By taking the energy to be a Morse-like function of the number of electrons, E(N) = α{1 - e(-β(N-δ))}(2) - κ, the electronic chemical potential and global hardness values for a set of atoms and some molecules are calculated from the accurate definitions of these two concepts and using the hybrid B3LYP functional and 6-311++G** basis set. By a comparison between the obtained hardnesses and the corresponding experimental values, it is found that the proposed model yields better values for hardnesses with respect to those that are obtained from the other frequently used methods. It is claimed that the difference between the calculated and experimental hardness values may arise from the approximate equation used for the evaluation of experimental hardnesses. Both of the calculated and experimental molecular hardnesses are used to investigate the change of hardness during the course of some exothermic reactions according to the maximum hardness principle (MHP). It is shown that the obtained hardnesses of reactions from the calculated hardnesses (Δη(calc)) are more successful in predicting the directions of these reactions than those that are evaluated from the experimental hardnesses (Δη(exp)).