Why does water in a solution have a lower chemical potential than pure water?
For an “ideal solution” (a solution in which all molecules interact in the same way) the chemical potential of water in the solution is given by µsolution water = µpure water + RT ln xsolution water where R is the gas law constant (8.314 J/mol K), T is the temperature, and xsolution water is the mole fraction of water in the solution. As salt is added to the water, the concentration of water in the solution goes down. That makes xsolution water less than one, and the natural log of a number less than one is negative. That makes the concentration correction negative, so the chemical potential of water will drop as more salt is added. Note that this has nothing to do with ordering of the water around the salt ions, because in an ideal solution salt-water interactions are assumed to be identical to water-water interactions. The decrease in chemical potential occurs because there is a lower concentration of water in the solution than in the pure liquid. Statistically, fewer water molecules
