The pH of an aqueous solution of ${C H}_{3} C O O N a$ of concentration $C (M)$ if given by

7 - \frac{1}{2} p K_{a} - \frac{1}{2} log C

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\frac{1}{2} p K_{w} + \frac{1}{2} p K_{b} + \frac{1}{2} log C

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\frac{1}{2} p K_{w} - \frac{1}{2} p K_{b} - \frac{1}{2} log C

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\frac{1}{2} p K_{w} + \frac{1}{2} p K_{a} + \frac{1}{2} log C

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Solution

The correct option is D $\frac{1}{2} p K_{w} + \frac{1}{2} p K_{a} + \frac{1}{2} log C$
${C H}_{3} C O O N a + H_{2} O ⇌ {C H}_{3} C O O H W e a k a c i d + N a O H S t r o n g b a s e$
As sodium acetate is a salt of weak acid and strong base, in hydrolysis of sodium acetate the pH is given by
$p H = \frac{1}{2} p K_{w} + \frac{1}{2} p K_{a} + \frac{1}{2} log C$

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