Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Website: TA: Pete Praserthdam, Graduate Teaching Fellow: Leonardo Gomez-Ballesteros,

TA office hours Pete Praserthdam, Office hours: Wednesdays, 2-3pm, JEB 632

TEAMS Please group in teams of 4-5 students each Designate a team coordinator Team coordinator: Please send an to stating the names of all the students in your team (including yourself) no later than next First HW is due January 27.

Introduction to phase equilibrium Chapter 10 (but also revision from Chapter 6)

Equilibrium Absence of change Absence of a driving force for change Example of driving forces – Imbalance of mechanical forces => work (energy transfer) – Temperature differences => heat transfer – Differences in chemical potential => mass transfer

Energies Internal energy, U Enthalpy H = U + PV Gibbs free energy G = H – TS Helmholtz free energy A = U - TS

Phase Diagram Pure Component a d c b e  What happens from (a) to (f) as volume is compressed at constant T. f

P-T for pure component

P-V diagrams pure component

Equilibrium condition for coexistence of two phases (pure component) Review Section 6.4 At a phase transition, molar or specific values of extensive thermodynamic properties change abruptly. The exception is the molar Gibbs free energy, G, that for a pure species does not change at a phase transition

Equilibrium condition for coexistence of two phases (pure component, closed system) d(nG) = (nV) dP –(nS) dT Pure liquid in equilibrium with its vapor, if a differential amount of liquid evaporates at constant T and P, then d(nG) = 0 n = constant => ndG =0 => dG =0 G l = G v Equality of the molar or specific Gibbs free energies (chemical potentials) of each phase

Chemical potential in a mixture : Single-phase, open system:  i :Chemical potential of component i in the mixture

Phase equilibrium: 2-phases and n components Two phases, a and b and n components: Equilibrium conditions:  i a =  i b (for i = 1, 2, 3,….n) T a = T b P a = P b

A liquid at temperature T The more energetic particles escape A liquid at temperature T in a closed container Vapor pressure

Fugacity of 1 = f 1 Fugacity of 2 = f 2

For a pure component   =   For a pure component, fugacity is a function of T and P

For a mixture of n components  i  =  i  for all i =1, 2, 3, …n in a mixture: Fugacity is a function of composition, T and P

Lets recall Raoult’s law for a binary We need models for the fugacity in the vapor phase and in the liquid phase

Raoult’s law

Model the vapor phase as a mixture of ideal gases: Model the liquid phase as an ideal solution

VLE according to Raoult’s law:

Homework # 1 download from web site Due Wednesday, 1/27