The standard enthalpies of formation of `CO_(2)(g)` and HCOOH (l) are `-393.7 kJ"mol"^(-1)` and `-409.2 kJ"mol"^(-1)` respectively. Which of the following statements are correct?

Options

A. `-393.7 kJ "mol"^(-1)` is the enthalpy change for the reaction, `C(s) + O_(2)(g) to CO_(2)(g)`
B. The enthalpy change for the reaction, `CO_(2)(g) + H_(2)(g) to HCOOH(l)`, would be `-15.5 kJ"mol"^(-1)`.
C. The enthalpy change for the reaction, `H_(2)(g) + CO_(2)(g) to H_(2)O(l) + CO(g)`, is `-409.2 kJ"mol"^(-1)`
D. The final temperature achieved is 291.8 K

Explanation

To solve the problem regarding the standard enthalpies of formation of \( CO_2(g) \) and \( HCOOH(l) \), we will analyze the given data and the statements provided.

### Given Data:
- Standard enthalpy of formation of \( CO_2(g) \): \( \Delta H_f^\circ = -393.7 \, \text{kJ/mol} \)
- Standard enthalpy of formation of \( HCOOH(l) \): \( \Delta H_f^\circ = -409.2 \, \text{kJ/mol} \)

### Analyzing the Statements:

1. **Statement 1**: The enthalpy change for the reaction \( C + O_2 \rightarrow CO_2 \) is \( -393.7 \, \text{kJ/mol} \).
- **Analysis**: This is correct. The standard enthalpy of formation of \( CO_2 \) is defined as the enthalpy change when one mole of \( CO_2 \) is formed from its elements in their standard states (carbon in solid form and oxygen in gaseous form).

2. **Statement 2**: The enthalpy change for the reaction \( CO_2 + H_2 \rightarrow HCOOH \) would be \( -15.5 \, \text{kJ/mol} \).
- **Analysis**: To find this, we can use Hess's law. The enthalpy change for the formation of \( HCOOH \) can be expressed as:
\[ \Delta H = \Delta H_f^\circ(HCOOH) - \Delta H_f^\circ(CO_2) - \Delta H_f^\circ(H_2) \]
Since the standard enthalpy of formation of \( H_2 \) is \( 0 \, \text{kJ/mol} \), we have:
\[ \Delta H = -409.2 \, \text{kJ/mol} - (-393.7 \, \text{kJ/mol}) = -409.2 + 393.7 = -15.5 \, \text{kJ/mol} \]
- This statement is also correct.

3. **Statement 3**: The enthalpy change for the reaction \( H_2 + CO_2 \rightarrow HCOOH \) is \( -409.2 \, \text{kJ/mol} \).
- **Analysis**: This statement is incorrect. The enthalpy change for the formation of \( HCOOH \) from its elements is \( -409.2 \, \text{kJ/mol} \), but the reaction \( H_2 + CO_2 \rightarrow HCOOH \) does not equal the enthalpy of formation directly. The enthalpy change for this specific reaction is actually \( -15.5 \, \text{kJ/mol} \) as calculated above.

4. **Statement 4**: The final temperature is \( 291.8 \, \text{K} \).
- **Analysis**: This statement does not provide enough context or relevance to the enthalpy changes discussed. Therefore, we cannot determine its correctness based on the information given.

### Summary of Correct Statements:
- **Correct Statements**: 1 and 2
- **Incorrect Statements**: 3 and 4

### Final Answer:
The correct statements are:
1. The enthalpy change for the reaction \( C + O_2 \rightarrow CO_2 \) is \( -393.7 \, \text{kJ/mol} \).
2. The enthalpy change for the reaction \( CO_2 + H_2 \rightarrow HCOOH \) would be \( -15.5 \, \text{kJ/mol} \).