To calculate the enthalpy change for the combustion of methane gas in a bomb calorimeter, we need to know the balanced chemical equation for the combustion of methane and the standard enthalpies of formation for each compound involved in the reaction.The balanced chemical equation for the combustion of methane is:CH g + 2O g CO g + 2HO l Now, we need the standard enthalpies of formation Hf for each compound involved in the reaction. These values are typically found in a reference book or online database. The values are:Hf CH = -74.8 kJ/molHf O = 0 kJ/mol since O is an element in its standard state Hf CO = -393.5 kJ/molHf HO = -285.8 kJ/molUsing Hess's Law, we can calculate the enthalpy change for the reaction Hrxn as follows:Hrxn = [Hf products - Hf reactants ]Hrxn = [1 * -393.5 kJ/mol + 2 * -285.8 kJ/mol ] - [1 * -74.8 kJ/mol + 2 * 0 kJ/mol]Hrxn = -393.5 - 571.6 - -74.8 Hrxn = -965.1 + 74.8Hrxn = -890.3 kJ/molSo, the enthalpy change for the combustion of methane gas in a bomb calorimeter is approximately -890.3 kJ/mol.