Calculate `Delta_(f)H^(@)` for the reaction,
`CO_(2)(g) + H_(2)(g) to CO(g) + H_(2)O(g)` Given that `Delta_(f)H^(@)` for `CO_(2)(g)`, `CO(g)` and `H_(2)O(g)` are -393.5, -111.3 and `-241.8 kJ mol^(-1)` respectively. ( Round of your answer in two digits and in KJ)

Explanation

To calculate the standard enthalpy change of the reaction given by:

\[ \text{CO}_2(g) + \text{H}_2(g) \rightarrow \text{CO}(g) + \text{H}_2\text{O}(g) \]

we will use the standard enthalpy of formation values provided for each substance involved in the reaction.

### Step-by-Step Solution:

1. **Identify the Enthalpy of Formation Values**:
- For \(\text{CO}_2(g)\): \(\Delta_f H^\circ = -393.5 \, \text{kJ/mol}\)
- For \(\text{CO}(g)\): \(\Delta_f H^\circ = -111.3 \, \text{kJ/mol}\)
- For \(\text{H}_2\text{O}(g)\): \(\Delta_f H^\circ = -241.8 \, \text{kJ/mol}\)
- For \(\text{H}_2(g)\): \(\Delta_f H^\circ = 0 \, \text{kJ/mol}\) (elements in their standard state have an enthalpy of formation of zero)

2. **Write the Reaction**:
\[ \text{CO}_2(g) + \text{H}_2(g) \rightarrow \text{CO}(g) + \text{H}_2\text{O}(g) \]

3. **Apply the Formula for Enthalpy Change**:
The enthalpy change for the reaction can be calculated using the formula:
\[ \Delta H^\circ = \sum (\Delta_f H^\circ \text{ of products}) - \sum (\Delta_f H^\circ \text{ of reactants}) \]

4. **Calculate the Enthalpy of Products**:
- For products:
\[ \Delta_f H^\circ \text{ of CO} + \Delta_f H^\circ \text{ of H}_2\text{O} = (-111.3) + (-241.8) = -353.1 \, \text{kJ/mol} \]

5. **Calculate the Enthalpy of Reactants**:
- For reactants:
\[ \Delta_f H^\circ \text{ of CO}_2 + \Delta_f H^\circ \text{ of H}_2 = (-393.5) + (0) = -393.5 \, \text{kJ/mol} \]

6. **Substitute Values into the Formula**:
\[ \Delta H^\circ = (-353.1) - (-393.5) \]
\[ \Delta H^\circ = -353.1 + 393.5 = 40.4 \, \text{kJ/mol} \]

7. **Final Answer**:
The standard enthalpy change for the reaction is:
\[ \Delta H^\circ = 40.4 \, \text{kJ/mol} \]

### Summary:
The calculated standard enthalpy change for the reaction \(\text{CO}_2(g) + \text{H}_2(g) \rightarrow \text{CO}(g) + \text{H}_2\text{O}(g)\) is **40.4 kJ/mol**.