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

The question involves understanding the thermodynamics of dissolution and dilution of hydrochloric acid (HCl) gas in water, represented by two reactions with their enthalpy changes (\(\Delta H\)).

1. The process of dissolving a gas in water is generally exothermic, meaning it releases heat. That is why the enthalpy change (\(\Delta H\)) is negative in both reactions given in the question.
2. The first option, "Dissolution of gas in water is an endothermic process," is incorrect because dissolution is exothermic (negative \(\Delta H\)).
3. The second option, "The heat of solution depends on the amount of solvent," suggests that the amount of heat evolved or absorbed can vary with different amounts of solvent. This statement matches our data, as the heat of solution does change between the two cases (\(10\) and \(40\) \(\text{H}_2\text{O}\)). Thus, this option is correct.
4. The third option involves calculating the heat of dilution from \(\text{HCl.10 H}_2\text{O}\) to \(\text{HCl.40 H}_2\text{O}\). The heat of dilution can be determined by calculating the \(\Delta H\) for the change in the number of water molecules: \[ \Delta H_{\text{dilution}} = \Delta H(\text{HCl.40 H}_2\text{O}) - \Delta H(\text{HCl.10 H}_2\text{O}) \] \[ \Delta H_{\text{dilution}} = -72.79 \, \text{kJ/mol} - (-69.01 \, \text{kJ/mol}) = -3.78 \, \text{kJ/mol} \] Thus, this option is correct as well, since it calculates the heat of dilution correctly.
5. The fourth option claims both expressions represent heat of formation, but generally, they represent the heat of solution rather than formation. Therefore, it does not accurately describe the scenario provided.

Hence, the correct statement is: "The heat of solution depends on the amount of solvent," highlighting the impact of the volume of solvent on the enthalpy change during solution formation.

Answer 2

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.