H2O(l) = H2O(g) deltaHvap = + 40.7kJ shows the change in enthalpy when 1mol of liquid water vaporizes into water vapor. This is called the molar heat of vaporization. Given this information which is the proper value for the molar heat of condensation?
The heat of vaporization is the same number as the heat of condensation. The only difference is that vaporization is when going from liquid to vapor and the condensation (obviously) is from vapor to liquid. For vaporization we are adding energy so it is +40.7 kJ/mol; for condensation, it is -40.7 kJ/mol and we are releasing heat.
The molar heat of condensation is the reverse process of the molar heat of vaporization, meaning it represents the change in enthalpy when 1 mol of water vapor condenses into liquid water. Since the molar heat of vaporization is +40.7 kJ/mol, the molar heat of condensation will have the opposite sign but the same magnitude.
Therefore, the proper value for the molar heat of condensation is -40.7 kJ/mol.