First slide

Basic Buffer

Question

The pH 0.005 M codeine ( $C_{18} H_{21} {NO}_{3}$ ) solution is 995. Its ${pK}_{b}$ value is

Difficult

A

8.92
B

5.81
C

3.76
D

4.29

Solution

$C_{18} H_{21} {NO}_{3} + H_{2} O ⇌ Codeine H^{+} + {OH}^{-}$
$pH = 9.95 P^{OH} = 14 - 9.95 = 4.05$
$P^{OH} = - \log [{OH}^{-}]$
$\log [{OH}^{-}] = - 4.05 = \bar{5} . 95$
$[{OH}^{-}] = antilog \bar{5} . 95 = 8.913 \times 10^{- 5}$
$K_{b} = \frac{[Codeine H^{+}] [{OH}^{-}]}{[Codeine]} = \frac{{[{OH}^{-}]}^{2}}{[Codeine]}$
$K_{b} = \frac{{(8.913 \times 10^{- 5})}^{2}}{0.005} = 1.588 \times 10^{- 6}$
${pK}_{b} = - \log [K_{b}] = - \log [1.588 \times 10^{- 6}]$
${pK}_{b} = 6 + (- 0.2009) = 5.7791 \approx 5.80 \approx 5.81$

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