Acid-base equilibrium in biological systems. Buffer solutions.
A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. It has the property that the pH of the solution changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications. Many life forms thrive only in a relatively small pH range; an example of a buffer solution is blood.
Principles of Buffering
Buffer solutions achieve their resistance to pH change because of the presence of an equilibrium between the acid HA and its conjugate base A–.
HA
H+ + A–
When some strong acid is added to an equilibrium mixture of the weak acid and its conjugate base, the equilibrium is shifted to the left, in accordance with Le Chatelier’s principle. Because of this, the hydrogen ion concentration increases by less than the amount expected for the quantity of strong acid added. Similarly, if strong alkali is added to the mixture the hydrogen ion concentration decreases by less than the amount expected for the quantity of alkali added.
The effect is illustrated by the simulated titration of a weak acid with pKa = 4.7. The relative concentration of undissociated acid is shown in blue and of its conjugate base in red. The pH changes relatively slowly in the buffer region, pH = pKa ± 1, centered at pH = 4.7 where [HA] = [A-], but once the acid is more than 95% deprotonated the pH rises much more rapidly.
Henderson–Hasselbalch equation
In chemistry, the Henderson–Hasselbalch equation describes the derivation of pH as a measure of acidity (using pKa, the acid dissociation constant) in biological and chemical systems. The equation is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions (it is widely used to calculate the isoelectric point of proteins).
Two equivalent forms of the equation are

and

Acidic buffer solutions
An acidic buffer solution is simply one which has a pH less than 7. Acidic buffer solutions are commonly made from a weak acid and one of its salts – often a sodium salt.
Alkaline buffer solutions
An alkaline buffer solution has a pH greater than 7. Alkaline buffer solutions are commonly made from a weak base and one of its salts.
Composition of buffer solutions by Brønsted–Lowry theory:
a) weak acid with their conjugate base
Н2СО3 / НСО3– Bicarbonate buffer solution
СН3СООН / СН3СОО– -Acetate buffer solution
H2PO4–/ HPO42- – Phosphate buffer solution
b) weak base with their conjugate acid
NН3 / NH4+ – ammonia
Protein Buffer Systems
Proteins are the most important and widely operating buffers in the body fluid. The protein buffer system is an integral component of the body’s pH controlling mechanism. Protein buffers are either intracellular or extracellular. Their functionality is mainly intracellular focused and include haemoglobin (Hb). Hb is the protein that functions to transport oxygen within the body. Plasma proteins function as buffers but their amount is small in comparison with the intracellular protein buffers. Protein buffers include basic group, and acidic protein buffer groups, that act as hydrogen ion depletors or donors to maintain the pH level at 7.4. The most well-known protein buffers include
Phosphate Buffer System
The phosphate buffer system is comprised of two ions: hydrogen phosphate ions and dihydrogen phosphate ions. The pH level of the blood drops below 7.4 when the H+ ions in the bloodstream increase. Hydrogen phosphate ions accept all additional H+ ions to reestablish the equilibrium between the hydroxide and hydrogen ions in the blood. When the pH level of the blood increases above 7.4, the dihydrogen phosphate ions release additional hydrogen ions to reinstate the pH level of the blood to its optimal 7.4.
Bicarbonate Buffer System
The bicarbonate buffer system functions to maintain the pH level in the blood of mammals. It also plays a major role in the formation of acid in the stomach, and to neutralize the pH of chyme that enters the small intestine from the stomach. The bicarbonate buffer system manages acid/base imbalances and effectively manages the release of excess carbon dioxide as a bi-product of cellular respiration.
Buffer capacity
Buffer capacity, β, is a quantitative measure of the resistance of a buffer solution to pH change on addition of hydroxide ions. It can be defined as follows.
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where dn is an infinitesimal amount of added base and d(p[H+]) is the resulting infinitesimal change in the logarithm of the hydrogen ion concentration.
ACIDS, BASES, AND pH
Acids and Bases
What are acids and bases? There are three major definitions. We will look at two (the third, the Arrheus definition, is not needed for our study).
