Buffer capacity is a measure of a buffer solution\'s resistance to changes in pH

Question

Buffer capacity is a measure of a buffer solution's resistance to changes in pH as strong acid or base is added. An ideal buffer has equal concentrations of acid and conjugate base for a [base] to [acid] ratio of 1. A buffer has lost its capacity when the ratio of [base] to [acid] is less than 0.10 or greater than 10 Suppose that you have 175 mL of a buffer that is 0.180 M in both benzoic acid (CsHsCOOH) and its conjugate base (C6H5COo). Calculate the maximum volume of 0.340 M HCl that can be added to the buffer before its buffering capacity is lost. Number 42.06 mL

Explanation / Answer

Solution:-

pKa of HF = 3.20

pH = pKa + log [NaF / HF]

     = 3.20 + log [0.180 / 0.180]

pH = 3.20

buffer capacity lost when pH of a buffer changes by 1 unit

2.20 = 3.20 + log [F- / HF]

[F- / HF] = 0.10

moles of acid and base present = 175 x 0.180 = 31.5

31.5 - x / 31.5 + x = 0.10

31.5 - x = 3.15 + 0.1 x

x = 25.77

moles of acid = 25.77

volume of HCl = 25.77 / 0.340

volume of HCl = 75.79 mL

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