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Salt of Strong Acid and Weak Base

0.25M solutio...

Question

$0.25 M$ solution of pyridium chloride $C_{5} H_{6} N^{+} {C l}^{-}$ was found to have a $p H$ of $2.699$ . What is $p K_{b}$ for pyridine, $C_{5} H_{5} N$ ?

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Solution

$C_{6} H_{6} N^{+} + H_{2} O ⇌ C_{5} H_{5} N O H + H^{+}$
$p H = \frac{1}{2} [p K_{w} - p K_{b} - log C]$
$2.699 = \frac{1}{2} [14 - p K_{b} + 0.6]$
$2.398 = 14.6 - p K_{b}$
$p K_{b} = 14.6 - 2.398 = 12.2$

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