Brønsted Definition:
Acids are proton donors.
Bases are proton acceptors.
Note that there is no restriction as to solvent, and many substances besides hydroxide ion can contribute basicity.
Although I will signify protons in water as H+, you should realize that naked protons do not exist in water – they are always hydrated. At a minimum we see the hydronium ion, H3O+. But hydronium ion is in fact also generally though to t be hydrated, so you will sometimes see hydrogen ion represented as H5O2+, H7O3+
o Note that there is no restriction as to solvent, and many substances besides hydroxide ion can contribute basicity.
A consequence of the Brønsted definition all acids and bases are related to one or more conjugate bases or acids. That is, when an acid dissociates to give a proton, it also generates a conjugate base which can react with (accept) a proton in the reverse reaction.
Strong and weak acids and bases: These terms have nothing to do with concentration, rather they refer to the degree of dissociation of an acid or base:
· A Strong acid is 100% dissociated at all concentrations up to 1M. Common strong acids include:
o Nitric acid (HNO3)
o Hydrochloric acid (HCl)
o Sulfuric acid (H2SO4) for the first dissociation only: H2SO4 HSO´4– + H+. The second dissociation is weak, that is it hardly dissociates at 1M.
· A Weak acid is only partly dissociated at 1M. The degree of dissociation varies widely, from a few percent to an infinitesimal degree. Common weak acids include:
o Acetic acid (HC2H3O2 or CH3CO2H, etc.)
o Formic acid (HCO2H)
o Hydrofluoric acid (HF)
o Most acids of biological origin such as amino acids, fatty acids, metabolites, nucleic acids etc.
· A Strong base is 100% dissociated at all concentrations up to 1M. Common strong bases include:
o Sodium hydroxide (NaOH)
o Potassium hydroxide (KOH)
· A Weak base is only partly dissociated at 1M. The degree of dissociation varies widely, from a few percent to an infinitesimal degree. Common weak acids include:
o Ammonia (NH3)
o Aluminum hydroxide (Al(OH)3)
o Magnesium hydroxide (Mg(OH)2)
Let’s look at the equation for the dissociation of a weak organic acid, CH3CO2H (acetic acid, HOAc): CH3CO2H =H+ + CH3CO2–
or, HOAc = H+ + OAc–
The equilibrium expression for this reactions is: Ka = [H+][OAc–] / [HOAc]
and Ka = 1.8 x 10-5
The values of Ka for most of the acids we will be interested are very small, and it is often convenient to express them iegative logrythmic form, analogous to pH, as pKa values: pKa = -logKa = -log (1.8 x 10-5) = 4.76.
pKa is a general measure of acidity, or the tendency of a substance to give up hydrogen ions, and has a tremendously broad range in this sense as seen in the table in your text and below:
Acidity vs. Molecular Structure
So why do some substances tend to dissociate readily, loosing a hydrogen ion, whereas others hold onto their hydrogens very tightly? A number of factors contribute, but we can look at it from the overall perspective of the stability of the resulting conjugate base. Factors then include:
· Electronegativity within a Period: Note the acidity of methane (pKa = 51) vs. ammonia (pKa = 38) vs. water (pKa = 15.7) vs. hydrogen flouride (pKa = 3.5). The more electronegative elements are better able to carry the excess negative charge in the anion form, so form more stable anions and thus stronger acids.
· Anion Size going Down a Row: HF (pKa = 3.5) vs. HCl (pKa = -7) vs. HBr (pKa = -8) vs. HI (pKa = -9). The larger elements are better able to carry the excess negative charge in the anion form because its spread over a greater volume. The proton counter ion also can’t appraoch as closely to the positive nucleus, so is less strongly held. The larger elements thus form more stable anions and thus stronger acids.
· Inductive Effect: CH3CO2H (pKa = 4.76) vs. CF3CO2H (pKa = 0.3). The fluorines, because of their high electronegativities pull electrons away from the carbon, again spreading the negative charge over a greater volume, stablizing the anion and thus making the acid stronger.
Acids & Bases, cont.
