We have studied the Kelvin relation, e.g., an equilibrium between a two-component drop (in which the solute is involatile) and the vapor of the solvent component. This equilibrium and its stability have been analyzed previously, but not in a thermodynamically disciplined manner that employs the appropriate thermodynamic potential. Using the theory of the thermodynamic potential, we verify the previous conclusion that regimes of both stable and unstable equilibrium exist. However, we are able to show in addition that, contrary to the conventional wisdom, it is possible to have unstable equilibrium even in undersaturated solvent vapor. Also, because our analysis is based on the thermodynamic potential, we are able to characterize the fluctuations in drop size and to emphasize the experimental importance of the critical-like behavior that occurs at the boundary between a stable and an unstable regime. Finally, we are able to provide a general analytical description of the surface representing the free energy of the system as a function of drop composition at fixed super(under)saturation. This allows us to establish the connection (and continuity) between studies of the Kelvin relation (micrometer range) and of nucleation (nanometer range).