To calculate the enthalpy change for the combustion of methane gas, we can use the given thermodynamic data and the concept of Hess's Law. Hess's Law states that the enthalpy change of a reaction is the same whether it occurs in one step or several steps. We can break down the combustion of methane into two steps:Step 1: Formation of water from hydrogen and oxygen given 2H2 g + O2 g -> 2H2O g ; H = -483.7 kJ/molStep 2: Formation of carbon dioxide from methane and oxygen unknown CH4 g + 2O2 g -> CO2 g + 2H2O g ; H = ?We can rearrange Step 1 to get the formation of hydrogen and oxygen from water:Step 1': 2H2O g -> 2H2 g + O2 g ; H = 483.7 kJ/molNow, we can add Step 1' and Step 2 to get the overall reaction:Step 1': 2H2O g -> 2H2 g + O2 g ; H = 483.7 kJ/molStep 2: CH4 g + 2O2 g -> CO2 g + 2H2O g ; H = ?Overall: CH4 g + 2O2 g -> CO2 g + 2H2 g + O2 g ; H = 483.7 kJ/mol + H Step 2 Since the overall reaction is the same as the combustion of methane, we can set the enthalpy changes equal to each other:H Combustion of methane = 483.7 kJ/mol + H Step 2 Now, we can solve for the enthalpy change of Step 2, which is the combustion of methane:H Step 2 = H Combustion of methane - 483.7 kJ/molH Step 2 = -483.7 kJ/molTherefore, the enthalpy change for the combustion of methane gas CH4 at standard conditions is -483.7 kJ/mol.