Question

Given 1.00 L of a solution that is 0.200 M HC3H5O2 and 0.250 M KC3H5O2,

a.) What is the buffer capacity of the solution? That is, how many millimoles of strong acid or strong base can be added to the solution before any significant change in pH occur?

b.) Over what pH range will this solution be an effective buffer?

Answer 1

ans)

The reaction occurring is

The K_a of propionic acid (HC₃H₅O₂) is 1.34 X 10^-5.

We know pKa = -log(K_a) = -log(1.34 X 10^-5) = 4.87

Using the Henderson Hasselbalch equation,

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

pH = 4.87 + log(0.250/0.2) = 4.97

Buffer capacity is a measure of the efficiency of the buffer. We need to find the millimoles of strong acid or strong base which can be added to the solution before any significant change in pH occurs. a significant change in pH is defined as a change of 1 unit. When you add a strong acid, the pH drops.

pH_acid = pH - 1 (for a significant change)

pH_acid = 4.97 - 1 = 3.97

Let's say n represents the number of moles of strong acid that must be added in order to get the pH to 3.97.

According to the chemical equation, 1 mole of the conjugate base will react with 1 mole of strong acid to give 1 mole of weak acid.

Since the buffer contains 0.2 moles of weak acid and 0.250 moles of conjugate base, at pH = 3.97 there will be (0.2 + n) moles of

weak acid and (0.250 - n) moles of conjugate base. From the Henderson Hasselbalch equation,

3.97=4.97+log((0.250 - n) /(0.2 + n)

((0.250 -n) /(0.2 + n) = 0.1

0.250 - n = 0.02 + 0.1 n which gives n = 0.209. Since n represents moles,

Number of millimoles of strong acid = 0.209X 10³ = 209 millimoles, we can find the millimoles of the strong base similarly.

Buffers are generally effective over the range pH = pKa 1. Thus, the pH range in which the buffer will be effective is 3.87 - 5.87.