Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1 AP Chem h/w , 17, 19, 23, 24, 26, 28, 30, 31

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 2 Chemistry FIFTH EDITION Chapter 16 Spontaneity, Entropy, and Free Energy

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 3 Figure 16.1 Methane and Oxygen React

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 4 Spontaneous Processes A spontaneous process is one that occurs without outside intervention. Thermodynamics : predicts whether a process will occur spontaneously. gives no info about time required for the process (kinetics)

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 5 Figure 16.2 Rate of Reaction

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 6 Entropy The driving force for a spontaneous process is an increase in the entropy of the universe. Entropy, S, can be viewed as a measure of randomness, or disorder.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 7 Entropy and probabilty System tends towards disorder simply because there are more “disordered states” than “ordered” states. Nature spontaneously goes to states with a higher probability of existing. Ex.: deck of cards

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 8 Figure 16.3 The Expansion of an Ideal Gas into an Evacuated Bulb

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 9 Figure 16.4 Three Possible Arrangements (microstates) of Four Molecules in a Two- Bulbed Flask

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 10 Probability of finding all molecules in left bulb # molecules prob. 11/2 21/2 x1/2 = 1/4 3 1/2 x 1/2 x 1/2 = 1/8 4 1/16 n 1/2 n One mole1/2 avogadro = small #

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 11 Positional Entropy A gas expands into a vacuum because the expanded state has the highest positional probability of states available to the system. