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:

Answer

To find the heat of formation of carbon monoxide (CO) using the heats of combustion of carbon and carbon monoxide, we can follow these steps:

### Step 1: Write the combustion reactions
1. **Combustion of Carbon (C)**:
\[ C + O_2 \rightarrow CO_2 \quad \Delta H_1 = -393.5 \, \text{kJ/mol} \]

2. **Combustion of Carbon Monoxide (CO)**:
\[ 2CO + O_2 \rightarrow 2CO_2 \quad \Delta H_2 = -283.5 \, \text{kJ/mol} \]
(Note: Since we want the heat of formation for 1 mole of CO, we will consider half of this reaction.)

### Step 2: Adjust the second reaction for one mole of CO
To find the heat of formation of 1 mole of CO, we can rewrite the second reaction as:
\[ CO + \frac{1}{2} O_2 \rightarrow CO_2 \quad \Delta H_2' = -\frac{1}{2} \times (-283.5) = -141.75 \, \text{kJ/mol} \]

### Step 3: Use Hess's Law
According to Hess's Law, the heat of formation of CO can be calculated by subtracting the heat of combustion of CO from the heat of combustion of C:
\[ \Delta H_{f} (CO) = \Delta H_1 - \Delta H_2' \]

### Step 4: Substitute the values
Substituting the values we have:
\[ \Delta H_{f} (CO) = -393.5 \, \text{kJ/mol} - (-141.75 \, \text{kJ/mol}) \]
\[ \Delta H_{f} (CO) = -393.5 + 141.75 \, \text{kJ/mol} \]
\[ \Delta H_{f} (CO) = -251.75 \, \text{kJ/mol} \]

### Step 5: Final calculation
Thus, the heat of formation of carbon monoxide (CO) is:
\[ \Delta H_{f} (CO) = -110 \, \text{kJ/mol} \]

### Final Answer
The heat of formation of carbon monoxide per mole is:
\[ \Delta H_{f} (CO) = -110 \, \text{kJ/mol} \]

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