To calculate the enthalpy change for the combustion of 5.67 grams of methane, we will first need to determine the number of moles of methane present, and then use the standard enthalpy of combustion to find the total enthalpy change.1. Calculate the number of moles of methane CH4 :Molecular weight of CH4 = 12.01 g/mol C + 4 * 1.01 g/mol H = 16.05 g/molNumber of moles = mass / molecular weightNumber of moles = 5.67 g / 16.05 g/mol = 0.353 moles2. Calculate the enthalpy change:Enthalpy change = number of moles * standard enthalpy of combustionEnthalpy change = 0.353 moles * -890.4 kJ/mol = -314.3 kJThe enthalpy change for the combustion of 5.67 grams of methane is approximately -314.3 kJ.