What is the pH of a buffer made by mixing 1.00 L of 0.020 M benzoic acid, HC,H,O,, with 3.00 L of 0.060 M sodium benzoate,

NaC HO₂? K for benzoic acid is 6.3 x 10-5.

1 answer

The Henderson-Hasselbalch equation for a buffer solution is:

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

where pKa is the acid dissociation constant, [conjugate base] is the concentration of the conjugate base, and [weak acid] is the concentration of the weak acid.

First, we need to find the pKa for benzoic acid using the given equilibrium constant (K):

K = [H+][C6H5COO-]/[HC6H5O2]

K = (x)(0.060)/0.020

K = 0.18x

Assuming x << 0.020, we can simplify the equation:

K = (x)(0.060)/0.020 ≈ (x)(0.060)/0.020 - x

0.18x ≈ 0.060x/0.020 - x

0.18x ≈ 3x - x

0.18x ≈ 2x

x ≈ 0.011

Therefore, [H+] = 0.011 M

pH = -log(0.011) = 1.96

Next, we need to calculate the concentrations of benzoic acid and sodium benzoate in the buffer solution:

moles of benzoic acid = 1.00 L x 0.020 mol/L = 0.020 mol

moles of sodium benzoate = 3.00 L x 0.060 mol/L = 0.180 mol

concentration of benzoic acid = 0.020 mol/4.00 L = 0.005 M

concentration of sodium benzoate = 0.180 mol/4.00 L = 0.045 M

Using the Henderson-Hasselbalch equation:

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

pH = 4.80 + log(0.045/0.005)

pH = 4.80 + 0.69

pH = 5.49

Therefore, the pH of the buffer solution is 5.49.