The heats of combustion of carbon and carbon monoxide are `-393.5and-283.5kJmol^(-1)` respectively. The heat of formation (in kJ) of carbon monoxide per mole is:

Options

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

Answer

To find the heat of formation of carbon monoxide (CO) using the heats of combustion of carbon and carbon monoxide, we can apply Hess's Law, which states that the total enthalpy change of a reaction is independent of the route taken.

### Step-by-Step Solution:

1. **Write the combustion reactions**:
- The combustion of carbon (C) can be represented as:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \quad \Delta H_1 = -393.5 \, \text{kJ/mol} \]
- The combustion of carbon monoxide (CO) can be represented as:
\[ 2CO(g) + O_2(g) \rightarrow 2CO_2(g) \quad \Delta H_2 = -283.5 \, \text{kJ/mol} \]

2. **Identify the heat of formation reaction**:
- The formation of carbon monoxide from its elements can be represented as:
\[ C(s) + \frac{1}{2}O_2(g) \rightarrow CO(g) \quad \Delta H_f \]

3. **Relate the heats of combustion to the heat of formation**:
- According to Hess's Law, we can express the heat of formation of carbon monoxide in terms of the heats of combustion:
\[ \Delta H_f = \Delta H_1 - \Delta H_2 \]

4. **Substitute the values**:
- Substitute the given heats of combustion into the equation:
\[ \Delta H_f = (-393.5 \, \text{kJ/mol}) - (-283.5 \, \text{kJ/mol}) \]

5. **Calculate the heat of formation**:
- Perform the calculation:
\[ \Delta H_f = -393.5 + 283.5 = -110 \, \text{kJ/mol} \]

### Final Answer:
The heat of formation of carbon monoxide (CO) is \(-110 \, \text{kJ/mol}\).

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