## Wednesday, November 14, 2007

### Phase Transitions and Chemical Potentials

A substance's phase diagram tells us at what temperatures and pressures we will observe the six common phase transitions [fusion, freezing, vaporization, condensation, sublimation, deposition]. The triple point, where all three common phases are in mutual equilibrium, is a convenient phase transition marker: below it, you will typically see sublimation/deposition as temperature is changed and above it, vaporization/sublimation. When more than one crystalline form exists in the solid phase, more than one triple point is possible.

To truly understand phase transitions, we can plot the chemical potential μ vs T. Since (∂μ/∂T)P=–Sm, it is apparent that these plots trend downwards, and the slope cusps at the transition temperature. Where the solid and liquid lines intersect will be the substance's melting point (μS=μL). In fact, we can take this statement as the thermodynamic definition of the melting point. Analogously, the boiling point is that temperature at which the chemical potential of the liquid phase equals that of the vapor phase.

Pressure effects on the transition temperatures can be seen from the relationship (∂μ/∂P)T=Vm. Clearly an increase in pressure will similarly increase the chemical potential and the magnitude of this change is proportional to that phases molar volume. This leads to a boiling point elevation and freezing point elevation for most substances; in water, however, whose molar volume of solid is greater than that of the liquid phase, we see a freezing point depression as pressure is increased (as at the bottom of the ocean).

Since chemical potentials are equal for two phases in equilibrium, we are able to quickly derive the Clapeyron equation [dP/dT = ∆transS/∆transV] and its sister, the Clausius-Clapeyron equation: [dP/dT = ∆transH/T∆transV]. The latter equation allows us to easily obtain, in mathematical form, general formulas for the SL, LG and SG coexistence curves.

Chemical potential is a BIG idea in chemical thermodynamics – more for you to love! – and esplaining phase transitions is another eye-watering demonstration of the mad POWER of thermo.