Question

Assuming that the degree of hydrolysis is small, the pH of \[0.1{\text{ M}}\] solution of sodium acetate \[\left( {{K_a} = {\text{ }}1.0{\text{ }} \times {\text{ }}{{10}^{ - 5}}} \right)\] will be:
A. 6.0
B. 8.0
C. 9.0
D. 5.0

Answer 1

Hint:First identify the type of salt such as the salt of weak acid with strong base or salt of strong acid with weak base. Then use the formula for pH of the salt that is relevant to the type of salt you have determined.

Complete answer:
Sodium acetate is the salt of strong base sodium hydroxide and weak acid acetic acid.
In aqueous solution of such salts, the anion (acetate ion) undergoes hydrolysis to form hydroxide ions. Due to this, the solution is basic in nature with pH being more than 7. The hydroxide concentration is greater than hydronium ion concentration.
 \[{\text{C}}{{\text{H}}_{\text{3}}}{\text{CO}}{{\text{O}}^ - }{\text{ + }}{{\text{H}}_2}{\text{O }} \to {\text{ C}}{{\text{H}}_{\text{3}}}{\text{COOH + O}}{{\text{H}}^ - }\]
For acetic acid, the acid dissociation constant \[{K_a} = {\text{ }}1.0{\text{ }} \times {\text{ }}{10^{ - 5}}\]
Write the expression for the pH of the salt of a strong base with weak acid.
\[{\text{pH = }}\dfrac{1}{2}\left[ {{\text{p}}{{\text{K}}_{\text{w}}} - {{\log }_{10}}{{\text{K}}_{\text{a}}}{\text{ }} + {\text{ logC}}} \right]\]
Here, \[{\text{p}}{{\text{K}}_{\text{w}}} = 14\] represents the negative logarithm of the ionic product of water. C represents the concentration of the salt.
Substitute values and calculate the pH of the solution.
\[\Rightarrow {\text{pH = }}\dfrac{1}{2}\left[ {{\text{14}} - {{\log }_{10}}1.0{\text{ }} \times {\text{ }}{{10}^{ - 5}} + {\text{ log0}}{\text{.1}}} \right]\]
\[\Rightarrow {\text{pH = }}\dfrac{1}{2}\left[ {{\text{14}} + 5 - {\text{1}}} \right]\]
\[\Rightarrow {\text{pH = }}\dfrac{1}{2}\left[ {18} \right] \\ \]
\[\Rightarrow {\text{pH = }}9\]
Hence, the pH of \[0.1{\text{ M}}\] solution of sodium acetate will be 9.0.

Hence, the correct option is the option (C) 9.0.

Note:
When a salt is dissolved in the aqueous solution, I may or may not undergo hydrolysis. If it undergoes hydrolysis, then from the products of the hydrolysis, you can determine if the solution is acidic, basic or neutral.