Carbon and carbon monoxide burn in oxygen to form carbon dioxide according to the following reactions
`C+O_(2)rarrCO_(2), DeltaH=-394 " kJ mol"^(-1)`
`2CO+O_(2)rarr2CO_(2),DeltaH=-569 " kJ mol"^(-1)`
The heat of formation of 1 mol of carbon monoxide is thus

Options

A. `-219.0 kJ mol^(-1)`
B. `-109.5 kJ mol^(-1)`
C. `-175.0 kJ mol^(-1)`
D. `-87.5 kJ mol^(-1)`

Explanation

To find the heat of formation of 1 mole of carbon monoxide (CO), we can use Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction.

We have the following reactions:

1. \( C + O_2 \rightarrow CO_2 \) with \( \Delta H = -394 \, \text{kJ/mol} \)
2. \( 2CO + O_2 \rightarrow 2CO_2 \) with \( \Delta H = -569 \, \text{kJ/mol} \)

We want to find the heat of formation of carbon monoxide, which can be represented as:

\[ C + \frac{1}{2}O_2 \rightarrow CO \]

### Step 1: Write down the reactions and their enthalpy changes

- For the first reaction:
\[ C + O_2 \rightarrow CO_2 \quad (\Delta H_1 = -394 \, \text{kJ}) \]

- For the second reaction (we will divide it by 2 to find the formation of 1 mole of CO):
\[ 2CO + O_2 \rightarrow 2CO_2 \quad (\Delta H_2 = -569 \, \text{kJ}) \]
Dividing the reaction by 2 gives:
\[ CO + \frac{1}{2}O_2 \rightarrow CO_2 \quad (\Delta H_2' = -284.5 \, \text{kJ}) \]

### Step 2: Reverse the second reaction

To find the heat of formation of CO, we need to reverse the second reaction:
\[ CO_2 \rightarrow CO + \frac{1}{2}O_2 \quad (\Delta H = +284.5 \, \text{kJ}) \]

### Step 3: Combine the reactions

Now we can add the first reaction and the reversed second reaction:
1. \( C + O_2 \rightarrow CO_2 \quad (\Delta H = -394 \, \text{kJ}) \)
2. \( CO_2 \rightarrow CO + \frac{1}{2}O_2 \quad (\Delta H = +284.5 \, \text{kJ}) \)

Adding these reactions:
\[ C + O_2 + CO_2 \rightarrow CO_2 + CO + \frac{1}{2}O_2 \]

This simplifies to:
\[ C + \frac{1}{2}O_2 \rightarrow CO \]

### Step 4: Calculate the total enthalpy change

Now, we can calculate the total enthalpy change:
\[ \Delta H_{\text{formation of CO}} = -394 \, \text{kJ} + 284.5 \, \text{kJ} = -109.5 \, \text{kJ/mol} \]

### Final Answer

The heat of formation of 1 mole of carbon monoxide is:
\[ \Delta H_f (CO) = -109.5 \, \text{kJ/mol} \]

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