Equilibrium and Kinetics

Mechanical Equilibrium Rectangular Block Mechanical Equilibrium Centre Of Gravity

Pot. Energy Height of CG Configuration Unstable Metastable state

Global minimum = STABLE STATE Local minimum = METASTABLE STATE Kind of equilibrium can be understood by making small perturbations Global minimum = STABLE STATE Local minimum = METASTABLE STATE Maximum = UNSTABLE STATE

Intensive Properties Extensive Properties Independent of the size of the system e.g. P, T Extensive Properties Dependent on the quantity of material e.g. V, E, H, S, G

Internal Energy = E = KE + PE Some thermodynamic terms Interactions in the solid (bonds) Internal Energy = E = KE + PE Vibration / Translation / Rotation

Enthalpy = H = E + PV Measure of the heat content of the system At constant pressure the heat absorbed or evolved is given by H Transformation / reaction will lead to change of enthalpy of system Enthalpy = H = E + PV Work done by the system For condensed phases PV << E  H ~ E H0 represents energy released when atoms are brought together from the gaseous state to form a solid at zero Kelvin Gaseous state is considered as the reference state with no interactions

Gibbs Free Energy = G = H  TS For a transformation that occurs at constant temperature and pressure the relative stability of the system is determined by its GIBBS FREE ENERGY Absolute Temperature Gibbs Free Energy = G = H  TS Entropy Entropy is a measure of the randomness of a solid G =  H  T  S Even endothermic reactions are allowed if offset by TS

No. of different configurations of equal PE Entropy Microscopic Macroscopic Thermal Configurational + other H,E –ve at zero K But thermal S is zero Sthermal increases on melting at constant temperature Zero or +ve Boltzmann constant No. of different configurations of equal PE Actually these are two interpretations of Entropy

Configurational Entropy change due to mixing A and B (pure elements) S = Smixed state  Spure elements (A & B) Zero Stirling’s approximation Ln(r!)=r ln(r)  r

Possible configurations of in an 1D system of 4 sites and two different species Due to the statistical nature of the configurational entropy the equation is valid for a large number of species

Helmholtz Free Energy = A = E  TS For a transformation that occurs at constant temperature and volume the relative stability of the system is determined by its HELMHOLTZ FREE ENERGY Helmholtz Free Energy = A = E  TS

KINETICS

Arrhenius equation Order wrt A Rate Constant Concentrations Activation Energy Affected by catalyst Arrhenius equation T in Kelvin Frequency factor A is a term which includes factors like the frequency of collisions and their orientation. It varies slightly with temperature, although not much. It is often taken as constant across small temperature ranges.

Fraction of species having energy higher than Q (statistical result) ln (Rate) → 0 K

Reactants Products A + BC AB + C A + BC (ABC)* AB + C Activated complex

(ABC)* ΔH Energy A + BC AB + C Configuration Activated complex Preferable to use G ΔH Energy A + BC AB + C Configuration

The average thermal energy is insufficient to surmount the The average thermal energy is insufficient to surmount the activation barrier (~ 1eV) The average thermal energy of any mode reaches 1eV at ~ 12000 K But reactions occur at much lower temperatures Fraction of species with energies above the activation barrier make it possible Lost species by reaction are made up by making up the distribution Rate  fraction of species with sufficient energy Rate  vibrational frequency (determines the final step) Rate  n