Question

Consider the given data: $$ \text{(a) HCl(g) + 10H}_2\text{O(l)} \rightarrow \text{HCl.10} \text{ H}_2\text{O} \quad \Delta H = -69.01 \, \text{kJ/mol}^{-1} $$ $$ \text{(b) HCl(g) + 40H}_2\text{O(l)} \rightarrow \text{HCl.40} \text{ H}_2\text{O} \quad \Delta H = -72.79 \, \text{kJ/mol}^{-1} $$ Choose the correct statement:

• A. Dissolution of gas in water is an endothermic process
• B. The heat of solution depends on the amount of solvent
• C. The heat of dilution for the HCl (HCl.10H\(_2\)O to HCl.40H\(_2\)O) is 3.78 kJ/mol
• D. The heat of formation of HCl solution is represented by both (a) and (b)

Hint:

The heat of solution for a substance can depend on the amount of solvent used. A larger amount of solvent typically reduces the heat released during dissolution, as seen in the negative change in \( \Delta H \) between reactions (a) and (b).

Answer 1

The Correct Option is B

In the given data, we have two reactions: 
1. Reaction (a): The dissolution of HCl in 10 moles of water gives a heat of solution of \( \Delta H = -69.01 \, \text{kJ/mol} \). 
2. Reaction (b): The dissolution of HCl in 40 moles of water gives a heat of solution of \( \Delta H = -72.79 \, \text{kJ/mol} \). 
The negative values for both enthalpy changes indicate that both processes are exothermic, meaning heat is released when HCl dissolves in water. This contradicts the statement (1), which suggests that the dissolution is endothermic. 
Step 1: Calculation of the Heat of Dilution
Now, to understand how the heat of solution changes with the amount of solvent, we subtract the enthalpy change of reaction (a) from that of reaction (b): \[ \Delta H = -72.79 \, \text{kJ/mol} - (-69.01 \, \text{kJ/mol}) = -3.78 \, \text{kJ/mol} \] This value represents the difference in heat of solution when the amount of solvent changes from 10 moles of water to 40 moles of water. This shows that the heat of solution depends on the amount of solvent used, confirming that statement (2) is correct. 
Step 2: Why Statement (3) is Incorrect
Statement (3) suggests that the heat of dilution for the HCl (HCl.10H\(_2\)O to HCl.40H\(_2\)O) is 3.78 kJ/mol. 
However, the value we calculated is actually the difference in heat of solution, not the heat of dilution itself. 
Therefore, statement (3) is incorrect.