Chapter 19 Spontaneous Change: Entropy and Gibbs Energy

1. Chapter 19Spontaneous Change:Entropy and Gibbs Energy

2. Contents in Chapter 19 19-1 Spontaneity: The Meaning of Spontaneous Change 19-2 The Concept of Entropy 19-3 Evaluating Entropy and Entropy Changes 19-4 Criteria for Spontaneous Change: The Second Law of Thermodynamics 19-5 Standard Gibbs Energy Change, ΔGo 19-6 Gibbs Energy Change and Equilibrium 19-7 ΔGo and K as Functions of Temperature 19-8 Coupled Reactions

3. Chemical thermodynamics information: • Stability of particular substances • The Spontaneity of a chemical reaction • Equilibrium constant (Keq) of a chemical reaction • Predict the proportions of products and reactants at equilibrium • The optimum temperature, pressure, and choice of solvent etc. for a particular reaction.

4. Kinetics versus Thermodynamics • Thermodynamics tells us what processes are possible. • Kinetics tells us whether the process is practical. • (high activation energy can effectively block a reaction although that is thermodynamically favored)

5. 19-1 Spontaneity: The Meaning of Spontaneous Change • Spontaneous process: A process that occurs in a system left to itself; once started, no action from outside the system (external action) is necessary to make the process continue. • A nonspontaneous process will not occur unless some external action is applied. • If a process is spontaneous, the reverse process is nonspontaneous. • “spontaneous” signifies nothing about how fast a process occurs. • Enthalpy change (ΔH) is not a sufficient criterion for predicting spontaneous change.

6. (Continuous) • Examples of spontaneous with endothermic processes: • The melting of ice at room temperature • The evaporation of liquid diethyl ether from an open beaker • The dissolving of ammonium nitrate in water

7. 19-2 The Concept of Entropy Expansion Mixing Internal change (ΔU)=0, enthalpy change (ΔH)=0.

8. (Continuous) • Entropy (S): The number of energy levels among which the energy of a system is spread. The greater the number of energy levels for a given total energy, the greater the entropy. • The Boltzmann Equation for Entropy S = klnW S: entropy, k: Boltzmann constant, W: number of microstates • Entropy change (ΔS): The difference in entropy between two states of a system

9. (Continuous) • Generalizations of the Entropy Change***** • SSolid < SLiquid < SGas • S(small atom or molecule) < S(large atom or molecule) • S(simple molecule) < S(complex molecule) • S(low temperature) < S(high temperature) • S(solute) + S(solvent) < S(solution) • S(less amount of gases) < S(more amount of gases)

11. 19-3 Evaluating Entropy and EntropyChanges • Entropy Change • The more energy added to a system (as heat), the greater the number of energy levels available to the microscopic particles. • For a given quantity of heat, the proportional increase in number of energy levels is greatest at low temperatures.

12. (Continuous) • Entropy Change for Phase Transitions

13. (Continuous) • Absolute Entropies • The third Law of Thermodynamics: The entropy of a pure perfect crystal at 0 K is zero. (At 0 K, the atoms in a pure perfect crystal do not move) • The particular S of a substance is calculated from the amount of heat required to raise the temperature from 0 K. • In a particular state, S slow increase with increasing T, the temperature dependence of S: S(T2) = S(T1) + Cpln(T2 –T1) Cp: Heat capacity of the substance • The S sharply change at phase change/transition: S(phase 2) = S(phase 1) + ΔH/T example: ΔSfus = ΔHfus/Tmp)

14. (Continuous) • Standard molar entropy (So): The entropy of one mole (or 1 M) of a substance in its standard state. (Appendix D) • Evaluating entropy change of a chemical reaction by tabulated standard molar entropy: • For a chemical reaction: • aA + bB → cC + dD • Standard entropy change of the reaction (Sorxn ): • Sorxn = (cSoC + dSoD) − (aSoA + bSoB)