Lewis Definition: In this definition:
An acid is an electron pair acceptor – it accepts an electron pair to form a covalent bond.
Note that HCl is a Lewis acid, just as it was a Brønsted acid.
But H+ is also a Lewis acid, whereas it is the species donated in the Brønsted definition.
Note also that a Lewis acid need not have any protons.
A base is then an electron pair donor. A base accepts an electron pair to form a covalent bond.
Many biomolecules have acidic or basic properties. There are several possible definitions of these important classes of ionic compound. For our purposes, however, an acid may be defined as а hydrogen ion donor, and а base as а hydrogen ion acceptor. Strong acids (HCI) and bases (NaOH) ionize almost completely in water:
HCI = Н+ + CI–
NaOH = Na+ + ОН–
Acids and Bases. In 1923, two chemists, J. N. Bronsted in Denmark and J. М. Lowry its England, independently proposed а theory of acid/base behavior that it particularly useful in analytical chemistry. According to the Bronsted-Lowry theory, an acid is а proton donor and а base is а proton acceptor. In order for а species to behave as an acid, а proton acceptor (or base) must be present. The reverse is also true.
Conjugate Acids and Bases. An important feature of the Brltlnsted-Lowry concept is that when an acid gives up а proton, а conjugate base is formed that is capable of accepting a proton. For example, when the species Acid1 gives up а proton, the species Base1 is formed, as shown by the reaction:
Acid1 = Base1 + Proton
Here, Acid1 and Base1 are а conjugate acid/base pair.
Similarly, every base produces its conjugate acid as а result of accepting а proton. That is,
Ваве2 + Proton = Acid2
Acid1 + Base2 = Base1 + Acid2
The extent to which this reaction proceeds depends upon the relative tendencies of the two bases to accept а proton (or of the two acids to Innate а proton).
Many solvents are proton donors or proton acceptors and can thus induce basic or acidic behavior in solutes dissolved in them. For example, in an aqueous solution of ammonia, water donates а proton and thus acts as an acid with respect to the solute: Н2О + NН3 « ОН– + NН+4
In this reaction, ammonia (Base1) reacts with water, which is labeled Acid1, to give the conjugate acid ammonium ion (Acid2) and hydroxide ion, which is the conjugate base (Base2) of the acid water. In contrast, water acts as а proton acceptor, or base, in an aqueous solution of nitrous acid:
НNО2 + Н2О ® NO2– + Н3О+
Acid2 Base1 Conjugate Conjugate
Base2 Acid1
Nitrite ion is the conjugate base of the acid НNО2, Н3О+ is the conjugateacid of the base H2O. Neither NH3 nor HNO2 reacts completely withН2O; therefore, ammonia and nitrous acid are both termed weak electrolytes.
Chemical equilibrium. The reactions used in analytical chemistry are seldom complete. Instead they proceed to а state of chemical equilibrium in which the ratio of concentrations of reactants and products is constant. Equilibrium-constant expressions are algebraic equations that describe the concentration relationships among reactants and products at chemical equilibrium. Such relationships permit calculation of the quantity of analyte that remains unreacted when а steady state has been reached, From these data the error resulting from incompleteness of the reaction upon which an analysis is based can be computed.
The discussion that follows demonstrates the use of equilibrium- constant expressions to gain information about analytical systems in which no more than one or two equilibria are important.
The Equilibrium State. Consider the chemical equilibrium
H3AsO4 + 3I– + 2H+ « H3AsO3 + I3– + H2O
The rate of this reaction and the extent to which it proceeds to the right can be readily judged by observing the orange-red color of the triiodide ion (I3–) since all the other participants in the reaction are colorless. If, for example, 1 mmol of arsenic acid (H3AsO4) is added to 100 ml of а solu1ion containing 3 mmol of potassium iodide, the red color of the triiodide ion appears almost immediately, and within а few seconds the intensity of the color becomes constant, which shows that the triiodide concentration has become constant. А solution of identical color intensity (and hence identical triiodide concentration) can also be produced by adding 1 mmol of arsenous acid (H3AsO3) to 100 ml of а solution containing 1 mmol of triiodide ion. Here, the color intensity is initially greater than in the first solution but rapidly decreases as а result of the reaction:
H3AsO3 + I3– + H2O « H3AsO4 + 3I– + 2H+
Ultimately the color of the two solutions is identical. Many other combinations of the four reactants can be employed to yield solutions that are indistinguishable from the two just described.
