Number of Basic Aqueous Solutions Among Given Salt Compounds

To determine the total number of compounds whose aqueous solution turns red litmus paper blue, we need to identify the compounds that form basic (alkaline) aqueous solutions ($\text{pH} > 7$).

Red litmus paper turns blue in basic medium, which typically occurs for salts formed from a strong base and a weak acid, as they undergo anionic hydrolysis to release hydroxide ions ($\text{OH}^-$):

$\text{A}^- + \text{H}_2\text{O} \rightleftharpoons \text{HA} + \text{OH}^-$

Let us analyze each of the given salts in aqueous solution:

1. $\text{KCN}$:

   • Formed from a strong base ($\text{KOH}$) and a weak acid ($\text{HCN}$).
   • Undergoes anionic hydrolysis ($\text{CN}^- + \text{H}_2\text{O} \rightleftharpoons \text{HCN} + \text{OH}^-$).
   • Solution is basic ($\text{pH} > 7$). $\rightarrow$ Turns red litmus blue

2. $\text{K}_2\text{SO}_4$:

   • Formed from a strong base ($\text{KOH}$) and a strong acid ($\text{H}_2\text{SO}_4$).
   • Neither ion undergoes hydrolysis significantly.
   • Solution is neutral ($\text{pH} = 7$). $\rightarrow$ No change

3. $(\text{NH}_4)_2\text{C}_2\text{O}_4$:

   • Formed from a weak base ($\text{NH}_4\text{OH}$) and a weak acid ($\text{H}_2\text{C}_2\text{O}_4$).
   • Since $K_a \text{ of oxalic acid} > K_b \text{ of ammonium hydroxide}$, the solution is slightly acidic ($\text{pH} < 7$). $\rightarrow$ No change

4. $\text{NaCl}$:

   • Formed from a strong base ($\text{NaOH}$) and a strong acid ($\text{HCl}$).
   • Solution is neutral ($\text{pH} = 7$). $\rightarrow$ No change

5. $\text{Zn(NO}_3)_2$:

   • Formed from a weak base ($\text{Zn(OH)}_2$) and a strong acid ($\text{HNO}_3$).
   • Undergoes cationic hydrolysis ($\text{Zn}^{2+} + 2\text{H}_2\text{O} \rightleftharpoons \text{Zn(OH)}_2 + 2\text{H}^+$).
   • Solution is acidic ($\text{pH} < 7$). $\rightarrow$ No change

6. $\text{FeCl}_3$:

   • Formed from a weak base ($\text{Fe(OH)}_3$) and a strong acid ($\text{HCl}$).
   • Undergoes cationic hydrolysis ($\text{Fe}^{3+} + 3\text{H}_2\text{O} \rightleftharpoons \text{Fe(OH)}_3 + 3\text{H}^+$).
   • Solution is acidic ($\text{pH} < 7$). $\rightarrow$ No change

7. $\text{K}_2\text{CO}_3$:

   • Formed from a strong base ($\text{KOH}$) and a weak acid ($\text{H}_2\text{CO}_3$).
   • Undergoes anionic hydrolysis ($\text{CO}_3^{2-} + \text{H}_2\text{O} \rightleftharpoons \text{HCO}_3^- + \text{OH}^-$).
   • Solution is basic ($\text{pH} > 7$). $\rightarrow$ Turns red litmus blue

8. $\text{NH}_4\text{NO}_3$:

   • Formed from a weak base ($\text{NH}_4\text{OH}$) and a strong acid ($\text{HNO}_3$).
   • Undergoes cationic hydrolysis ($\text{NH}_4^+ + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4\text{OH} + \text{H}^+$).
   • Solution is acidic ($\text{pH} < 7$). $\rightarrow$ No change

9. $\text{LiCN}$:

   • Formed from a strong base ($\text{LiOH}$) and a weak acid ($\text{HCN}$).
   • Undergoes anionic hydrolysis ($\text{CN}^- + \text{H}_2\text{O} \rightleftharpoons \text{HCN} + \text{OH}^-$).
   • Solution is basic ($\text{pH} > 7$). $\rightarrow$ Turns red litmus blue

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Conclusion:

The basic compounds are $\text{KCN}$, $\text{K}_2\text{CO}_3$, and $\text{LiCN}$.

Thus, the total number of compounds whose aqueous solution turns red litmus paper blue is $3$.