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Understanding Thermodynamics: Entropy, Spontaneity, and Reactions

Explore the concepts of entropy, spontaneity, and reactions in thermodynamics, including the role of entropy in predicting changes. Learn about the Second Law of Thermodynamics, free energy, and the relationship between entropy and spontaneity.

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Understanding Thermodynamics: Entropy, Spontaneity, and Reactions

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  1. Thermodynamics Chapter 20

  2. Thermodynamics • Prediction of whether change will occur • No indication of timeframe • Spontaneous: • occurs without external intervention • Nonspontaneous: • requires outside “push”

  3. Entropy and Spontaneity • Driving force for a spontaneous change is an • increase in entropy of the universe • Entropy, S: measure of disorder • Spontaneous change implies: • more order  less order • fewer ways of arranging particles  more

  4. Second Law of Thermodynamics • In any spontaneous change, there is always an increase in entropy of the universe. • Units: J • K

  5. Entropy • 1877 Ludwig Boltzmann: • k = Boltzmann constant, R/NA • W = no. of possible arrangements • Third Law of Thermodynamics: • The entropy of a perfect crystal at 0 K is zero.

  6. Positional Entropy • Why does a gas expand into a vacuum? • Expanded state has highest positional probability of states available.

  7. Other factors in entropy • Size: • increase in S with increasing size (mass) • Molecular complexity: • increase in S with increasing complexity • Generally effect of physical state >> complexity

  8. Reactions • For a spontaneous reaction: • NaOH(s) + CO2(g) Na2CO3(s) + H2O(l) • S0 64.45 213.7 139 69.94 J/K • Is the reaction spontaneous as written?

  9. Spontaneity and S • Spontaneous: Suniv > 0 • Nonspontaneous: Suniv < 0 • At equilibrium: Suniv = 0 • DSsys can be positive if DSsurr increases enough

  10. Surroundings and Suniv • Surroundings add or remove heat • Exothermic: • Dqsys < 0 • Dqsurr > 0 so DSsurr > 0 • Endothermic: • Dqsys > 0 • Dqsurr < 0 so DSsurr < 0

  11. DSsurr and DSsys • DSsurr: DSsurr - Dqsys • DSsurr 1/T • At constant pressure:

  12. The Math • Given: • @constant P: • Multiply by  T: • Result:

  13. Reactions and DG • DG0: Standard Free Energy • Reactants in standard states are • converted to products in standard states

  14. Gibb’s Free Energy • Overall criterion for spontaneity • from the standpoint of the system • A process at constant temp. and pressure is spontaneous in the direction DG decreases

  15. G = H - TS

  16. Summary • DG < 0 Spontaneous as written • DG > 0 Not spontaneous as written • Reverse process spontaneous • DG = 0 At equilibrium

  17. A Closer Look… • TDS: • energy not avail. for doing work • DG: • E avail. as heat – E not avail. for work •  max. work available (constant T and P) • Amount of work actually obtained depends on path

  18. DG and Work • DG • Spontaneous max. work obtainable • Nonspontaneous min. work required • Work and path-dependence • wmax (wmin) process performed reversibly • theoretical • wactual < wmax performed irreversibly • real world

  19. Reversible vs. Irreversible Processes • Reversible: • The universe is exactly the same as it was before the cyclic process. • Irreversible: • The universe is different after the cyclic process. • All real processes are irreversible. • Some work is changed to heat.

  20. Free Energy and Pressure • Q: reaction quotient from mass action law

  21. Free Energy and Equilibrium • K: equilibrium constant • At • equilibrium: DG = 0 • K = Q

  22. A B

  23. DG and Extent of Reaction A B DG0B < DG0A Spontaneous C D DG0D> DG0C Nonspontaneous

  24. Temperature Dependence of K • Plot lnK vs. 1/T • slope = -DH0/R intercept = DS0/R • *assumes DH0, DS0 relatively T independent

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