Given that `C+O_(2)rarrCO_(2),DeltaH^(@)=-xKJ` and `2CO+O_(2)rarr2CO_(2),DeltaH^(@)=-yKJ` The enthalpy of formation of carbon monoxide will be

Options

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

Explanation

To find the enthalpy of formation of carbon monoxide (CO) from the given reactions, we will use Hess's Law. Let's denote the reactions and their enthalpy changes as follows:

1. Reaction 1:
\[ C + O_2 \rightarrow CO_2 \quad \Delta H_1 = -x \text{ kJ} \]

2. Reaction 2:
\[ 2CO + O_2 \rightarrow 2CO_2 \quad \Delta H_2 = -y \text{ kJ} \]

We need to find the enthalpy of formation of carbon monoxide:
\[ C + \frac{1}{2}O_2 \rightarrow CO \quad \Delta H_3 = ? \]

### Step 1: Manipulate the Reactions
To derive the enthalpy of formation of CO, we can manipulate the first two reactions.

- From Reaction 2, we can divide the entire equation by 2:
\[ CO + \frac{1}{2}O_2 \rightarrow CO_2 \quad \Delta H_2' = \frac{-y}{2} \text{ kJ} \]

### Step 2: Add the Reactions
Now we can add Reaction 1 and the modified Reaction 2:

1. Reaction 1:
\[ C + O_2 \rightarrow CO_2 \quad \Delta H_1 = -x \]

2. Modified Reaction 2:
\[ CO + \frac{1}{2}O_2 \rightarrow CO_2 \quad \Delta H_2' = \frac{-y}{2} \]

Now, we will subtract the modified Reaction 2 from Reaction 1:

\[ C + O_2 - (CO + \frac{1}{2}O_2 \rightarrow CO_2) \]

This gives us:
\[ C + O_2 - CO - \frac{1}{2}O_2 \rightarrow CO_2 - CO_2 \]

### Step 3: Simplify the Reaction
This simplifies to:
\[ C + \frac{1}{2}O_2 \rightarrow CO \]

### Step 4: Calculate the Enthalpy Change
Now we can calculate the enthalpy change for this reaction:
\[ \Delta H_3 = \Delta H_1 + \Delta H_2' = -x + \left(\frac{-y}{2}\right) \]
\[ \Delta H_3 = -x + \frac{y}{2} \]

### Step 5: Rearranging the Equation
To express \(\Delta H_3\) in a standard form, we can rearrange:
\[ \Delta H_3 = \frac{y - 2x}{2} \]

Thus, the enthalpy of formation of carbon monoxide is:
\[ \Delta H_f (CO) = \frac{y - 2x}{2} \]

### Conclusion
The enthalpy of formation of carbon monoxide is:
\[ \Delta H_f (CO) = \frac{y - 2x}{2} \]