Which of the following equations has/have enthalpy changes equal to `DeltaH_(comb)C`?
I. `C(s)+O_(2)(g)toCO_(2)(g)`
II. `C(s)+(1)/(2)O_(2)(g)toCO(g)`
III. `CO(g)+(1)/(2)O_(2)(g)toCO_(2)(g)`

Options

A. I, II
B. I, II, III
C. I, III
D. I

Explanation

To determine which of the given equations has an enthalpy change equal to the enthalpy of combustion of carbon (ΔH_comb C), we need to analyze each reaction based on the definition of combustion.

### Step-by-Step Solution:

1. **Understand the Definition of Enthalpy of Combustion**:
- The enthalpy of combustion (ΔH_comb) of a substance is defined as the heat energy released when one mole of that substance is burned completely in oxygen to form carbon dioxide (CO₂) and water (H₂O), if applicable.

2. **Analyze Each Reaction**:
- **Reaction I**:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \]
- This reaction involves the complete combustion of solid carbon (C) to form carbon dioxide (CO₂). Therefore, this reaction represents the enthalpy of combustion of carbon.

- **Reaction II**:
\[ C(s) + \frac{1}{2} O_2(g) \rightarrow CO(g) \]
- This reaction involves the formation of carbon monoxide (CO) from carbon and oxygen. This is not a complete combustion reaction, as it does not produce carbon dioxide. Thus, it does not correspond to the enthalpy of combustion of carbon.

- **Reaction III**:
\[ CO(g) + \frac{1}{2} O_2(g) \rightarrow CO_2(g) \]
- This reaction describes the combustion of carbon monoxide to form carbon dioxide. While this is a combustion reaction, it is not the combustion of carbon itself, but rather the combustion of carbon monoxide. Therefore, it does not represent the enthalpy of combustion of carbon.

3. **Conclusion**:
- From the analysis, only Reaction I corresponds to the enthalpy of combustion of carbon. Thus, the answer to the question is that only Reaction I has an enthalpy change equal to ΔH_comb C.

### Final Answer:
- The equation that has an enthalpy change equal to ΔH_comb C is:
- **I. \( C(s) + O_2(g) \rightarrow CO_2(g) \)**