Question

What molar ratio of CH3COOH to CH3COONa should be used in order to prepare an acetic acid / sodium acetate buffer solution with a pH of 4.00 ± 0.02? [Ka(CH3COOH) = 1.8 × 10-5]

a. 5.6
b. 2.3
c. 7.8
d. 4.1

Answer 1

The molar ratio of CH3COOH to CH3COONa required for a buffer with a pH of 4.00 is approximately 5.6, based on the Henderson-Hasselbalch equation and the given Ka value of acetic acid.

Step-by-step explanation:

To find the molar ratio of CH3COOH to CH3COONa for a buffer solution with a pH of 4.00, we use the Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base (CH3COO-) and [HA] is the concentration of the acid (CH3COOH). The pKa is the negative log of the Ka value of acetic acid.

First, calculate the pKa value:

pKa = -log(1.8 × 10^-5) = 4.74

Now, insert the known values into the Henderson-Hasselbalch equation to solve for the ratio of [A-]/[HA]:

4.00 = 4.74 + log([A-]/[HA])
=> log([A-]/[HA]) = 4.00 - 4.74
=> log([A-]/[HA]) = -0.74
=> [A-]/[HA] = 10^-0.74 ≈ 0.183

The ratio that corresponds to a pH of 4.00 is about 0.183, which means for every 1 mol of acetic acid, we need 0.183 mol of sodium acetate. This can also be expressed as approximately 1 part of acetic acid to 5.46 parts of sodium acetate since 1/0.183 ≈ 5.46. The closest answer is option (a), which gives a ratio of 5.6.

Therefore, the molar ratio of CH3COOH to CH3COONa needed to prepare an acetic acid/sodium acetate buffer solution with a pH of 4.00 is about 5.6 (option a).