Question

Answer and explain:

5. True or False: The entropy of mixing perfect gases is always positive.

6. True or False: The chemical potential of pure liquid water at standard conditions is higher than the standard chemical potential of liquid water in an aqueous solution

Answer 1

5. True

Thus mixing of gases (eg. by diffusion), always results in increase in entropy. Mixing is spontaneous!

6. True

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

µ_{solution water} = µ_{pure water} + RT ln x_{solution water}

where R is the gas law constant (8.314 J/mol K), T is the temperature, and x_{solution 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 x_{solution 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.