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A buffer solution is prepared in which the concentration of \(\mathrm{NH}_{3}\) is \(0.30 \mathrm{M}\) and the concentration of \(\mathrm{NH}_{4}^{+}\)is \(0.20 \mathrm{M}\). If the equilibrium constant, \(\mathrm{K}_{\mathrm{b}}\) for \(\mathrm{NH}_{3}\) equals \(1.8 \mathrm{x}\) \(10^{-5}\), what is the pH of this solution? ( \(\log 2.7=0.43\) )
(a) \(9.08\)
(b) \(9.43\)
(c) \(11.72\)
(d) \(8.73\)

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The correct option is: (b) \(9.43\)
Explanation:
$$
\begin{aligned}
&{\left[\mathrm{NH}_{3}\right]=0.30 \mathrm{M}, K_{b}=1.8 \times 10^{-5}} \\
&{\left[\mathrm{NH}_{4}^{+}\right]=0.20 \mathrm{M}} \\
&\mathrm{pOH}=\mathrm{p} K_{b}+\log \frac{[\text { salt }]}{[\text { base }]} \\
&=4.74+\log \frac{0.2}{0.3}=4.56 \\
&\mathrm{pH}=(14-4.56)=9.44
\end{aligned}
$$
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