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)/2 eta(-/+), 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.