Ch. 9 K&K: Gibbs Free Energy and Chemical Reactions Recall (ch. 8): Free energyconditions. Helmholtz F isothermal Enthalpy H constant pressure Gibbs G const. pressure and temp

Ch. 9 K&K: Gibbs Free Energy and Chemical Reactions Recall (ch. 8): Free energyconditions. Helmholtz F isothermal Enthalpy H constant pressure Gibbs G const. pressure and temp Recall (ch. 3) pg. 68: “The Helmoltz free energy will be a minimum for a system S in thermal contact with a reservoir R if the volume of the system is constant.”

Chemical reactions (and other experiments) are often carried out at constant pressure and constant temperature: Gibbs free energy G(U,  P,V) = U –  + PV (Gibbs free energy; Thermodynamic potential)

Chemical reactions (and other experiments) are often carried out at constant pressure and constant temperature: Gibbs free energy G(U,  P,V) = U –  + PV dG = dU –  d  –  d  + PdV + VdP (Gibbs free energy; Thermodynamic potential)

Chemical reactions (and other experiments) are often carried out at constant pressure and constant temperature: Gibbs free energy G(U,  P,V) = U –  + PV dG = dU –  d  –  d  + PdV + VdP (Gibbs free energy; Thermodynamic potential) Isothermal d  Isobaric dP = 0 So, for a system S at equilibrium: dG S = dU S –  d  S + PdV S

dG = 0 at equilibrium Comparing to eqn ( dU S =  d  S – PdV S +  dN S ) shows dG S = dU S –  d  S + PdV S dG S =  dN S = 0, since dN S = 0 at equilibrium

Chemical reactions in equilibrium H 2 + Cl 2 = 2HCl 1 A A A 3 + …. m A m = 0 A 1 = H 2 1 = 1 A 2 = Cl 2 1 = 1 A 3 = HCl 1 = -2  j A j = 0

Want to find expression of chemical equilibrium under conditions of constant temperature and pressure dG =  j dN j The unknown details of the chemical reactions are summarized by the various chemical potentials. j Chemical reactions in equilibrium

At equilibrium, dG = 0 Chemical reactions in equilibrium

K(t) for an ideal gas with internal degrees of freedom

Chemical reaction rates