The foregoing observations illustrate that the concentration relationship at chemical equilibrium (that is, the position of equilibrium) is independent of the route by which the equilibrium state is achieved. Moreover, а system that is in equilibrium will not spontaneously depart from this condition unless а stress is applied to the system. Such stresses include changes in temperature, in pressure (if one of the reactants or products is а gas), or in total concentration of а reactant or а product. These effects can be predicted qualitatively from the principle of Lе Chatelier, which states that the position of chemical equilibrium always shifts in the direction that tends to relieve the effect of an applied stress. Thus, an increase in temperature alters the concentration relationship in the direction that tends to absorb heat, and an increase in pressure favors those participants that occupy а smaller total volume.
In an analysis, the effect of introducing an additional amount of а раrticipating species to the reaction mixture is particularly important. Here, the resulting stress is relieved by а shift in equilibrium in the direction that partially uses up the added substance. Thus, for the equilibrium we have been considering, the addition of either arsenic acid (H3AsO4) or hydrogen ions causes an increase in color as more triiodide ion and arsenous acid are formed; the addition of arsenous acid has the reverse effect. An equilibrium shift brought about by changing the amount of one of the participating species is called а mass-action effect.
If it were possible to examine the system under discussion at the molecular level, we would find that interactions among the participating species continue unabated even after equilibrium is achieved. The constant concentration ratio of reactants and products results from the equality in the rates of the forward and reverse reactions. In other words, Chemical equilibrium is а dynamic state in which the rates of the forward and reverse reactions are identical.
Equilibrium-Constant Expressions. The influence of concentration (or pressure if the species are gases) on the position of а chemical equilibrium is conveniently described in quantitative terms by means of an equilibrium-constant expression. Such expresions are readily derived from thermodynamic theory. They are great practical importance because they permit the chemist to predict the direction and completeness of а chemical reaction. We must emphasize, however, that an equilibrium-constant expression yields no information concerning the rate at which equilibrium is approached. In fact, we sometimes encounter reactions that have highly favorable equilibrium constants but are of little analytical use because their rates are low. This limitation can often be overcome by the use of а catalyst, which speeds the attainment of equilibrium without changing its position.
Let us consider а generalized equation for а chemical equilibrium:
wW + xX « yY + zZ
where the capital letters represent the formulas of participating chemical species and the lower case italic letters are the small whole numbers required to balance the equation. Thus, the equation states that w mol of W reacts with x mol of Х to form y mol of Y and z mol of Z.
1. Molar concentration if the species is а dissolved solute.
2. Partial pressure in atmospheres if the species is a gas; in fact, we will often replace the square-bracketed term with the symbol pz , which stands for the partial pre atmospheres.
3. Unity if the species is (а) а pure liquid, (b) a pure solid? Or (c) the solvent in а dilute solution.
The constant К (in equation 1) is а temperature-dependent numerical quantity called the equilibrium constant. By convention, the concentrations of the products as the equation is written, are always placed in the numerator and the concentrations of the reactants in the denominator.
Equation.1. is only an approximate form of the termodynamic equilibrium-constant expression. Generally we will use the approximate form of this equation because it is less tedious and time-consuming to use.
Acid and Base Dissociation Constants. Many acids and bases, however, do not dissociate completely. Organic acids, compounds with carboxyl groups, do not completely dissociate in water. They are referred to as weak acids. Organic bases have а small but measurable capacity to combine with hydrogen ions. Many common weak bases contain amino groups.
Note that the unprotonated product of the dissociation reaction is referred to as а conjugate base. For example, acetic acid (СН3СООН) dissociates to form the conjugate base acetate (СНЗCOO–).
