Question

pK_a of a weak acid (HA) and pK_b of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is :

• A. 7.0
• B. 1.0
• C. 7.2
• D. 6.9

Answer 1

The correct option is D

6.9

Explanation for correct answer:-

Option (D) 6.9

Step 1: Given data

pK_a of a weak acid (HA) is 3.2

pK_b of a weak base (BOH) is 3.4

Step 2: Calculating the pH of the salt

The complete reaction between the acid and base is:

$\underset{\mathrm{Acid}}{\mathrm{HA}}+\underset{\mathrm{Base}}{\mathrm{BOH}}\to \underset{\mathrm{Salt}}{\mathrm{BA}}+\underset{\mathrm{Water}}{{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)}$

Now we know that,

$$\begin{gathered} \mathrm{pH}=\frac{1}{2}\left({\mathrm{pK}}_{\mathrm{w}}+{\mathrm{pK}}_{\mathrm{a}}-{\mathrm{pK}}_{\mathrm{b}}\right) \\ \Rightarrow \mathrm{pH}=\frac{1}{2}\left(14+3.2-3.4\right) \\ \Rightarrow \mathrm{pH}=\frac{1}{2}\left(14-0.2\right) \\ \Rightarrow \mathrm{pH}=\frac{1}{2}\times 13.80 \\ \Rightarrow \mathrm{pH}=6.9 \end{gathered}$$

Therefore, The pH of their salt (AB) solution is option (D) 6.9