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Introduction

The pH of a s...

Question

The $p H$ of a solution of $N H_{3}$ is $11.43$ . If its concentration is $0.40 M$ , then what is the value of $p K_{b}$ ?

A

3.12

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B

4.74

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C

7.6

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D

10.12

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Solution

The correct option is B 4.74
Since , $p H + p O H = 14 p O H = 14 - p H$
$p O H = 2.57$

The aqueous solution of $N H_{3}$ forms $N H_{4} O H$ which is a weak base. The formula of pOH for a weak base is :
$p O H = \frac{1}{2} p K_{b} - \frac{1}{2} log C o r, 2.57 \times 2 = p K_{b} - log C$
$o r, 5.14 = p K_{b} - log 0.4$
$o r, 5.14 = p K_{b} - (2 log 2 - log 10) p K_{b} = 4.74$

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