An expression for tile bond energy between two chemical species, A and B, in terms of the chemical potentials, the hardnesses, and the condensed Fukui functions of the isolated species, and the hardness of the system AB at equilibrium, is derived by dividing the total interaction energy into two contributions, one that corresponds to the charge-transfer process between A and B, at constant external potential, and a second one that corresponds to a reshuffling of the electronic density, at constant chemical potential, and by assuming that the softness of the system AB when A and B ate. very far apart from each other is equal to the sum of the softnesses of A and B when they are isolated from each other. The calculated bond energies agree rather well with the experimental values and. show that the chemical potential difference term is much smaller than the hardness difference term, In addition, an expression for the bond energy only in terms of the chemical potentials and the hardnesses of the isolated species is derived by making use of the arithmetic average principle for the molecular softness. This expression also provides reasonable estimates of the bond energies. Finally, it is shown that, in general, the reaction energy is negative when the sum of the hardnesses of the products is greater than the sum of tile hardnesses of the reactants, and it is positive when the opposite occurs, in agreement with the experimental evidence. The overall situation seems to indicate that the bond energy is practically determined by the hardnesses difference, a result that shows that the hardness and softness concepts play a fundamental role in the description of chemical events and that provides strong support for a principle of maximum hardness.