ΔH⁰_f for CO₂(g)  and H₂O(g) are –393.5, –110.5 and –241.8 kJ mol^-1 respectively. The standard enthalpy change (in kJ) for the reaction CO₂ (g) + H₂ (g) → CO(g) + H₂O(g) is

Given data:

$\Delta H$_f⁰(CO₂(g)) = –393.5 kJ·mol^–1

$\Delta H$_f⁰(CO(g)) = –110.5 kJ·mol^–1

$\Delta H$_f⁰(H₂O(g)) = –241.8 kJ·mol^–1

For an elemental gas the standard enthalpy of formation is zero, so $\Delta H$_f⁰(H₂(g)) = 0.

Reaction to evaluate:

$CO$₂(g) + H₂(g) → CO(g) + H₂O(g)

Standard enthalpy change of the reaction is obtained from the Hess’s law expression:

$\Delta H$_rxn⁰ = Σ ΔH_f⁰(products) – Σ ΔH_f⁰(reactants)

Insert the values:

$\Delta H$_rxn⁰ = [ΔH_f⁰(CO(g)) + ��H_f⁰(H₂O(g))] – [ΔH_f⁰(CO₂(g)) + ΔH_f⁰(H₂(g))]

$=\; [(-110.5)\; +\; (-241.8)]\; –\; [(-393.5)\; +\; 0]$

$=\; (–352.3)\; –\; (–393.5)$

$=\; +41.2 kJ$

Thus the standard enthalpy change for the reaction is +41.2 kJ, which matches the given correct option.