Question

derive henderson hesselbalch equation for acidic buffer​

Answer 1

Answer:

Henderson–Hasselbalch Equation

The Henderson–Hasselbalch equation was developed independently by the American biological chemist L. J. Henderson and the Swedish physiologist K. A. Hasselbalch, for relating the pH to the bicarbonate buffer system of the blood (see below). In its general form, the Henderson–Hasselbalch equation is a useful expression for buffer calculations. It can be derived from the equilibrium constant expression for a dissociation reaction of the general weak acid (HA) in Equation (1.3):

(1.4)

where K is the equilibrium constant at a given temperature. For a defined set of experimental conditions, this equilibrium constant is designated as K′ (K prime) and referred to as an apparent dissociation constant. The higher the value of K′, the greater the number of H+ ions liberated per mole of acid in solution and hence the stronger the acid. K′ is thus a measure of the strength of an acid. Rearrangement of Equation (1.4) yields

(1.5)

Taking logarithms of both sides of Equation (1.5) and multiplying throughout by -1 gives

(1.6)

Substituting pH for −log[H+] and pK′ for - log K′ yields

(1.7)

or

(1.8)

This relationship is represented by the Henderson–Hasselbalch equation.

Since a buffer is intended to give only a small change in pH with added H+ or OH−, the best buffer for a given pH is the one that gives the smallest change. As may be seen from the Henderson–Hasselbalch equation, when the pH of the solution equals the pK′ of the buffer, [conjugate base] = [acid], and the buffer can therefore respond equally to both added acid and added base. It also follows from Equation (1.7) that when the pH of the solution is one pH unit above or below the pK′ value, the solution contains approximately 9% unprotonated or protonated species, respectively. Similarly, if the pH of the solution is two units above or below the pK′ value, the solution contains almost entirely (99%) unprotonated or protonated species, respectively. Table 1-3 provides percent unprotonated species and the corresponding unprotonated/protonated ratios for selected (pH-pK’) values.