To calculate the enthalpy of adsorption of hydrogen gas on the surface of activated charcoal, we need to consider the heat of combustion of hydrogen gas at constant pressure and the heat of vaporization of hydrogen gas at its boiling point. The heat of combustion at constant volume is not relevant to this problem.First, let's find the number of moles of hydrogen gas that can be adsorbed on the surface of activated charcoal. The surface area of activated charcoal is 500 m/g, and the weight of activated charcoal used is 0.5 g. Therefore, the total surface area of activated charcoal is:Total surface area = Surface area per gram Weight of activated charcoal Total surface area = 500 m/g 0.5 gTotal surface area = 250 mAssuming that 1 mole of hydrogen gas can be adsorbed on 1 m of activated charcoal surface area, the number of moles of hydrogen gas that can be adsorbed is:Number of moles of H = Total surface areaNumber of moles of H = 250 molesNow, let's calculate the enthalpy change for the adsorption process. The enthalpy change for the adsorption process can be calculated as the difference between the heat of combustion at constant pressure and the heat of vaporization:H_adsorption = H_combustion - H_vaporizationWe are given the heat of combustion of hydrogen gas at constant pressure as -241.8 kJ/mol and the heat of vaporization of hydrogen gas at its boiling point as 0.452 kJ/mol. Plugging these values into the equation:H_adsorption = -241.8 kJ/mol - 0.452 kJ/mol H_adsorption = -242.252 kJ/molSo, the enthalpy of adsorption of 1 mole of hydrogen gas on the surface of activated charcoal is -242.252 kJ/mol.