited to salts that fall into the “sparingly soluble” category.

They drive double-displacement (metathesis) reactions to completion

The importance of sparingly soluble solids arises from the fact that formation of such a product can effectively remove the corresponding ions from the solution, thus driving the reaction to the right.

Consider, for example, what happens when we mix solutions of strontium nitrate and potassium chloride in a 1:2 mole ratio. Although we might represent this process by

Sr(NO₃)₂(aq)+ 2 KCl(aq)→ SrCl(aq)+ 2 KNO₃(aq)(1)

the net ionic equation

Sr²⁺ + 2 NO₃^– + 2 K⁺ + 2 Cl^– → Sr²⁺ + 2 NO₃^– + 2 K⁺ + 2 Cl^–

indicates that no net change at all has taken place!

Of course if the solution were than evaporated to dryness, we would end up with a mixture of the four salts shown in Eq. 1, so in this case we might say that the reaction is half-complete.

Contrast this with what happens if we combine equimolar solutions of barium chloride and sodium sulfate:

BaCl₂(aq)+ Na₂SO₄(aq)→ 2 NaCl(aq)+ BaSO₄(s)(2)

whose net ionic equation is

Ba²⁺ + 2 Cl^– + 2 Na⁺ + SO₄^2– → 2 Na⁺ + 2 Cl^– + BaSO₄(s)

which after canceling out like terms on both sides, becomes simply

Ba²⁺ + SO₄^2– → BaSO₄(s)(3)

Figure. The standard qualitative analysis separation scheme

They form the basis of “wet chemistry” analysis

Because the formation of sparingly soluble solids is “complete” (that is, equilibria such as the one shown above for barium sulfate lie so far to the right), virtually all of one or both of the contributing ions are essentially removed from the solution. Such reactions are said to be quantitative, and they are especially important in analytical chemistry:

Qualitative analysis

This most commonly refers to a procedural scheme, widely encountered in first-year laboratory courses, in which a mixture of cations (usually in the form of their dissolved nitrate salts) is systematically separated and identified on the basis of the solubilities of their various anion salts such as chlorides, carbonates, sulfates, and sulfides.

Although this form of qualitative analysis is no longer employed by modern-day chemists (instrumental techniques such as atomic absorption spectroscopy are much faster and comprehensive), it is still valued as an educational tool for familiarizing students with some of the major classes of inorganic salts, and for developing basic skills relating to observing, organizing, and interpreting results in the laboratory.

Quantitative gravimetric analysis

In this classical form of chemical analysis, an insoluble salt of a cation is prepared by precipitating it by addition of a suitable anion. The precipitate is then collected, dried, and weighed (“gravimetry”) in order to determine the concentration of the cation in the sample.

For example, a gravimetric procedure for determining the quantity of barium in a sample might involve precipitating the metal as the sulfate according to Eq. 3 above, using an excess of sulfate ion to ensure complete removal of the barium.

This method of quantitative analysis became extremely important in the latter half of the nineteenth century, by which time reasonably accurate atomic weights had become available, and sensitive analytical balances had been developed. It was not until the 1960’s that it became largely supplanted by instrumental techniques which were much quicker and accurate.

Gravimetric analysis is still usually included as a part of more advanced laboratory instruction, largely as a means of developing careful laboratory technique.

Solubility products and equilibria

Some salts and similar compounds (such as some metal hydroxides) dissociate completely when they dissolve, but the extent to which they dissolve is so limited that the resulting solutions exhibit only very weak conductivities. In these salts, which otherwise act as strong electrolytes, we can treat the dissolution-dissociation process as a true equilibrium. Although this seems almost trivial now, this discovery, made in 1900 by Walther Nernst who applied the Law of Mass Action to the dissociation scheme of Arrhenius, is considered one of the major steps in the development of our understanding of ionic solutions.

Using silver chromate as an example, we express its dissolution in water as

Ag₂CrO₄(s)→ 2 Ag⁺(aq)+ CrO₄^2–(aq)(4a)

When this process reaches equilibrium (which requires that some solid be present), we can write (leaving out the “(aq)s” for simplicity)

Ag₂CrO₄(s) 2 Ag⁺ + CrO₄^2– (4b)

The equilibrium constant is formally

K = [Ag⁺]² [CrO₄^2–] / [Ag₂CrO₄(s)](5a)

But because solid substances do not normally appear in equilibrium expressions, the equilibrium constant for this process is

[Ag⁺]² [CrO₄^2–] = K_s = 2.76E–12(5b)

Because equilibrium constants of this kind are written as products, the resulting K‘s are commonly known as solubility products, denoted by K_sor sometimes K_sp.

