To calculate the enthalpy of desorption, we need to consider the heat of adsorption and the enthalpy of vaporization of water.The heat of adsorption is given as -50 kJ/mol. This means that 50 kJ of energy is released when 1 mole of water is adsorbed onto the activated carbon. The negative sign indicates that the process is exothermic releases energy .The boiling point of water is 100C. At this temperature, water undergoes a phase transition from liquid to vapor. The enthalpy of vaporization for water is approximately 40.7 kJ/mol. This is the amount of energy required to convert 1 mole of liquid water to water vapor at 100C.The enthalpy of desorption is the energy required to remove the adsorbed water molecules from the activated carbon and convert them back into water vapor. This process is the reverse of adsorption, so the enthalpy change will be the opposite sign. Therefore, the enthalpy of desorption for water vapor adsorbed on activated carbon will be the sum of the heat of adsorption and the enthalpy of vaporization of water:Enthalpy of desorption = - Heat of adsorption + Enthalpy of vaporizationEnthalpy of desorption = - -50 kJ/mol + 40.7 kJ/molEnthalpy of desorption = 50 kJ/mol + 40.7 kJ/molEnthalpy of desorption = 90.7 kJ/molSo, the enthalpy of desorption for water vapor adsorbed on activated carbon is 90.7 kJ/mol.