Question

Buffer capacity is a measure of a buffer solution\'s resistance to changes in pH as strong acid or base is added. Suppose that you have 175 mL of a buffer that is 0.240 M in both formic acid (HCOOH) and its conjugate base (HCOO–). Calculate the maximum volume of 0.380 M HCl that can be added to the buffer before its buffering capacity is lost.

Answer 1

The buffer capacity is lost when the pH of 1 L of buffer changes in 1 unit.

pH of the original buffer= pKa of formic acid (just because the concentration of acid and conjugated base is the same).

pKa formic acid= 3.75

So, the buffer capacity will be lost when pH is 2.75. So we have to calculate how much HCl we must add in order to decrease pH to that value.

mol of acid= mol conjugated base= 0.175L x 0.24M= 0.042 mol

total moles= 0.042 +0.042= 0.084 mol

Now, suppose X is the mol of conjugated base at final solution, so, 0.084 -X is mol of acid.

pH= pKa + log[A-]/[HA]

2.75= 3.75 + log[conjugated base]/[acid]

-1=log(X)/(0.084-X)

0.1=(X)/(0.084-X)

X= 7.64x10^-3 mol of conjugated base in final buffer.

This means that the moles reduced from 0.042 mol to 7.64x10^-3 mol. Mol of conjugated base consumed= 0.042 - 7.64x10^-3 = 0.03436 mol

in order to consume 0.03436 mol of conjugated base we need 0.03436 mol of HCl.

volume of HCl= 0.03436 mol/0.38M = 0.09 L= 90mL