Strictly speaking, concentration units do not appear in equilibrium constant expressions. But many instructors prefer that students show them anyway, especially when using solubility products to calculate concentrations. If this is done, K_s in Eq. 5b would have units of mol³ L^–3.

Equilibrium and non-equilibrium in solubility systems

Ion product vs. solubility product

An expression such as [Ag⁺]² [CrO₄^2–] in known generally as an ion product — this one being the ion product for silver chromate. An ion product can in principle have any positive value, depending on the concentrations of the ions involved. Only in the special case when its value is identical with K_s does it become the solubility product. A solution in which this is the case is said to be saturated. Thus when [Ag⁺]² [CrO₄^2–] = 2.76E-12 at the temperature and pressure at which this value K_s of applies, we say that the “solution is saturated in silver chromate”.

A solution must be saturated to be in equilibrium with the solid. This is anecessary condition for solubility equilibrium, but it is not by itselfsufficient. True chemical equilibrium can only occur when all components are simultaneously present.

Failure to appreciate this is a very common cause of errors in solving solubility problems.

Undersaturated and supersaturated solutions

If the ion product is smaller than the solubility product, the system is not in equilibrium and no solid can be present. Such a solution is said to beundersaturated.

A supersaturated solution is one in which the ion product exceeds the solubility product. A supersaturated solution is not at equilibrium, and no solid can ordinarily be present in such a solution. If some of the solid is added, the excess ions precipitate out and until solubility equilibrium is achieved.

How to know the saturation status of a solution

This is just a simple matter of comparing the ion product Q_s with the solubility product K_s. Recall that

so for the system

Ag₂CrO₄(s)  2 Ag⁺ + CrO₄^2– (4b)

a solution in which Q_s < K_s (i.e., K_s /Q_s > 1) is undersaturated (blue shading) and the no solid will be present. The combinations of [Ag⁺] and [CrO₄^2–] that correspond to a saturated solution (and thus to equilibrium) are limited to those described by the curved line. The pink area to the right of this curve represents a supersaturated solution.

 

Problem Example 1

A sample of groundwater that has percolated through a layer of gypsum (CaSO₄, K_s = 4.9E–5 = 10^–4.3) is found to have be 8.4E–5 M in Ca²⁺ and 7.2E–5 M in SO₄^2–. What is the equilibrium state of this solution with respect to gypsum?

Solution: The ion product Q_s = (8.4E–5)(7.2E-5) = 6.0E–4. This exceeds K_s , so the ratio K_s /Q_s > 1 and the solution is supersaturated in CaSO₄.

 

Determination of pH

Example

 

•         monoprotic acid                 · monoprotic base

   ??? pH   HNO₃    0.001 mol/l                 ??? pH  NaOH  0.001 mol/l

    HNO₃ = H⁺ + NO₃^–                                                 pH = 14 – pOH

    pH = – log /H⁺/                                    pOH = – log /OH^– / = -log 10^-3  = 3

    pH =  -log 10^-3  = 3                              pH = 14 – 3 = 11

                                          

 

•         diprotic acid

    ??? pH   H₂SO₄    0.001 mol/l

    H₂SO₄  =  2H⁺ + SO₄^2-

      pH = – log /H⁺/ = -log /2 x 10^-3/ = 3 – log 2 =2.7

 

Example

•         WHAT IS THE pH  OF WATER SOLUTION  OF 0.01 mol/l HCN (pK_a= 9.14)?

     pH= 1/2 pK_a –1/2 log [c_a]  

     pH = 4.56 – ½ log 10^-2

     pH = 4.56 – (-1 ) = 5.56

•         WHAT IS THE pH OF WATER SOLUTION OF  0.0001 mol/l  NH₄OH (pK_b = 4.76)?

     pH= 14 – 1/2 pK_b + ½ log[c_b]

     pH = 14 – 2.38 + (-2) = 9.62

•         WHAT IS pK_a of acetic acid, if its  K_a = 1.75 x 10^-5 mol/l?

     pK_a = -log K_a

     pK_a  = 5 – log 1.75 = 5 – 0.243 = 4.757

Example

Acids:

•           strong  pH= -log [H₃O⁺ ]

•           weak    pH= 1/2 pK_a – ½ log[c_a]  

Bases: 

•           strong  pH= 14 – log [OH^– ]

•           weak  pH= 14 – 1/2 pK_b + ½ log[c_b]

 

Example

Acid buffers:

pH=pK_a +log(c_salt/c_acid)

Alkaline buffers :

pH=14-[pK_b +log(c_salt/c_base)]

 

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.

 

Prepared by PhD Falfushynska H.