Protein Chemistry. Structure, Properties, Research Methods - Shendryk, A. N. 2022

Amino Acids
Amino Acids
Electronic Absorption Spectra and Acid-Base Properties of Amino Acids in Solutions — Buffer Systems. Henderson-Hasselbalch Equation

A buffer system is a solution that resists changes in hydrogen ion concentration upon The addition of an acid or a base. Alternatively, it is a solution capable of maintaining a relatively constant pH within certain limits when H⁺ Donors (acids) or H⁺ acceptors (bases) are introduced. Buffering properties are maintained in solutions by the presence of a conjugate acid-base pair. The magnitude of the buffering action is characterized by the buffer capacity ß. It is defined as The amount of a strong base (alkali) that must be added to a solution to change its pH by one unit:

The simplest and most widely used Buffer solutions in laboratory chemical practice typically comprise components of weak mineral or organic acids (an acid and its salt, salts of polybasic acids with varying degrees of substitution, etc.).

Buffer mixtures used for biochemical research must meet the following requirements:

> possess sufficient buffer capacity;

> be of a high degree of purity;

> be highly soluble in Water and unable to cross Introduction/36.html">Biological Membranes;

> be resistant to enzymatic degradation;

> exhibit no toxic or inhibitory effects;

> not absorb light in the visible and UV regions.

MECHANISM OF ACTION of buffer mixtures. pH of acid and base solutions

Let us consider the most general case. An acid (HA), upon dissociation by releasing a proton, converts into its conjugate base (A^-):

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Thus, the pair represents a conjugate acid-base pair.

For monoprotic strong acids (strong electrolytes) in dilute solutions, the hydrogen ion concentration can be assumed equal to the initial analytical concentration of the acid (C_k). Accordingly, the pH of strong acid solutions is expressed as:

рН = -lgC_k

and the pH of strong base solutions as:

рН = 14 - lgC_k

A weak acid dissociates incompletely (partially) in solution. In accordance with the law of mass action, the Equilibrium Constant for this dissociation process is expressed as follows:

The condition of overall electrical neutrality of the solution can be written as follows:

[A^-] + [HO^-] = [H⁺]

In aqueous solutions, the following inequality generally holds:

[HO^-]<<[A^-]

i.e., the overall electrical neutrality condition can be expressed as:

[A^-] ≌ [H⁺]

Considering the above, the expression for K_a takes the form:

Here, [HA] represents, as everywhere above, not the analytical concentration of the acid, but its equilibrium concentration. Naturally, it is lower than the initial concentration C, since the acid has partially dissociated into ions. The amount of acid dissociated into ions is determined as:

[HA] = С_k - [H⁺]

Then, for K_a we obtain:

Solving the last equation for [H⁺], we get:

For weak acids, the following inequality holds true:

С_k >> [H⁺]

and for K_a we can use a simpler and less cumbersome approximation:

K = [H⁺]²/C_k

Hence:

Or:

pH = (pK_a - lgC_k)/2

Accordingly, for weakly dissociating bases:

pH = (14 + pK_a + lgC)/2

where pK_a is the dissociation constant of the conjugate acid of the base.

pH of strong acid solutions in the presence of strong bases

The pH value of such solutions is calculated using roughly the same scheme as above. The only difference is that the electroneutrality condition of the solution must be supplemented with the concentration of the strong base cation (M⁺):

[M⁺] + [H⁺] = [A^-] + [OH^-] = [A^-],

Since in aqueous solutions used in practice the following inequality very often holds:

[A^-] >> [HO^-],

for a strong base, the following approximation is valid:

[M⁺] ≌ [MOH] ≌ C_o

where C_o is the analytical (initial) concentration of the strong base.

Taking into account the accepted assumptions, for K_a we obtain:

In this case, to find the equilibrium concentration of the acid [HA], we subtract from its analytical concentration both the concentration of hydrogen ions formed As a result of acid dissociation and the analytical concentration of the alkali. The latter decreases the amount of acid through the neutralization reaction.

The approximations:

C_k >> [H+] and C_o >> [H⁺]

remain valid. Then

Taking the logarithm, we get:

This equation is called the Henderson-Hasselbalch equation. It implies that pK_a is the pH value at which half of the acid molecules in the solution are in the dissociated state.

Experimentally, the pK_a value can be easily determined by potentiometric titration, the result of which is expressed as the dependence of the medium pH on the number of added equivalents of HO^- ions (see figure below)

Number of equivalents of OH

The first inflection point (at the bottom of the curve) is precisely the point where pH = pK_a. As can be seen from the figure, in the vicinity of this point, the addition of alkali to the solution causes little change in pH, i.e., a buffer effect is observed. Thus, the buffer capacity of the solution reaches its maximum at pH = pK_a.

Let us now consider a specific example of how a buffer system "works". Suppose we have a conjugate acid-base pair in solution: H₂PO₄^-/HPO₄^2-. When H⁺ ions are added to such a solution, they will be bound by the proton acceptor (the conjugate base), HPO₄^2-, leading to a decrease in the ratio: H₂PO₄^-/HPO₄^2-. Conversely, upon the introduction of HO^- ions, this ratio will increase, since H₂PO₄^- will act as a proton donor to bind HO^- into water molecules. If the initial buffer mixture contains the acid and its conjugate base in equimolar amounts, the pH of the solution equals the pK_a for this pair (see the Henderson-Hasselbalch equation). For the pH to change by 1, the H₂PO₄^-/HPO₄^2- ratio must change (decrease or increase) by a factor of 10. Is this a lot or a little?

Suppose we have an equimolar mixture of H₂PO₄^-/HPO₄^2- with a concentration of 0.1 M for both components. If 0.01 M of HO^- ions is introduced into it, lg([HPO₄^2-]/[H₂PO₄^-]) (and, accordingly, the pH of the solution) will increase by approximately 0.05 units. At the same time, the pH of a 0.01 M alkali solution is 12, meaning that dissolving 0.01 M of alkali simply in water would raise the pH of the resulting solution by 5 units (pH = 12 - 7).

The efficiency of a buffer system, i.e., its ability to maintain a stable solution pH, is maximal at equimolar acid-base ratios. It is generally accepted that a solution can function as a buffer in the range: lg([A^-]/[HA]) = ± 1.

In Cells, and in the Organism as a whole, physiological pH values are maintained by Amino Acids, NUCLEOTIDES, Proteins, Nucleic Acids, Lipids, and A number of other Biomolecules capable of existing in conjugate acid-base forms.