To calculate the enthalpy change for the combustion of methane gas CH4 at constant pressure, we can use Hess's Law, which states that the enthalpy change for a reaction is the same whether it occurs in one step or several steps. We can use the standard enthalpies of formation for the reactants and products to determine the enthalpy change for the reaction.The balanced chemical equation for the combustion of methane is:CH4 g + 2 O2 g CO2 g + 2 H2O l The enthalpy change for the reaction H can be calculated using the following equation:H = [Hf products ] - [Hf reactants ]where Hf represents the standard enthalpy of formation.For the products:1 mol of CO2: -393.5 kJ/mol2 mol of H2O: 2 * -285.8 kJ/mol = -571.6 kJ/molFor the reactants:1 mol of CH4: -74.8 kJ/mol2 mol of O2: 2 * 0 kJ/mol = 0 kJ/mol The standard enthalpy of formation for an element in its standard state is zero. Now, we can calculate the enthalpy change for the reaction:H = [ -393.5 + -571.6 ] - [ -74.8 + 0 ]H = -965.1 - -74.8 H = -890.3 kJ/molThe enthalpy change for the combustion of methane gas CH4 at constant pressure is -890.3 kJ/mol.