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. Suppose that you have 195 mL of a buffer that is 0.360 M in both benzoic acid (C_6H_5COOH) and its conjugate base (C6H5COO^-). Calculate the maximum volume of 0.110 M HCI that can be added to the buffer before its buffering capacity is lost. 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.

Explanation / Answer

we know that

moles = molarity x volume (L)

so

moles oof C6H5COOOH = 0.36 x 195 x 10-3

moles of C6H5COOOH = 70.2 x 10-3

now

moles of C6H5COO- = 0.36 x 195 x 10-3

moles of C6H5CO0- = 70.2 x 10-3

now

Let y ml of HCl is added

moles of HCl = 0.11 x y x 10-3

moles of HCl added = 0.11y x 10-3

now

the reaction is

C6H5COO- + H+ ---> C6H5COOH

we can see that

moles of C6H5COO- reacted = moles of HCl added = 0.11y x 10-3

moles of C6H5C00- left = (70.2 - 0.11y) x 10-3

now

moles of C6H5COOH formed = 0.11y x 10-3

new moles of C6H5COOH = ( 70.2 + 0.11y) x 10-3

now

[C6H5COO- / C6H5COOH] < 0.1

(70.2 - 0.11y) / (70.2 + 0.11y) < 0.1

70.2 - 0.11y < 7.02 + 0.011y

y >/ 522

So

522 ml of HCl can be added

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