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

Explanation

To find the enthalpy 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 the Given Reactions
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: Identify the Target Reaction
We want to find the enthalpy of formation for carbon monoxide, which can be represented as:
\[ C + \frac{1}{2}O_2 \rightarrow CO \]

### Step 3: Manipulate the Given Reactions
To derive the enthalpy change for the formation of CO, we can manipulate the two given reactions. We will need to reverse the second reaction and adjust it to fit our target reaction.

1. Reverse the second reaction:
\[ 2CO_2 \rightarrow 2CO + O_2, \quad \Delta H = +y \text{ kJ} \]

2. Now, we need to divide this reversed reaction by 2 to get the formation of 1 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 first reaction with the modified second reaction:
1. From the first reaction:
\[ C + O_2 \rightarrow CO_2, \quad \Delta H = -x \text{ kJ} \]
2. From the modified second reaction:
\[ CO_2 \rightarrow CO + \frac{1}{2}O_2, \quad \Delta H = \frac{y}{2} \text{ kJ} \]

### Step 5: Add the Enthalpy Changes
Now we can add the enthalpy changes of these two reactions:
\[ \Delta H_{formation} = (-x) + \left(\frac{y}{2}\right) \]
This simplifies to:
\[ \Delta H_{formation} = -x + \frac{y}{2} \]

### Step 6: Final Expression
We can express this as:
\[ \Delta H_{formation} = \frac{y - 2x}{2} \]

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

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