Given that `C + O_(2) rightarrow CO_(2), ` `Delta H^(@) = - x k J `
`2CO +O_(2) rightarrow 2CO_(2)`, `Delta H^(@) = -y kJ`
What is heat of formation of CO?

Options

A. `(y - 2x)/2`
B. `2x - y`
C. `y - 2x`
D. `(2x - y)/2`

Answer

To find the heat of formation of carbon monoxide (CO), we will use the given reactions and their enthalpy changes. Let's break it down step by step.

### Step 1: Write down the given reactions and their enthalpy changes.
1. The first reaction is:
\[ C + O_2 \rightarrow CO_2, \quad \Delta H = -x \text{ kJ} \]
2. The second reaction is:
\[ 2CO + O_2 \rightarrow 2CO_2, \quad \Delta H = -y \text{ kJ} \]

### Step 2: Reverse the first reaction to find the formation of CO.
To find the formation of CO, we need to reverse the first reaction:
\[ CO_2 \rightarrow C + O_2, \quad \Delta H = +x \text{ kJ} \]

### Step 3: Adjust the second reaction.
The second reaction can be divided by 2 to find the formation of one mole of CO:
\[ CO_2 \rightarrow CO + \frac{1}{2} O_2, \quad \Delta H = \frac{y}{2} \text{ kJ} \]

### Step 4: Combine the reactions.
Now we can combine the reversed first reaction and the adjusted second reaction:
1. From the reversed first reaction:
\[ CO_2 \rightarrow C + O_2 \quad (+x \text{ kJ}) \]
2. From the adjusted second reaction:
\[ CO_2 \rightarrow CO + \frac{1}{2} O_2 \quad \left(\frac{y}{2} \text{ kJ}\right) \]

### Step 5: Write the overall reaction.
Combining these gives us:
\[ C + O_2 \rightarrow CO + \frac{1}{2} O_2 \]
The enthalpy change for this overall reaction will be:
\[ \Delta H = +x + \frac{y}{2} \]

### Step 6: Solve for the heat of formation of CO.
The heat of formation of CO can be expressed as:
\[ \Delta H_f (CO) = \Delta H = +x + \frac{y}{2} \]

### Final Answer:
Thus, the heat of formation of CO is:
\[ \Delta H_f (CO) = \frac{y}{2} - x \text{ kJ} \]