Consider the following reactions:
I. `C(s) + 1/2 O_(2)(g) rarr CO(g)," "Delta H_(1) = x_(1)`
II. `CO(g) + 1/2 O_(2)(g) rarr CO_(2)(g), " "Delta H_(2) = x_(2)`
III. `C(s) + CO_(2)(g) rarr 2CO(g)," "Delta H_(3) = x_(3)`
Select the correct statements:

Options

A. Heat of formation of `CO_(2)` is `(x_1 + x_2)`
B. Heat of combusion of C is `(x_1 + x_2)`
C. `Delta H_(3) = Delta H_(1) - Delta H_(2)`
D. All of the above are correct statement(s)

Explanation

To solve the problem, we will analyze the three given reactions and their respective enthalpy changes (ΔH). We will determine the heat of formation of CO2 and evaluate the correctness of the statements provided.

### Step-by-Step Solution:

1. **Understanding the Reactions**:
- **Reaction I**: \( C(s) + \frac{1}{2} O_2(g) \rightarrow CO(g) \) with ΔH = \( x_1 \)
- **Reaction II**: \( CO(g) + \frac{1}{2} O_2(g) \rightarrow CO_2(g) \) with ΔH = \( x_2 \)
- **Reaction III**: \( C(s) + CO_2(g) \rightarrow 2CO(g) \) with ΔH = \( x_3 \)

2. **Heat of Formation of CO2**:
- The heat of formation of CO2 from its elements in their standard states is given by the reaction:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \]
- To obtain this reaction, we can add Reaction I and Reaction II:
- From Reaction I: \( C(s) + \frac{1}{2} O_2(g) \rightarrow CO(g) \) (ΔH = \( x_1 \))
- From Reaction II: \( CO(g) + \frac{1}{2} O_2(g) \rightarrow CO_2(g) \) (ΔH = \( x_2 \))
- Adding these two reactions gives:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \]
- The total ΔH for this reaction is:
\[ ΔH = x_1 + x_2 \]
- Therefore, the heat of formation of CO2 is \( x_1 + x_2 \).

3. **Heat of Combustion of Carbon**:
- The heat of combustion of carbon to form CO2 can be represented as:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \]
- The ΔH for this reaction is also \( x_1 + x_2 \), which means the heat of combustion of carbon is equal to the heat of formation of CO2.

4. **Analyzing Reaction III**:
- Reaction III can be rearranged to find the relationship between the enthalpy changes:
\[ C(s) + CO_2(g) \rightarrow 2CO(g) \]
- If we reverse Reaction II, we get:
\[ CO_2(g) \rightarrow CO(g) + \frac{1}{2} O_2(g) \]
- The ΔH for this reversed reaction is \( -x_2 \).
- Now, if we add Reaction I and the reversed Reaction II:
\[ C(s) + \frac{1}{2} O_2(g) + CO_2(g) \rightarrow 2CO(g) \]
- The total ΔH for this combined reaction is:
\[ ΔH = x_1 - x_2 \]
- Thus, we can conclude that:
\[ x_3 = x_1 - x_2 \]

5. **Final Conclusion**:
- The correct statements based on our analysis are:
- The heat of formation of CO2 is \( x_1 + x_2 \).
- The heat of combustion of carbon is also \( x_1 + x_2 \).
- The relationship \( x_3 = x_1 - x_2 \) holds true.

### Summary of Correct Statements:
- All the statements provided in the question are correct.