Question

derive henderson hasselbalch equation for weak acid

Answer 1

Consider a weak acid HX with acid ionization constant Ka. The ionization of the weak acid is given below.

HX:::::: H⁺ + X^-

At equilibrium,

Ka= [H⁺][X^-]/[HX]

[H⁺]= Ka[HX]/[X^-]

Add -log to both sides of the equation

-log[H^-] = -logKa - log[HX]/[X^-]

Recall that

-log[H⁺] = pH

While -logKa= pKa

Therefore, we will have

pH= pKa - log[HX]/[X^-]

pH= pKa + log[X-]/[HX].... 1.

Generally, we can express equation 1 as

pH= pKa + log[salt]/[weak acid]

Or

pH= pKa + log[conjugate base]/[weak acid]

This is the Henderson Hasselbalch equation.