Explanation:
It is known that the relation between pH and [tex]pK_{a}[/tex] is as follows.
pH = [tex]pK_{a} + log \frac{[salt]}{[acid]}[/tex]
and, [tex]pK_{a} = -log K_{a}[/tex]
Hence, first we will calculate the value of [tex]pK_{a}[/tex] as follows.
[tex]pK_{a} = -log K_{a}[/tex]
= [tex]-log (1.76 \times 10^{-5}[/tex]
= 4.75
Now, we will calculate the value of pH as follows.
pH = [tex]pK_{a} + log \frac{[\text{sodium acetate}]}{\text{acetic acid}}[/tex]
= [tex]4.75 + log \frac{0.172}{0.818}[/tex]
= 4.75 + (-0.677)
= 4.07
Therefore, we can conclude that the pH of given solution is 4.07.
