To calculate the enthalpy of adsorption of hydrogen gas on activated carbon, we can use the following equation:H_ads = H_gas - H_abswhere H_ads is the enthalpy of adsorption, H_gas is the molar enthalpy of hydrogen gas, and H_abs is the enthalpy of absorption.First, we need to calculate the enthalpy of absorption H_abs . We can use the ideal gas law to find the work done by the gas during the absorption process:PV = nRTwhere P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.Rearranging the equation to solve for V:V = nRT / PPlugging in the values:V = 0.025 moles * 8.314 J/molK * 298 K / 1 atm * 101.325 J/Latm V 0.0614 LNow, we can calculate the work done by the gas W :W = -PVSince the gas is absorbed by the activated carbon, the final volume is 0, so V = -0.0614 L. Plugging in the values:W = - 1 atm * 101.325 J/Latm * -0.0614 L W 6.22 JNow, we can calculate the enthalpy of absorption H_abs :H_abs = U + WSince the process is isothermal constant temperature , the change in internal energy U is 0. Therefore:H_abs = 0 + 6.22 JH_abs 6.22 JNow, we can calculate the enthalpy of adsorption H_ads :H_ads = H_gas - H_absThe molar enthalpy of hydrogen gas is given as -285.8 kJ/mol, so for 0.025 moles, it is:H_gas = -285.8 kJ/mol * 0.025 moles = -7.145 kJConverting H_abs to kJ:H_abs 6.22 J * 1 kJ / 1000 J = 0.00622 kJNow, we can find H_ads:H_ads = -7.145 kJ - 0.00622 kJH_ads -7.151 kJSo, the enthalpy of adsorption of hydrogen gas on activated carbon is approximately -7.151 kJ.