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, we need to analyze the standard enthalpies of formation for carbon dioxide (CO₂) and formic acid (HCOOH) and determine which statements about these reactions are correct.

### Step-by-Step Solution:

1. **Write the Reactions for Formation:**
- For the formation of CO₂:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \quad \Delta H_f = -393.7 \, \text{kJ/mol} \]
- For the formation of HCOOH:
\[ C(s) + H_2(g) + \frac{1}{2}O_2(g) \rightarrow HCOOH(l) \quad \Delta H_f = -409.2 \, \text{kJ/mol} \]

2. **Determine the Enthalpy Change for the Reaction:**
- To find the enthalpy change for the reaction:
\[ CO_2(g) + H_2(g) \rightarrow HCOOH(l) \]
- 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.
- We can rearrange the formation reactions:
- Reverse the reaction for CO₂:
\[ CO_2(g) \rightarrow C(s) + O_2(g) \quad \Delta H = +393.7 \, \text{kJ/mol} \]
- Keep the reaction for HCOOH as is:
\[ C(s) + H_2(g) + \frac{1}{2}O_2(g) \rightarrow HCOOH(l) \quad \Delta H = -409.2 \, \text{kJ/mol} \]

3. **Add the Reactions:**
- Adding these two reactions:
\[ C(s) + H_2(g) + \frac{1}{2}O_2(g) + CO_2(g) \rightarrow HCOOH(l) + C(s) + O_2(g) \]
- The \(C(s)\) and \(O_2(g)\) cancel out, leading to:
\[ CO_2(g) + H_2(g) \rightarrow HCOOH(l) \]

4. **Calculate the Enthalpy Change:**
- The overall enthalpy change for this reaction is:
\[ \Delta H = -409.2 \, \text{kJ/mol} + 393.7 \, \text{kJ/mol} = -15.5 \, \text{kJ/mol} \]

5. **Evaluate the Statements:**
- **Statement 1:** The enthalpy change for the formation of CO₂ is \(-393.7 \, \text{kJ/mol}\) (Correct).
- **Statement 2:** The enthalpy change for the reaction \(CO_2(g) + H_2(g) \rightarrow HCOOH(l)\) is \(-15.5 \, \text{kJ/mol}\) (Correct).
- **Statement 3:** The enthalpy change for the reaction \(H_2(g) + CO_2(g) \rightarrow H_2O + CO\) is incorrect as it does not relate to the formation of HCOOH (Incorrect).
- **Statement 4:** The statement about the final temperature achieved is nonsensical in this context (Incorrect).

### Conclusion:
The correct statements are:
- Statement 1 is correct.
- Statement 2 is correct.
- Statements 3 and 4 are incorrect.