Equilibrium and Kinetics

Chapter 2

Fig. 2.1

metastable

unstable

stable

Activation barrier

Fig. 2.2

Otherwise Unstable

Minimum Energy – STABLE EQUILIBRIUM

Maximum Energy – UNSTABLE EQUILIBRIUM

Global Minimum - Most STABLE

Local Minimum - METASTABLE

Intensive PropertiesPressureTemperature

Extensive Properties

Internal Energy E

Enthalpy H = E + PV

Eqn. (2.3)

Gibbs Free Energy

TSHG

Condition for equilibrium

≡ minimization of G

Local minimum ≡ metastable equilibrium

Global minimum ≡ stable equilibrium

(2.6)

G = GfinalGinitial

G = 0 reversible change

G < 0 irreversible or spontaneous change

G > 0 impossible

(2.7)

(2.8)

Josiah Willard Gibbs

Atomic

or

statistical

interpretation of entropy

Boltzmann’s Tomb

Central Cemetery,

Vienna, Austria

Boltzmann’s Epitaph

WkS lnW is the number of microstates corresponding to a given macrostate

(2.5)

N=16, n=8, W=12,870

)!(!

!

nNn

NCW n

N

(2.9)

Stirling’s Approximation

)ln()(lnln[ nNnNnnNNk nnnn ln!lnnnnn ln!ln

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

100!=

(2.11)

)ln()(lnln[ nNnNnnNNk WkS ln

)!(!

!ln

nNn

Nk

)]ln()(lnln[ nNnNnnNNk nnnn ln!ln (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

kT

E

N

nexp WkS lnFraction of atoms having an energy E

at temperature T

(2.14)

KINETICSSvante Augustus

Arrhenius

1859-1927

Nobel 1903

RT

QArate exp

(2.15)

R

Qslope

RT

QArate exp

ln (rate)

T

1

Fig. 2.4

A + BC AB + C

A + BC (ABC)* AB + C

Configuration

Fre

e E

nerg

y

A + BC

(ABC)*

AB + C

ΔG*

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.