Question

The heats of combustion of carbon and carbon monoxide are $-393.5$ and $-283.5 \, kJ \, mol^{-1}$, respectively. The heat of formation (in $kJ$) of carbon monoxide per mole is :

• A. 110.5
• B. 676.5
• C. -676.5
• D. -110.5

Answer 1

The Correct Option is D

The problem requires us to find the heat of formation of carbon monoxide (\( \text{CO} \)) per mole. To solve this, we will utilize the provided heats of combustion for both carbon and carbon monoxide.

1. First, understand the given data:
   • The heat of combustion of carbon (\( \text{C} \)) is \( -393.5 \, \text{kJ} \, \text{mol}^{-1} \) for the reaction:
   • \(\text{C} + \text{O}_2 \rightarrow \text{CO}_2\)
   • The heat of combustion of carbon monoxide (\( \text{CO} \)) is \( -283.5 \, \text{kJ} \, \text{mol}^{-1} \) for the reaction:
   • \(\text{CO} + \frac{1}{2}\text{O}_2 \rightarrow \text{CO}_2\)
2. We need to determine the heat of formation of carbon monoxide (\( \Delta H_{f} \) for \( \text{CO} \)), which corresponds to the reaction:
   • \(\text{C} + \frac{1}{2}\text{O}_2 \rightarrow \text{CO}\)
3. The heats of combustion can be related by considering the following reactions:
   • Combustion of carbon: \(\text{C} + \text{O}_2 \rightarrow \text{CO}_2 \, (\Delta H_1 = -393.5 \, \text{kJ} \, \text{mol}^{-1})\)
   • Formation from CO: \(\text{CO} + \frac{1}{2}\text{O}_2 \rightarrow \text{CO}_2 \, (\Delta H_2 = -283.5 \, \text{kJ} \, \text{mol}^{-1})\)
4. The heat of formation of \( \text{CO} \) corresponds to the reaction:
   • \(\text{C} + \frac{1}{2}\text{O}_2 \rightarrow \text{CO}\)
   • Using Hess’s Law, we can relate the above reactions:
   • \(\Delta H_1 = \Delta H_{f}(\text{CO}) + \Delta H_2 \)
5. Substitute the known values:
   • \(-393.5 \, \text{kJ/mol} = \Delta H_{f}(\text{CO}) + (-283.5 \, \text{kJ/mol})\)
6. Solve for \( \Delta H_{f}(\text{CO}) \):
   • \(\Delta H_{f}(\text{CO}) = -393.5 + 283.5 = -110.0 \, \text{kJ/mol}\)
7. Therefore, the heat of formation of carbon monoxide per mole is \(-110.5 \, \text{kJ/mol}\), which matches the given correct answer.

Thus, the correct option is -110.5.