The $ ext{p}K_b$ of dimethylamine and $ ext{p}K_a$ of acetic acid are $3.27$ and $4.77$ respectively at $T

Question

The $	ext{p}K_b$ of dimethylamine and $	ext{p}K_a$ of acetic acid are $3.27$ and $4.77$ respectively at $T	ext{ (K)}$. The correct option for the pH of dimethylammonium acetate solution is:

Accepted Answer

Dimethylammonium acetate is a salt formed from a weak acid (acetic acid) and a weak base (dimethylamine). For a salt of a weak acid and a weak base, the pH of its aqueous solution is calculated using the formula:
$	ext{pH} = 7 + \frac{1}{2}(	ext{p}K_a - 	ext{p}K_b)$

Given:
$	ext{p}K_a = 4.77$
$	ext{p}K_b = 3.27$

Substituting the given values into the formula:
$	ext{pH} = 7 + \frac{1}{2}(4.77 - 3.27)$
$	ext{pH} = 7 + \frac{1}{2}(1.50)$
$	ext{pH} = 7 + 0.75 = 7.75$

Therefore, the pH of the dimethylammonium acetate solution is $7.75$ .

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