By introducing an electron bath that represents the chemical environment in which a chemical species is immersed, and by making use of the second-order Taylor series expansions of the energy as a function of the number of electrons in the intervals between N - 1 and N, and N and N + 1, we show that the electrodonating (omega-) and the electroaccepting (omega+) powers may be defined as omega-/+ = (mu-/+)2/2eta-/+, where mu-/+ are the chemical potentials and eta-/+ are the chemical hardnesses, in their corresponding intervals. Approximate expressions for omega- and omega+ in terms of the ionization potential I and the electron affinity A are established by assuming that eta- = eta+ = eta = mu+ - mu-. The functions omega-/+(r) = omega-/+f -/+(r), where f -/+(r) are the directional Fukui functions, derived from a functional Taylor series for the energy functional truncated at second order, represent the local electrodonating and electroaccepting powers.