Step 1: Understanding the Question:
A substance that "turns blue litmus red" is fundamentally acidic. We must identify which of the given salts undergoes hydrolysis in water to produce an acidic solution (pH < 7).
Step 2: Detailed Explanation:
The acidity or basicity of a salt solution depends entirely on the relative strengths of the parent acid and parent base that combined to form the salt.
Let's evaluate the hydrolysis of each salt option:
(c) $\text{Na_2\text{SO}_4$ (Sodium sulfate):} Formed from Sodium hydroxide ($\text{NaOH}$, a strong base) and Sulfuric acid ($\text{H}_2\text{SO}_4$, a strong acid). Strong acid + strong base salts do not undergo hydrolysis. The solution is neutral (pH = 7).
(d) $\text{NaNO_3$ (Sodium nitrate):} Formed from $\text{NaOH}$ (strong base) and Nitric acid ($\text{HNO}_3$, a strong acid). The solution is neutral (pH = 7).
(b) $\text{Na_2\text{CO}_3$ (Sodium carbonate):} Formed from $\text{NaOH}$ (strong base) and Carbonic acid ($\text{H}_2\text{CO}_3$, a weak acid). The strong base dominates, and the weak conjugate base ($\text{CO}_3^{2-}$) undergoes anionic hydrolysis to release $\text{OH}^-$ ions. The solution is basic (pH > 7), turning red litmus blue.
(a) $\text{CuSO_4$ (Copper(II) sulfate):} Formed from Copper(II) hydroxide ($\text{Cu(OH)}_2$, a weak base) and Sulfuric acid ($\text{H}_2\text{SO}_4$, a strong acid). The strong acid dominates. The weak conjugate acid ($\text{Cu}^{2+}$) undergoes cationic hydrolysis, reacting with water to release $\text{H}^+$ ions into the solution ($\text{Cu}^{2+} + 2\text{H}_2\text{O} \rightleftharpoons \text{Cu(OH)}_2 + 2\text{H}^+$). This excess of $\text{H}^+$ makes the solution explicitly acidic (pH < 7), causing it to turn blue litmus paper red.
Step 3: Final Answer:
$\text{CuSO}_{4}$ turns blue litmus red, matching option (a).