Calculate the heat of formation of CO using given equations
`C+O_2rarrCO_2,DeltaH=X`
`CO+1/2O_2rarrCO_2,DeltaH=Y`

Options

A. X - Y
B. X + Y
C. Y - 2X
D. 2X - Y

Answer

To calculate the heat of formation of carbon monoxide (CO) using the provided equations, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Reactions:**
- Reaction 1: \( C + O_2 \rightarrow CO_2 \) with \(\Delta H = X\)
- Reaction 2: \( CO + \frac{1}{2} O_2 \rightarrow CO_2 \) with \(\Delta H = Y\)

2. **Reverse Reaction 2:**
- To find the heat of formation of CO, we need to reverse Reaction 2:
- Reaction 3: \( CO_2 \rightarrow CO + \frac{1}{2} O_2 \)
- The enthalpy change for this reaction will be \(\Delta H_3 = -Y\).

3. **Add Reaction 1 and Reaction 3:**
- Now, we add Reaction 1 and Reaction 3:
- \( C + O_2 \rightarrow CO_2 \) (Reaction 1)
- \( CO_2 \rightarrow CO + \frac{1}{2} O_2 \) (Reaction 3)
- When we add these two reactions, we get:
- \( C + \frac{1}{2} O_2 \rightarrow CO \)

4. **Calculate the Overall Enthalpy Change:**
- The overall enthalpy change for this reaction (let's call it Reaction 4) is:
- \(\Delta H_4 = \Delta H_1 + \Delta H_3\)
- Therefore, \(\Delta H_4 = X + (-Y) = X - Y\).

5. **Conclusion:**
- The heat of formation of CO, \(\Delta H_f\), is equal to \(\Delta H_4\):
- \(\Delta H_f = X - Y\).

### Final Answer:
The heat of formation of CO is \(X - Y\).

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