Consider the following reactions:
`C(s)+O_(2)(g)toCO_(2)(g)+x " kJ"`
`CO(g)+(1)/(2)O_(2)(g)toCO_(2)(g)+y" kJ"`
The heat formation of CO(g) is :

Options

A. `-(x+y)" kJ"//mol`
B. (x-y) kJ`//`mol
C. (y-x) kJ`//` mol
D. None of these

Answer

To find the heat of formation of carbon monoxide (CO), we will use the given reactions and apply Hess's law. Let's break down the solution step by step.

### Step 1: Write the Given Reactions
We have two reactions:
1. \( C(s) + O_2(g) \rightarrow CO_2(g) \quad \Delta H_1 = -X \, \text{kJ} \)
2. \( CO(g) + \frac{1}{2} O_2(g) \rightarrow CO_2(g) \quad \Delta H_2 = -Y \, \text{kJ} \)

### Step 2: Identify the Target Reaction
We need to find the heat of formation of carbon monoxide (CO) from its elements:
\[ C(s) + \frac{1}{2} O_2(g) \rightarrow CO(g) \]

### Step 3: Manipulate the Given Reactions
To derive the target reaction from the given reactions, we will manipulate them:
- From the first reaction, we have \( C(s) + O_2(g) \rightarrow CO_2(g) \) with a heat change of \(-X\).
- From the second reaction, we have \( CO(g) + \frac{1}{2} O_2(g) \rightarrow CO_2(g) \) with a heat change of \(-Y\).

### Step 4: Subtract the Second Reaction from the First
To obtain the desired reaction, we will subtract the second reaction from the first:
1. Write the first reaction as is:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \quad \Delta H = -X \]
2. Reverse the second reaction:
\[ CO_2(g) \rightarrow CO(g) + \frac{1}{2} O_2(g) \quad \Delta H = +Y \]

### Step 5: Combine the Reactions
Now, we combine the two reactions:
- From the first reaction, we have \( C(s) + O_2(g) \rightarrow CO_2(g) \).
- From the reversed second reaction, we have \( CO_2(g) \rightarrow CO(g) + \frac{1}{2} O_2(g) \).

When we combine these:
\[ C(s) + O_2(g) + CO_2(g) \rightarrow CO_2(g) + CO(g) + \frac{1}{2} O_2(g) \]

### Step 6: Cancel Out Common Terms
The \( CO_2(g) \) cancels out:
\[ C(s) + \frac{1}{2} O_2(g) \rightarrow CO(g) \]

### Step 7: Calculate the Heat of Formation
The heat change for the overall reaction is:
\[ \Delta H = (-X) + Y = Y - X \]

### Conclusion
Thus, the heat of formation of carbon monoxide (CO) is:
\[ \Delta H_f = Y - X \, \text{kJ} \]

### Final Answer
The heat of formation of CO(g) is \( Y - X \, \text{kJ} \).

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