Hydrogen ion concentration. The hydrogen ion is one of the most important ions in biological systems. The concentration of this ion affects most cellular and organismal processes. For example, the structure and function of proteins and the rates of most biochemical reactions are strongly affected by hydrogen ion concentration. Additionally, hydrogen ions play а major role in processes such as energy generation and endocytosis. The pH scale has been devised as а convenient method of expressing hydrogen ion concentration. pH has been defined as the negative logarithm of the concentration of hydrogen ions: pH = – log [H+]
On the рН scale, neutrality is defined as а рН of 7 ([H+] is equal to 1 . 10–
Note: It is important to realize that while pH and рКa use similar mathematical expressions, рН (the negative log of the hydrogen ion concentration of а system) may vary; рКa (the negative log of the acid ionization constant) will not vary at constant temperature.
BUFFER SOLUTIONS
By definition, а buffer solution is one that resists changes in рН. Most buffers consist of either а weak acid and its conjugate base or а weak base and its conjugate acid. Chemists use buffers whenever they need to maintain the pH of а solution at а constant and predetermined level. You will find many references to the use of buffers throughout this text.
А buffer solution is formed whenever а weak acid is partially neutralized with а strong base or а weak base is partially neutralized with a strong acid. As а consequence of buffering, titration curves for weak acids and weak bases are significantly different from the titration curves we have thus far encountered.
Because hydrogen ion concentration affects living processes so profoundly, it is not surprising that regulation of pH has proven to be а universal and essential component of living organisms. Hydrogen ion concentration is typically kept withiarrow limits. For example, normal blood pH is 7.4. It may vary between 7.35 and 7.45, despite the fact that blood normally contains many acidic or basic waste products dissolved in it. Certain disease processes result in pH changes that, if not corrected, can be disastrous. Acidosis, а condition that occurs when blood pH falls below 7.35, results from an excessive production of acid in the tissues, loss of base from body fluids, or the failure of the kidneys to excrete acidic metabolites. Acidosis occurs in certain diseases (е.g., diabetes mellitus) and during starvation. If blood pH drops below 7, the central nervous system becomes depressed. This results in coma and eventually death. When blood pH rises above 7.45, alkalosis results. This condition, brought on by prolonged vomiting or by ingestion of excessive amounts of alkaline drugs, causes the central nervous system to become overexcited. Muscles then go into а state of spasm. If left uncorrected, this process results in convulsions and respiratory arrest.
Regulation of hydrogen ion concentration is obviously essential in living organisms. Such control is accomplished in living systems by а variety of substances that act as buffers. Because of their capacity to combine with Н+ ions or to release Н+ under different conditions, buffets help maintain а relatively constant hydrogen ion concentration. The most common buffers consist of weak acids and their conjugate bases. The ability of а “buffered” solution to resist pH changes depends on the establishment of an equilibrium between the buffer’s components. Therefore buffers obey Lе Chatelier’s principle, which states that if а stress is applied to а reaction at equilibrium, the equilibrium will be displaced in such а direction as to relieve that stress. Consider а solution containing acetate buffer, which consists of acetic acid and sodium acetate. The buffer is created by neutralizing acetic acid with the base NaOH: СН3СООН + ОН– = СН3СОО– + Н2O
If hydrogen ions are added to а solution containing acetate buffer, they will combine with the acetate anion to form acetic acid:
Н+ + СН3СОО– =СН3СООН
рH = рКa = 4.76
This reaction removes the added Н+ from solution and maintains the pH near its original value. If more ОН– ions are added, there is а further dissociation of acetic acid to furnish additional Н+ ions for the formation of water.
СН3СООН + ОН– = СН3СОО– + Н2O
Again the Н+ ion concentration remains unchanged.
Properties of Buffer Solutions. In this section we illustrate the resistance of buffers to changes in pH brought about either by dilution or by addition of strong acids or bases.
