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 155 mL of a buffer that is 0.180 M in both formic acid (HCOOH) and its conjugate base (HCOO−) . Calculate the maximum volume of 0.450 M HCl that can be added to the buffer before its buffering capacity is lost.

The maximum buffer capacity that you can have with HCOOH-HCOO⁻ is when the acid and its conjugate base are in the same proportions, that means [HCOOH] = 0,090M and [HCOO⁻] = 0,090M.

In moles: 0,155L×0,090M = 0,01395 moles

Hendersson-Hasselbalch equation for this system is:

pH = 3,74 + log₁₀ [HCOO⁻] /[HCOOH]

The pH of this buffer is equal to pka = 3,74.

A buffer lost is buffering capacity when pH is pka-1 or pka+1. Under addition of HCl the buffer will lost is buffering capacity when pH = 2,74. Using Henderson-Hasselbalch equation:

2,74 = 3,74 + log₁₀ [HCOO⁻] /[HCOOH]

0,1 = [HCOO⁻] /[HCOOH] (1)

The reaction of HCl with HCOO⁻ is:

HCOO⁻ + HCl → HCOOH + Cl⁻

Using this reaction and moles of formic/formiate buffer:

0,1 = [0,01395-x] / [0,01395+x]

Being x the moles of HCl added in the reaction.

0,001395+0,1x = 0,01395 - x

1,1x = 0,012555

x = 0,0114 moles of HCl you need to add.

As the concentration of the HCl solution is 0,450M

0,0114 mol ×[tex]\frac{1L}{0,450mol}[/tex] = 0,0253L ≡ 25,3 mL that are the maximum volume you can add.

I hope it helps!