Buffer solutions (buffers) resist a change in рН when small amounts of acid or base are added. pH of such solutions stays constant after addition of water (dilution) as well. The composition of these systems includes:
1) weak acid and its salt like СН3СООН + СН3СООNa; (acidic buffer);
2) weak base and its salt like NH4OH + NH4Cl; (basic buffer);
3) salts of polyatomic acids like Na2HPO4 + NaH2PO4); (salt buffer);
4) ampholytes like proteins; (ampholyte buffer).
The mechanism of action of any buffer system consists in neutralization of added acids and bases by the components of buffer solution. For example, acetic buffer (СН3СООН + СН3СООNa) binds excess of hydrogen ions (H+), which appear in the system, in accordance with equation:
H+ + CH3COO– ↔ CH3COOH (remember that the main source of acetate-ions is salt as sodium acetate is a strong electrolyte).
Excess of hydroxyl ions (OH–) combines with acetic acid:
OH– + CH3COOH ↔ CH3COO– + H2O (acetic acid is weak, exists mostly in molecular form, not ionic).
Thus, buffer system keeps constant value of pH when the excess of either acidic or basic solutions are added.
In order to calculate the value of рН in buffer mixture, we use the dissociation constant (K):
CH3COOH ↔ H+ + CH3COO–;
K = [H+ ] · [CH3COO–] / [CH3COOH].
Expressing the concentration of hydrogen ions,
[H+] = К · [CH3COOH] / [CH3COO–], or [H+] = К · [acid] / [salt],
and finding logarithm of both left and right parts of this equation, we get the pH:
рН = рК – lg ([CH3COOH] / [CH3COO–]) = рК + lg ([CH3COO–] / [CH3COOH]),
or
рН = рК + lg ([salt] / [acid]).
Some books prefer to use [conjugate base] instead of [salt], but it was shown above that the main source of the conjugate base in the mentioned system is salt, so we consider [conjugate base] = [salt].
This formula is called Henderson–Hasselbalch equation and is used to calculate the value of pH in any buffer system. In case when we need to prepare the buffer and to use analytical concentrations (initial molarity of each component), we use the following formulae:
for the acidic buffer pH = рКa + lg (Csalt · Vsalt / (Cacid · Vacid)); (4.1)
for the basic buffer: pH = 14 – [рКb + lg (Csalt · Vsalt / (Cbase · Vbase))]. (4.2)
Analyzing these equations, we conclude that the pH of the buffer system depends on the ratio of concentrations, and this is the reason why dilution does not have an influence on the pH: increase of volume as a result of the addition of water decreases the concentration of salt (numerator of formulae), but also decreases the concentration of acid (or base) the same number of times (denominator). So we cancel it as if no changes occured.
Buffer capacity
The buffer capacity (B) is the number of equivalents of acid (or base), which must be added to 1 L of the buffer system in order to change pH by 1 unit.
The following formula allows to calculate the value of acidic buffer capacity (Bac):
Bac = Cacid · Vacid / (∆pH · Vbuf ), (4.3)
where Cacid — normality of acid, N; Vacid — the volume of acid, mL; Vbuf — the volume of buffer, mL; ∆pH = |pH1–pH0|, the difference between final and initial values of pH.
To find Bb(basic buffer capacity) we use (Cbase · Vbase) instead of (Cacid · Vacid) in formula (4.3).
Actually, the buffer capacity characterizes the ability of the buffer to keep a constant value of pH. This is a “measure of resistance” to the influence of acidic or basic substances. The greater amount of acid (or base) may be added with no changes in pH — the greater counteraction, the greater buffer capacity.
Buffer capacity depends on the amounts of the weak acid and its salt, or the amounts of the weak base and its salt, that are present in the buffer mixture. The greater concentrations of components, the greater B.
The ratio of concentrations is also very important. A 1:1 ratio of acid to salt is the most efficient for handling the addition of either a base or an acid. If the buffer contains much more acid than the conjugate base (salt), it is less efficient in handling an acid. Alternatively, a buffer with much more of the conjugate base than of acid can not efficiently counteract the addition of a base. For example, the hydrocarbonate buffer (H2CO3 / HCO3–) in blood has a 1:20 ratio of acid to salt. Blood is then more effective in counteracting acids, which are the products of metabolism.
The interval рН = рК ± 1 is called “zone of buffer action”, which correlates with the ratio Сsalt / Сacid from 1/10 to 10/1. The buffer system works effectively in this range.
Вac(blood) = 0,05 M = 50 mM; Вac(plasma) = 0,03 M = 30 mM; Вac(serum) = 0,025 M = 25 mM