Chemical potentials in a three-component, 1-dimensional liquid.

The chemical potential of a dilute solute in a mixed solvent in a one-dimensional, three-component fluid model is calculated exactly. The results depend on three parameters derived from the interparticle potentials. An explicit formula for the leading deviations from ideality is obtained. For arbitrary cosolvent concentration, but still dilute solute, the chemical potential of the solute is obtained numerically. A lattice model of the same system is also treated exactly. The results depend on three parameters in precisely the same way as do those of the continuum model. However, the parameters have a different physical meaning. In the special case of a hard-core plus-square-well potential, the results of the two models become the same in the high-density limit.