  The chemical potentials of multicomponent fluids are derived in terms of the
pair correlation functions for arbitrary number of components, interaction
potentials, and dimensionality. The formally exact result is particularized to
hard-sphere mixtures with zero or positive nonadditivity. As a simple
application, the chemical potentials of three-dimensional additive hard-sphere
mixtures are derived from the Percus-Yevick theory and the associated equation
of state is obtained. This Percus-Yevick chemical-route equation of state is
shown to be more accurate than the virial equation of state. An interpolation
between the chemical-potential and compressibility routes exhibits a better
performance than the well-known Boubl\'ik-Mansoori-Carnahan-Starling-Leland
equation of state.