15. (Continuous) • Molar entropy as a function of temperature Methyl chloride (CH3Cl) for example:

18. 19-4 Criteria for Spontaneous Change: The Second Law of Thermodynamics • The second law of thermodynamics: All spontaneous processes produce an increase in the entropy of the universe (Suniv). For a spontaneous process: ΔSuniv = ΔSsys + ΔSsurr > 0 Universe System (reaction vessel) Surroundings

19. 19-4 (Continuous) • Gibbs Energy and Gibbs Energy Change

20. (Continuous)

21. (Continuous) • Gibbs energy (G): A thermodynamic function designed to produce a criterion for spontaneous change. It is defined through the equation G = H – TS. • Gibbs energy change (ΔG): The change in Gibbs energy that accompanies a process and can be used to indicate the direction of spontaneous change: ΔG < 0 : spontaneous process ***** ΔG = 0 : at equilibrium ΔG > 0 : nonspontaneous process

22. Applying the Gibbs equation***** ΔG = ΔH –TΔS

23. 19-5 Standard Gibbs Energy Change, ΔGo • Standard Gibbs energy change (ΔGo): The Gibbs energy change of a process when the reactants and products are all in their standard states. • Standard Gibbs energy of formation (ΔGfo): The standard free energy change associated with the formation of 1 mol of compound from its elements in their most stable forms at standard state. (Listed in Appendix D) • Standard state: • 1 bar and commonly 25oC • 1 mole substance • Solute in aqueous solution activity = 1 ( 1 M). • The element in most stable forms and H+ at standard state, ΔGfo=0

24. (Continuous) • Calculating standard Gibbs energy change (ΔGo) Method 1: Using Gibbs equation: ΔGo = ΔHo – TΔSo Calculate ΔHorxn and ΔSorxn from tabulated thermodynamic data, then calculated the free energy change (Grxn): ΔGorxn = ΔHorxn – TΔSorxn Method 2: Using tabulated ΔGfo For a chemical reaction: aA + bB → cC + dD Gorxn = (cGfoC + dGfoD) − (aGfoA + bGfoB)

26. 19-6 Gibbs Energy Change and Equilibrium • Relationship of ΔGo To ΔG for Nonstandard Conditions • ΔGorxndescribes the Gibbs energy change at standard states. • ΔGrxndescribesthe Gibbs energy change at any specified state. • Grxn and Gorxn are related through the reaction quotient, Q, by the following equation (memorize it): Grxn = Gorxn + RTlnQ (R: 8.314 Jmol–1K–1, T: K) • At equilibrium, Grxn = 0, also Q = Keq, therefore, Gorxn = –RTlnKeq = –2.303RTlogKeq or lnKeq = －Gorxn/RT

28. (Continuous) • The Thermodynamic Equilibrium Constant: Activities • Activities (effective concentrations) are the dimensionless quantities replaced the apparent concentration in thermodynamic equilibrium constant Keq. • The thermodynamic Keq is also dimensionless quantities. • For pure solid and liquid phases: The activity, a = 1. • For gases: Activities close to the numerical value of the gas partial pressure (unit in bar). • For solutes in aqueous solution: Activities close to the numerical value of the solute concentration (unit in molarity, M).

32. 19-7 ΔGo and K as Functions of Temperature • For a particular reaction, H and S do not change much for different temperature. • At standard state: Go = Ho – TSo (1) Go = – RTlnKeq (2) Combing (1) and (2) Ho – TSo = Go = – RTlnKeq Therefore,

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35. (Continuous) • Van’t Hoff equation • Clausius-Clapeyron equations For vaporization A(l)→ A(g) For sublimation: A(s) → A(g)

38. 19-8 Coupled Reactions • Coupled reactions: A set of chemical reactions that occur together. One (or more) of the reactions taken alone is (are) nonspontaneous and other(s), spontaneous. The overall reaction is spontaneous. For example:

39. End of Chapter 19