Question

1- Explain the qualitative differences between the Gibbs free energy and the chemical potential.

2- Explain what is wrong with the following statement: If two (or three) phases of a pure material have the same chemical potential, temperature, and pressure, then the equilibrium state of the system will allow a phase transition between the two (or three) phases.

3- Explain qualitatively the differences between Raoult's law and Henry's law, including the composition range in which they are valid.

Answer 1

1- Difference between Gibbs free energy and Chemical potential:

• Gibbs free energy can be intensive property associated with the pure substances while chemical potential is an extensive gibbs free energy associated with gas mixture, solutions and liquid mixtures and solutions.
• Gibbs free energy is pure substance property while chemical potential is a partial molar property
• Gibbs free energy is a function of temperature and pressure while chemical potential is function of temperature, pressure and number of moles of each component present in the mixture or solution.

2) If two phases have the same chemical potential, temperature and pressure, they are said to be in equilibrium. Since all the variables are fixed, the system cannot for allow phase transition. For example, in the below phase diagram, at fixed temperature and pressure and chemical potential, the composition of the water is uniquely specified. Hence, it cannot undergo phase transition, However, if the pressure is not fixed, it transition from solid to liquid or liquid to vapor and so on by changing pressure.

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