Step 1: Understanding the Concept:
Hydrolysis is a reaction with water where water molecules are split into $\text{H}^+$ and $\text{OH}^-$ ions, which react with the ions of a dissolved salt. Salts formed from a strong acid and a strong base do not undergo hydrolysis because their constituent ions are very stable in water and do not accept or donate protons significantly.
Step 2: Detailed Explanation:
Let's analyze the given salts:
(A) Sodium acetate ($\text{CH}_3\text{COONa}$): It is a salt of a weak acid (Acetic acid, $\text{CH}_3\text{COOH}$) and a strong base (Sodium hydroxide, $\text{NaOH}$). The acetate ion undergoes hydrolysis to make the solution basic.
(B) Ammonium chloride ($\text{NH}_4\text{Cl}$): It is a salt of a weak base (Ammonia, $\text{NH}_3$) and a strong acid (Hydrochloric acid, $\text{HCl}$). The ammonium ion undergoes hydrolysis to make the solution acidic.
(C) Sodium carbonate ($\text{Na}_2\text{CO}_3$): It is a salt of a weak acid (Carbonic acid, $\text{H}_2\text{CO}_3$) and a strong base (Sodium hydroxide, $\text{NaOH}$). The carbonate ion undergoes hydrolysis to make the solution basic.
(D) Sodium chloride ($\text{NaCl}$): It is a salt of a strong acid ($\text{HCl}$) and a strong base ($\text{NaOH}$). Neither the $\text{Na}^+$ ion nor the $\text{Cl}^-$ ion reacts with water to form $\text{H}^+$ or $\text{OH}^-$. Thus, it does not undergo hydrolysis, and its aqueous solution remains neutral ($\text{pH} = 7$).
Step 3: Final Answer:
Sodium chloride does not undergo hydrolysis. The correct option is (D).