Question

Calculate the pH of a buffer solution made from 0.50 M HC₂H₃O₂ and 0.80 M C₂H₃O₂^- that has an acid dissociation constant for HC₂H₃O₂ of 1.5 x 10^-5

Answer 1

Q170302

Calculate the pH of a buffer solution made from 0.50 M HC₂H₃O₂ and 0.80 M C₂H₃O₂^- that has an acid dissociation constant for HC₂H₃O₂ of 1.5 x 10^-5.

Solution:

HC₂H₃O₂ is acetic acid. It is a weak acid. Its dissociation is given as

HC₂H₃O₂ (aq) + H₂O (l) ⇄  C₂H₃O₂^-  (aq) + H₃O⁺ (aq)

Weak acid conjugate base

HC₂H₃O₂ and C₂H₃O₂^-  will form a buffer solution. We can find the pH of this buffer solution by

using Henderson- Hasselbalch equation.

$pH = pK_a + log [\frac{conjugate\space base }{Weak\space acid }]$

$pH = pK_a + log [\frac{[A-] }{[HA] }]$ ; where $pK_a = -log [K_a]$

K_a is the acid dissociation constant.

$pK_a = -log [1.5 * 10^{-5} ] = 4.824;$

substitute, pK_a = 4.824, [HA] = 0.50M, and [A-] = 0.80M in the Henderson-Hasselbalch equation we have

$pH = 4.824 + log [\frac{0.80M }{0.50M }]$

$= 4.824 + log [{1.6}]$

$= 4.824 + 0.20412$

$= 5.028 ;$

which in the correct significant figure is 5.0.

Hence the pH of a buffer solution made from 0.50 M HC₂H₃O₂ and 0.80 M C₂H₃O₂^-  is 5.0