Question

The pH of an aqueous solution of $0.1M$ solution of the salt of a weak base $(K_b=1.0\times {10}^{-5})$ and a strong acid is:

• A. $4.5$
• B. $5.0$
• C. $5.5$
• D. $6.0$

Answer 1

Answer: (B)

$5.0$

Given:

$K_w={10}^{-14},K_b={10}^{-5},C=0.1M$

$p{K}_w=-log\left(K_w\right)=-log\left({10}^{-14}\right)=14$

$p{K}_b=-log\left(K_b\right)=-log\left({10}^{-5}\right)=5$

pH of a weak base and strong acid is given by the following formula:

$pH=\frac{1}{2}p{K}_w-\frac{1}{2}p{K}_b-\frac{1}{2}log\left(C\right)\Rightarrow pH=\frac{1}{2}\left(14\right)-\frac{1}{2}\left(5\right)-\frac{1}{2}log\left(0.1\right)\Rightarrow pH=7-2.5+\left(\frac{1}{2}\right)\Rightarrow pH=5$