Classical description of a single component system Lecture 10 Classical description of a single component system Gibbs free energy and equilibrium phases as a function of temperature Phase diagram Molar properties and Clapeyron equation Problem 11.4

Gibbs free energy Typically we control pressure and temperature - therefore for a single component system to find equilibrium phase we need to consider Gibbs free energy, G (P, T). In general for each phase, : From chapter 4 we know that

G as a function of T for a given pressure Entropy of vapor > entropy of liquid > entropy of solid vapor liquid solid At the melting point Gsolid = Gliquid At the boiling point Gliquid = Gvapor

Enthalpy Since G = H-TS also Latent heat - heat of fusion vapor liquid H solid Latent heat - heat of fusion Heat of vaporization

Phase diagram solid liquid vapor

Molar properties - converting extensive into intensive variables Mole fraction Molar entropy etc.

Gibbs-Duhem equation The original equation for each phase Dividing by Gives for two phases,  and 

Clapeyron equation Along the coexistence line Also for a single component in  and  phases Therefore From which Since in equilibrium coexistence

Coexistence with vapor slope

Problem 11.4 Calculate the vapor pressure at 300 K of an element for which melting point is 1000 K, the normal boiling point is 2500 K, the heat of vaporization is 240, 000 J/mol and the heat of fusion is 12,000 J/mol.