What will be the enthalpy of combustion of carbon to produce carbon monoxide on the basis of data given below:
`C_((s))+O_(2(g))rarrCO_(2(g))-393.4kJ`
`CO_((g))+(1)/(2)O_(2(g))rarrCO_(2(g))-283.0kJ`

Options

A. `+676.4kJ`
B. `-676.4kJ`
C. `-110.4kJ`
D. `+110.4kJ`

Explanation

To find the enthalpy of combustion of carbon to produce carbon monoxide, we can use Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction.

### Given Reactions:
1. \( C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)} \) with \( \Delta H = -393.4 \, \text{kJ} \)
2. \( CO_{(g)} + \frac{1}{2} O_{2(g)} \rightarrow CO_{2(g)} \) with \( \Delta H = -283.0 \, \text{kJ} \)

### Step-by-Step Solution:

**Step 1: Write the combustion reaction for carbon to produce carbon monoxide.**
The combustion of carbon to produce carbon monoxide can be represented as:
\[ C_{(s)} + \frac{1}{2} O_{2(g)} \rightarrow CO_{(g)} \]

**Step 2: Rearrange the given reactions.**
We need to manipulate the given reactions to derive the desired reaction. We can use the first reaction as it is and reverse the second reaction.

**Step 3: Reverse the second reaction.**
When we reverse the second reaction, we get:
\[ CO_{2(g)} \rightarrow CO_{(g)} + \frac{1}{2} O_{2(g)} \]
The enthalpy change for this reaction will be the opposite of the given value:
\[ \Delta H = +283.0 \, \text{kJ} \]

**Step 4: Add the modified reactions.**
Now we add the first reaction and the reversed second reaction:
1. \( C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)} \) (with \( \Delta H = -393.4 \, \text{kJ} \))
2. \( CO_{2(g)} \rightarrow CO_{(g)} + \frac{1}{2} O_{2(g)} \) (with \( \Delta H = +283.0 \, \text{kJ} \))

Adding these reactions:
\[ C_{(s)} + O_{2(g)} + CO_{2(g)} \rightarrow CO_{(g)} + \frac{1}{2} O_{2(g)} + CO_{2(g)} \]
The \( CO_{2(g)} \) cancels out, giving us:
\[ C_{(s)} + \frac{1}{2} O_{2(g)} \rightarrow CO_{(g)} \]

**Step 5: Calculate the total enthalpy change.**
Now we can calculate the total enthalpy change for the reaction:
\[ \Delta H = -393.4 \, \text{kJ} + 283.0 \, \text{kJ} = -110.4 \, \text{kJ} \]

### Final Answer:
The enthalpy of combustion of carbon to produce carbon monoxide is:
\[ \Delta H = -110.4 \, \text{kJ} \]