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 given equations, we can follow these steps:

### Step 1: Write down the given equations and their enthalpy changes.
1. **Equation 1**:
\[ C + O_2 \rightarrow CO_2, \quad \Delta H = X \]
2. **Equation 2**:
\[ CO + \frac{1}{2} O_2 \rightarrow CO_2, \quad \Delta H = Y \]

### Step 2: Rearrange the equations to find the formation of CO.
To find the heat of formation of CO, we need to manipulate these equations. We can do this by subtracting Equation 2 from Equation 1.

### Step 3: Subtract Equation 2 from Equation 1.
When we subtract Equation 2 from Equation 1, we get:
\[ (C + O_2) - (CO + \frac{1}{2} O_2) \rightarrow CO_2 - CO_2 \]
This simplifies to:
\[ C - CO + \frac{1}{2} O_2 \rightarrow 0 \]
Rearranging gives us:
\[ C + \frac{1}{2} O_2 \rightarrow CO \]

### Step 4: Calculate the enthalpy change for the new equation.
The enthalpy change for this new equation (which represents the formation of CO) is:
\[ \Delta H = \Delta H_1 - \Delta H_2 = X - Y \]

### Conclusion:
Thus, the heat of formation of CO is:
\[ \Delta H_{f} (CO) = X - Y \]