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Equilibrium and Kinetics

Equilibrium and Kinetics. Chapter 2. Recap. In the last lecture we used the mechanical Analogy to understand the concept of Stability and metastability. Recap. Fig. 2.2. unstable. Mechanical push to overcome activation barrier. Activation barrier. P.E. metastable.

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Equilibrium and Kinetics

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  1. Equilibrium and Kinetics Chapter 2

  2. Recap In the last lecture we used the mechanical Analogy to understand the concept of Stability and metastability

  3. Recap Fig. 2.2 unstable Mechanical push to overcome activation barrier Activation barrier P.E metastable System automatically attains the stable state stable Configuration

  4. Recap If we want to transform the Local Minimum - METASTABLE to Global Minimum - Most STABLE then we have to overcome the activation barrier (could be by mechanical push, thermal activation)

  5. Thermodynamic functions

  6. U = internal energy At constant pressure Courtsey: H. Bhadhesia

  7. This expression can also be expressed as: U = Uo + Courtsey: H. Bhadhesia

  8. Sum of internal energy and external energy For solids and liquid the PV term is negligible The above expression can also be expressed as: H = Ho + Courtsey: H. Bhadhesia

  9. Courtsey: H. Bhadhesia

  10. P Courtsey: H. Bhadhesia

  11. Entropy Courtsey: H. Bhadhesia

  12. How do you measure the entropy? Courtsey: H. Bhadhesia

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

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

  15. The variation of G with temperature

  16. Atomic or statistical interpretation of entropy

  17. Entropy The entropy of a system can be defined by two components: Thermal: Configurational:

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

  19. (2.9) N=16, n=8, W=12,870

  20. If n>>>1 Stirling’s Approximation (2.11)

  21. (2.10) (2.12)

  22. Svante Augustus Arrhenius 1859-1927 Nobel 1903 KINETICS: Arrhenius equation (2.15) Rate of a chemical reaction varies with temperature

  23. Arrhenius plot ln (rate) Fig. 2.4

  24. 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)

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

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