Explanation:
It is given that pH is equal to 9.2. So, we will calculate the value of [tex]pK_{a}[/tex] as follows.
pH = [tex]pK_{a} + log \frac{[H_{3}O^{+}]}{[\text{solution}]}[/tex]
Putting the given values into the above formula as follows.
pH = [tex]pK_{a} + log \frac{[H_{3}O^{+}]}{[\text{solution}]}[/tex]
[tex]pK_{a} = pH - log \frac{\frac{1}{0.5}}{\frac{1}{10}}[/tex]
= 7.9
[tex]K_{a} = 10^{7.9}[/tex]
= [tex]1.26 \times 10^{-8}[/tex]
Since, the value of [tex]K_{a}[/tex] comes out to be positive. This means that there will occur an increase in the value of [tex]K_{a}[/tex] or [tex]K_{c}[/tex].