Equilibrium and Kinetics

Equilibrium and Kinetics Chapter 2

Fig. 2.1

Fig. 2.2 unstable Activation barrier metastable stable

Otherwise UnstableMinimum Energy – STABLE EQUILIBRIUMMaximum Energy – UNSTABLE EQUILIBRIUMGlobal Minimum - Most STABLELocal Minimum - METASTABLE

Intensive Properties Pressure Temperature Extensive Properties Internal Energy E Enthalpy H = E + PV Eqn. (2.3)

Gibbs Free Energy (2.6) Condition for equilibrium ≡ minimization of G Local minimum ≡ metastable equilibrium Global minimum ≡ stable equilibrium

G = GfinalGinitial (2.7) G = 0  reversible change G < 0  irreversible or spontaneous change (2.8) G > 0  impossible

Josiah Willard Gibbs

Atomic or statistical interpretation of entropy

Boltzmann’s Tomb Central Cemetery, Vienna, Austria

Boltzmann’s Epitaph (2.5) W is the number of microstates corresponding to a given macrostate

(2.9) N=16, n=8, W=12,870

Stirling’s Approximation (2.11) 100!=

(2.10) (2.12)

Thermal energy Average thermal energy per atom per mode of oscillation is kT Average thermal energy per mole of atoms per mode of oscillation is NkT=RT (2.13)

Maxwell-Boltzmann Distribution (2.14) Fraction of atoms having an energy  E at temperature T

Svante Augustus Arrhenius 1859-1927 Nobel 1903 KINETICS (2.15)

ln (rate) Fig. 2.4

A + BC AB + C A + BC (ABC)* AB + C

(ABC)* Free Energy ΔG* A + BC AB + C Configuration

The three laws of thermodynamics First Law: You cannot win, you can only break even. Second Law: You can break even only at absolute zero. Third Law: You can’t reach absolute zero.

Equilibrium and Kinetics