How Free Energy Depends on P ___________ So: For a perfect gas where G° is the ___________ _______defined at P°=1 bar At equilibrium and constant P and T: The equilibrium constant, Keq, is “________ ___ _________ ”: So: Modified by Jed Macosko 1/17/2019

How Free Energy Depends on T definition constant ___ fundamental eqn. from (3 & 1) But ______________Equation substitute (4) in (5) alternative form: By applying the Gibbs-Helmholtz equation to both __________ and ______________ of a chemical reaction,  Modified by Jed Macosko 1/17/2019

The Chemical Potential So far, our thermodynamic relations apply to ______________ systems. However, G, U, H, etc. are ____________ properties. _______ ______________ _______ are used to describe quantities which depend on composition. In general Chemical Potential The chemical potential for a pure substance is the ______________ ______________ energy:  For a perfect gas like eq 5.3.5 Modified by Jed Macosko 1/17/2019

Basic Thermodynamic Relations Laws Definitions Fundamental Equations With ___________ ______________ : etc. _________ potential also:  Modified by Jed Macosko 1/17/2019

Modified by Jed Macosko Free Energy of Mixing 1 Consider the mixing of two ______________ gases A and B at constant T and P. Before: where After mixing: ___________ Change: Mixing is ______________. Entropy of Mixing Enthalpy of Mixing Similarly, for ideal gases and solutions Modified by Jed Macosko 1/17/2019

Modified by Jed Macosko Free Energy of Mixing 2 For a binary system, DGmix is at its ______________ and DSmix at its _______________ when 0.2 0.4 0.6 0.8 1 cA DSmix cB DGmix Equilibrium and Mixing: Consider an equilibrium between two ideal gases Gmix composition B A G Gpure Gtotal The equilibrium composition is determined by the minimum in ___________. Modified by Jed Macosko 1/17/2019

Modified by Jed Macosko Reaction Equilibrium 1 Consider Suppose an amount dx of A turns into B. Then  like what is done in 2.5.10 µA and µB depend on composition, and therefore ___________ during the reaction. If µA ___ µB the reaction proceeds from A  B. If µA ___ µB the reaction proceeds from B  A. x B A G 1 eq At equilibrium see 5.3.6 Modified by Jed Macosko 1/17/2019

Modified by Jed Macosko Reaction Equilibrium 2 A reaction such as 2A + 3B  C + 2D can be written as 0 = –________ +C +2D or completely ________ as Then and at ________ , Modified by Jed Macosko 1/17/2019

Equilibrium Constants Consider ________________ Equilibrium Constant Some books still refer to the pressure equilibrium constant which in general has pressure units The equilibrium constant can also be expressed in ________ ________ : and in _______________ : where for this example Modified by Jed Macosko 1/17/2019

Equilibrium Calculations 2 NO + Cl2  2 ____ stoichiometry initial moles during reaction ______ _____ ____ ________ The value of a at equilibrium (and thus the equilibrium composition of the reaction mixture) depends on ________. Modified by Jed Macosko 1/17/2019

Temperature Dependence of KP ________ ________ substitute ___ _____ Equation 1/T ln K or Exothermic reactions: DH < 0 so K _____ with increasing T. Endothermic reactions: DH > 0 so K ____ with increasing T. Integrating, or from Modified by Jed Macosko 1/17/2019

Pressure Dependence of Equilibrium Since , But, ideal gas Although the _____________ equilibrium constant does not depend on pressure, the K for ______ ____ does if The equilibrium composition depends on pressure if ____ ________ Principle A system at equilibrium, when subjected to a perturbation, responds in a way that tends to minimize the effect. Modified by Jed Macosko 1/17/2019