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Salt of Strong Acid and Strong Bases

A buffer solu...

Question

A buffer solution is made by dissolving by $10^{- 2}$ mole ${C H}_{3} C O O H$ and $10^{- 2}$ mole of ${C H}_{3} {C O O}^{⊖} {N a}^{\oplus}$ in 100 ml of water.
(i) What is the pH of solution ?
(ii) If this solution is poured into a container having 10,000 litre of $H_{2} O$ , then what is the new pH?

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Solution

(i) $[C H_{3} C O O H] = \frac{10^{- 2}}{100 \times 10^{- 3}} = \frac{10^{- 2}}{0.1}, [C H_{3} C O O N a] = \frac{10^{- 2}}{0.1}$
$p H = p K_{a} + log \frac{[C H_{3} C O O N a]}{[C H_{3} C O O H]} = p K_{a} + log \frac{10^{- 2} / 0.1}{10^{- 2} / 0.1}$
$p H = p K_{a}$
(ii) Total volume= $V = 10000 + 0.1 = 10000.1$
$[C H_{3} C O O H] = \frac{10^{- 2}}{V}, [C H_{3} C O O N a] = \frac{10^{- 2}}{V}$
$p H = p K_{a} + log \frac{10^{- 2} / V}{10^{- 2} / V} = p K_{a}$ .

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