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If the ${pK}_{a}$ of acetic acid and ${pK}_{b}$ of dimethylamine are 4.76 and 3.26 respectively. The $pH$ of dimethyl ammonium acetate solution is

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7.75

7.0

6.75

6.0

answer is A.

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Detailed Solution

p H $= 7 + \frac{1}{2} [p K_{a} - p K_{b}]$

Here, $p K_{a} = 4.76, p K_{b} = 3.26$

$= 7 + \frac{1}{2} [4.76 - 3.26]$

$= 7 + \frac{1}{2} [1.50]$

$= 7 + 0.75 = 7.75$

Hence the correct answer (A) 7.75

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