`C + O_(2) rarr CO_(2),`
`CO + (1)/(2) O_(2) rarr CO_(2),`
Then `Delta_(f) H` for`CO` will be

Options

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

Explanation

To find the heat of formation (\( \Delta_f H \)) for carbon monoxide (CO) in terms of the heats of formation of the given reactions, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reactions**:
- Reaction A: \( C + O_2 \rightarrow CO_2 \)
- Reaction B: \( CO + \frac{1}{2} O_2 \rightarrow CO_2 \)

2. **Write the Target Reaction**:
- We need to find the heat of formation of CO, which can be represented as:
\[ C + \frac{1}{2} O_2 \rightarrow CO \]
- Let’s call this Reaction C.

3. **Relate Reaction C to Reactions A and B**:
- We can express Reaction C in terms of Reactions A and B. To do this, we can manipulate the equations:
- From Reaction A, we have:
\[ C + O_2 \rightarrow CO_2 \quad (X) \]
- From Reaction B, we can reverse it to express CO in terms of CO2:
\[ CO_2 \rightarrow CO + \frac{1}{2} O_2 \quad (-Y) \]

4. **Combine the Reactions**:
- If we add Reaction A and the reversed Reaction B, we can eliminate \( CO_2 \):
\[ (C + O_2 \rightarrow CO_2) + (CO_2 \rightarrow CO + \frac{1}{2} O_2) \]
- This results in:
\[ C + O_2 - CO_2 + CO_2 - \frac{1}{2} O_2 \rightarrow CO \]
- Simplifying gives us:
\[ C + \frac{1}{2} O_2 \rightarrow CO \]

5. **Write the Heat of Formation**:
- The heat of reaction for Reaction C (\( \Delta H_C \)) can be expressed in terms of the heats of reactions A and B:
\[ \Delta H_C = \Delta H_A - \Delta H_B \]
- Therefore, the heat of formation of CO is:
\[ \Delta_f H_{CO} = \Delta H_A - \Delta H_B \]

### Final Answer:
Thus, the heat of formation of CO is given by:
\[ \Delta_f H_{CO} = \Delta H_A - \Delta H_B \]