What Is A Buffer Solution?

Buffer solution is a combination of a weak acid and its conjugate base (i.e., its salt) or a weak base and its conjugate acid acts as a buffer. If 1 mL of a 0.1 N HCl solution is added to 100 mL of pure water, the pH is reduced from 7 to 3. If the strong acid is added to a 0.01 M solution containing equal quantities of acetic acid and sodium acetate, the pH is changed only 0.09 pH units because the base Ac⁻ ties up the hydrogen ions according to the reaction.

$$ Ac^-+H_3O^+⇌HAc+H_2O $$

If a strong base, sodium hydroxide, is added to the buffer mixture, acetic acid neutralizes the hydroxyl ions as follows:

$$ HAc+OH^-⇌H_2O+Ac^- $$

The Henderson-Hasselbalch Equation and Buffer Solution

Common Ion Effect and the Buffer Equation for a Weak Acid and Its Salt

The pH of a buffer solution and the change in pH upon the addition of an acid or base can be calculated by use of the buffer equation. This expression is developed by considering the effect of a salt on the ionization of a weak acid when the salt and the acid have an ion in common. For example, when sodium acetate is added to acetic acid, the dissociation constant for the weak acid,

$$ k_a=\frac{[H_3O^+][Ac^-]}{[HAc]}=1.75×10^{-5} $$

is momentarily disturbed because the acetate ion supplied by the salt increases the [Ac⁻]term in thenumerator. To reestablish the constant K_a at 1.75 × 10⁻⁵, the hydrogen ion term in the numerator [H3O⁺] is instantaneously decreased, with a corresponding increase in [HAc]. Therefore, the constant Ka remains unaltered, and the equilibrium is shifted in the direction of the reactants. Consequently, the ionization of acetic acid,

$$ HAc+H_2O⇌Ac^-+H_3O^+ $$

is repressed upon the addition of the common ion, Ac⁻. This is an example of the common ion effect. The pH of the final solution is obtained by rearranging the equilibrium expression for acetic acid:

$$ [H_3O^+]=k_a\frac{[HAc]}{[Ac^-]} $$

If the acid is weak and ionizes only slightly, the expression [HAc] may be considered to represent the total concentration of acid, and it is written simply as [Acid]. In the slightly ionized acidic solution, the acetate concentration [Ac⁻] can be considered as having come entirely from the salt, sodium acetate. Because 1 mole of sodium acetate yields 1 mole of acetateion,[Ac⁻] is equal to the total salt concentration and is replaced by the term [Salt]. Hence, the equation will be written as:

$$ [H_3O^+]=k_a\frac{[Acid]}{[Salt]} $$

This equation can be expressed in logarithmic form, with the signs reversed, as:

$$ -log([H_3O^+])=-log(k_a)-log(\frac{[Acid]}{[Salt]}) $$

from which is obtained an expression, known as the buffer equation or the Henderson–Hasselbalch equation, for a weak acid and its salt:

$$ pH=pk_a+log(\frac{[Salt]}{[Acid]}) $$

The Buffer Equation for a Weak Base and Its Salt

Buffer solutions are not ordinarily prepared from weak bases and their salts because of the volatility and instability of the bases and because of the dependence of their pH on pKw, which is often affected by temperature changes. Pharmaceutical solutions—for example, a solution of ephedrine base and ephedrine hydrochloride—however, often contain combinations of weak bases and their salts.

The buffer equation for solutions of weak bases and the corresponding salts can be derived in a manner analogous to that for the weak acid buffers. Accordingly,

$$ [OH^-]=k_b\frac{[Base]}{[Salt]} $$

and using the relationship [OH⁻]=K_w/[H₃O⁺], the buffer equation is obtained

$$ pH=pk_w-pk_b+log(\frac{[Base]}{[salt]}) $$

The buffer equation is important in the preparation of buffered pharmaceutical solutions; it is satisfactory for calculations within the pH range of 4 to 10.

Reference:

• Sinko, P. (2011). Martin’s Physical Pharmacy and Pharmaceutical Sciences. Baltimore, : Lippincott Williams & Wilkins, a Wolters Kluwer business.