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Basic Buffer Action

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Question

Calculate the ratio of pH of a solution containing 1 mol. of $C H_{3} C O O N a + 1 m o l$ of HCl per litre and of other solution containing 1 mol of $C H_{3} C O O N a + 1 m o l$ of $C H_{3} C O O H$ per litre.

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Solution

Case I: pH when 1 mol CH and 1 mol HCI are present
$C H_{3} C O O N a + H C l ⟶ C H_{3} C O O H + N a C l$
Before reaction 1 1 0 0
After reaction 0 0 1 1
$∴ [C H_{3} C O O H] = 1 M$
$∴ [H^{\oplus}] = C \cdot α = C \sqrt{(\frac{K_{a}}{C})} = \sqrt{K_{a} \cdot C} = \sqrt{(K_{a})} (∵ C = 1)$
$∴ p H_{1} = - \frac{1}{2} l o g K_{a}$
Case II: pH when 1 mol $C H_{3} C O O N a$ and 1 mole of $C H_{3} C O O H$ ; a buffer solution
$∴ p H_{2} = - l o g K_{a} + l o g \frac{[S a l t]}{[A c i d]}$

$[\begin{matrix} ∴ [S a l t] = 1 M ∴ [A c i d] = 1 M \end{matrix}]$

$p H_{2} = - l o g K_{a}$
$∴ \frac{p H_{1}}{p H_{2}} = \frac{1}{2} = 0.5$

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