A) \[7-\frac{1}{2}p{{K}_{a}}-\frac{1}{2}\log \,C\]
B) \[\frac{1}{2}p{{K}_{w}}+\frac{1}{2}p{{K}_{b}}+\frac{1}{2}\log \,C\]
C) \[\frac{1}{2}p{{K}_{w}}-\frac{1}{2}p{{K}_{b}}-\frac{1}{2}\log \,C\]
D) \[\frac{1}{2}p{{K}_{w}}+\frac{1}{2}p{{K}_{a}}+\frac{1}{2}\log \,C\]
Correct Answer: D
Solution :
\[C{{H}_{3}}COONa+{{H}_{2}}O\underset{s}{\mathop{C{{H}_{3}}COOH}}\,\]\[+\underset{\text{Strong}\,\text{base}}{\mathop{NaOH}}\,\] As sodium acetate is a salt of weak acid and strong base, in hydrolysis of sodium acetate the pH is given by \[pH=\frac{1}{2}p{{K}_{w}}+\frac{1}{2}p{{K}_{a}}+\frac{1}{2}\log C\]
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