The Preparation of Buffers. In principle, а buffer solution of any desired pH can be prepared by combining calculated quantities of а suitable conjugate acid/base pair. In practice, however, the pH values of buffers prepared from theoretically generated recipes differ from the predicted values (1) because of uncertainties in the numerical values of п1апу dissociation constants and (2) because of the simplifications used in calculations. Most important is the fact that the ionic strength of а buffer is usually so high that good values for the activity coefficients of the ions in the solution cannot be obtained from the Debye-Huckel relationship. Because of these uncertainties, we prepare buffers by making up а solution of approximately the desired pH and then adjust by adding acid or conjugate base until the required рН is indicated by а рН meter.
BUFFERING CAPACITY
Solution, which containing а conjugate acid/base pair possesses remarkable resistance to changes in рН. The ability of а buffer to prevent а significant change in pH is directly related to the total concentration of the buffering species as well as to their concentration ratio.
The buffer capacity of а solution is the number of moles of а strong acid or а strong base that causes
PHYSIOLOGICAL BUFFERS
The three most important buffers in the body are the bicarbonate buffer, the phosphate buffer, and the protein buffer. Each type has attributes that make it especially useful.
Bicarbonate Buffer.
Carbon Dioxide Transport
Carbon dioxide (CO2) combines with water forming carbonic acid, which dissociates into a hydrogen ion (H+) and a bicarbonate ions
CO2 + H2O ↔ H2CO3 ↔ H+ + HCO3−
95% of the CO2 generated in the tissues is carried in the red blood cells:
· The rest is converted — following the equation above — by the enzyme carbonic anhydrase into
o bicarbonate ions that diffuse back out into the plasma and
o hydrogen ions (H+) that bind to the protein portion of the hemoglobin (thus having no effect on pH).
Since the concentration of H2CO3 is very low in blood, the above equations may be simplified to СО2 + Н2О = Н+ + НСО3–
Recall that buffering capacity is greatest at or near the рКa of the acid-conjugate base pair. Bicarbonate buffer is clearly unusual in that its рКa is 6.1. It would appear at first glance that bicarbonate buffer is ill-suited to fulfill its role as an important buffering system of blood. The ratio of HCO3– to СО2 required to maintain а рН of 7.4 is approximately 20 to
Bicarbonate concentration is regulated by the kidneys. If bicarbonate concentration ([НСО3–]) decreases, the kidneys remove Н+ from the blood. This removal triggers а shift in the equilibrium to the right, thus increasing [HCO3–]. Carbonic acid lost in this process is quickly replenished by the hydration of СО2, а waste product of cellular metabolism. When excess amounts of HCO3– are produced, they are excreted by the kidney. As acid is added to the body’s bicarbonate system, [НСОЗ–] decreases and CO2 is formed. Since the excess CO2 is exhaled, the ratio of HCO3– to CO2 remains essentially unchanged.
Phosphate Buffer. Phosphate buffer consists of the weak acid-conjugate base pair H2PO4– and НРО4-2:
Н2РO4– = Н+ + HPO4-2
dihydrogen phosphate hydrogen phosphate
With а рКa of 7.2 it would appear that phosphate buffer is an excellent choice for buffering the blood. Although the blood рН of 7.4 is well within this buffer system’s capability, the concentrations of H2PO4– and HPO42- in blood are too low to have а major effect. Instead, the phosphate system is an important buffer in intracellular fluids. The phosphate concentration in intracellular fluid is approximately 75 mEq/L, while phosphate concentration in extracellular fluids such as blood is about 4 mEq/L. (An equivalent is defined as the mass of acid or base that can furnish or accept one mole of Н+ ions.
Protein Buffer. Proteins are а significant source of buffering capacity. Composed of amino acids linked together by peptide bonds, proteins contain ionizable groups that can donate or accept protons. Several of these groups have рКa values that are close to 7.4. Since protein molecules are present in significant concentration in living organisms, they are powerful buffers. For example, the oxygen-carrying protein hemoglobin is the most abundant biomolecule in red blood cells. Because of its structure and high cellular concentration, hemoglobin plays а major role in maintaining blood pH. Also present in high concentrations and contributing to the buffering capacity of the blood are the serum albumins and other proteins.