To calculate the enthalpy change for the reduction of iron III oxide to iron using hydrogen gas, we first need to write the balanced chemical equation for the reaction:Fe2O3 s + 3 H2 g 2 Fe s + 3 H2O l Now, we can use Hess's Law to find the enthalpy change for the reaction. Hess's Law states that the enthalpy change for a reaction is equal to the sum of the enthalpy changes for the formation of the products minus the sum of the enthalpy changes for the formation of the reactants.H reaction = H products - H reactants In this case, the products are 2 moles of Fe and 3 moles of H2O, and the reactants are 1 mole of Fe2O3 and 3 moles of H2. The standard enthalpy of formation for Fe2O3 is -824 kJ/mol, and for H2O is -286 kJ/mol. The standard enthalpy of formation for elements in their standard state, such as Fe s and H2 g , is zero.H reaction = [ 2 0 + 3 -286 ] - [ 1 -824 + 3 0 ]H reaction = [-858] - [-824]H reaction = -34 kJThe enthalpy change for the reduction of iron III oxide to iron using hydrogen gas is -34 kJ.