Question

A buffer is a mixed solution of a weak acid or base, combined with its conjugate. Note that this can be understood essentially as a common-ion problem: The conjugate is a common ion added to an equilibrium system of a weak acid or base. The addition of the conjugate shifts the equilibrium of the system to relieve the stress of the added concentration of the common ion. In a solution consisting of a weak acid or base, the equilibrium shift also results in a pH shift of the system.

It is the presence of the common ion in the system that results in buffering behavior, because both added H+ or OH− ions can be neutralized.

Part D

What is the pH change of a 0.300 M solution of citric acid (pKa=4.77) if citrate is added to a concentration of 0.145 M with no change in volume?

Express the difference in pH numerically to two decimal places.

Answer 1

The initial pH of the citric acid solution can be calulated using the ICE table

C₆H₈O₇      C₆H₈₇O₇^- + H⁺

initial 0.3 0 0

change -x +x +x

equilibrium 0.3-x x x

Ka = x²/0.3-x   pKa = -log(Ka); Ka = 10^-pka = 10^-4.77 = 1.69 x 10^-5

1.69 x 10^-5 = x²/0.3-x    (x in the denominatore will be small and can be ignored with respect to 0.3)

1.69 x 10^-5 x 0.3 = x²

x² = 5.09 x 10^-6

x = 0.00226 M

This is the H⁺ ion concentration

pH = -log H⁺

pH = -log 0.00226

pH = 2.64 This is the pH of 0.3 M citric acid solution

pH of the buffer containing citric acid and citrate can be calculated using henderson hasselbalch equation

pH = pKa + log base/acid

pH = 4.77 + log 0.145/0.3

pH = 4.77 - 0.316

pH = 4.45

Change in pH is 4.45 - 2.64 = 1.81