The of dimethylamine and of acetic acid are 3.27 and 4.77 respectively at . The correct option for the pH of dimethylammonium acetate solution is [2021]

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Solution

Q.
The $p K_{b}$ of dimethylamine and $p K_{a}$ of acetic acid are 3.27 and 4.77 respectively at $T (K)$ . The correct option for the pH of dimethylammonium acetate solution is [2021]

1 6.25

2 8.50

3 5.50

4 7.75

Ans.
(4)

For a salt of weak acid and weak base

$pH = 7 + \frac{1}{2} (p K_{a} - p K_{b})$

Given, $p K_{a} = 4.77, p K_{b} = 3.27$

$pH = 7 + \frac{1}{2} (4.77 - 3.27) = 7.75$

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