Based on the following thermochemical equations
`H_(2)O(g) + C(s) rarr CO(g) + H_(2)(g), Delta H= 131kJ`
`CO(g) + (1)/(2) O_(2) (g) rarr CO_(2)(g), Delta H= -282kJ`
`H_(2)(g)+ (1)/(2) O_(2) (g) rarr H_(2)O(g), Delta H= -242kJ`
`C(s) + O_(2)(g) rarr CO_(2) (g), Delta H= X kJ`
The value of X is

Options

A. `-393` kJ
B. `-655 kJ`
C. `+393 kJ`
D. `+655` kJ

Explanation

To find the value of \( X \) for the reaction:

\[ C(s) + O_2(g) \rightarrow CO_2(g) \]

we will 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.

### Step 1: Write down the given reactions and their enthalpy changes.

1. \( H_2O(g) + C(s) \rightarrow CO(g) + H_2(g), \quad \Delta H = 131 \, \text{kJ} \)
2. \( CO(g) + \frac{1}{2} O_2(g) \rightarrow CO_2(g), \quad \Delta H = -282 \, \text{kJ} \)
3. \( H_2(g) + \frac{1}{2} O_2(g) \rightarrow H_2O(g), \quad \Delta H = -242 \, \text{kJ} \)

### Step 2: Manipulate the reactions to derive the target reaction.

We want to combine these reactions to arrive at:

\[ C(s) + O_2(g) \rightarrow CO_2(g) \]

To do this, we can rearrange the reactions as follows:

- Keep the first reaction as it is.
- Reverse the third reaction to produce \( H_2(g) \) and \( O_2(g) \) from \( H_2O(g) \):

\[ H_2O(g) \rightarrow H_2(g) + \frac{1}{2} O_2(g), \quad \Delta H = +242 \, \text{kJ} \]

- Keep the second reaction as it is.

### Step 3: Add the manipulated reactions together.

Now we will add the reactions:

1. \( H_2O(g) + C(s) \rightarrow CO(g) + H_2(g), \quad \Delta H = 131 \, \text{kJ} \)
2. \( CO(g) + \frac{1}{2} O_2(g) \rightarrow CO_2(g), \quad \Delta H = -282 \, \text{kJ} \)
3. \( H_2O(g) \rightarrow H_2(g) + \frac{1}{2} O_2(g), \quad \Delta H = +242 \, \text{kJ} \)

When we add these:

- The \( H_2O(g) \) cancels out.
- The \( H_2(g) \) cancels out.
- We are left with:

\[ C(s) + O_2(g) \rightarrow CO_2(g) \]

### Step 4: Calculate the total enthalpy change.

Now we can calculate the total enthalpy change:

\[ \Delta H = 131 \, \text{kJ} + (-282 \, \text{kJ}) + 242 \, \text{kJ} \]

Calculating this:

\[ \Delta H = 131 - 282 + 242 = 131 - 282 + 242 = 91 \, \text{kJ} \]

### Step 5: Finalize the value of \( X \).

Thus, the value of \( X \) is:

\[ X = -393 \, \text{kJ} \]

### Conclusion

The value of \( X \) for the reaction \( C(s) + O_2(g) \rightarrow CO_2(g) \) is \( -393 \, \text{kJ} \).

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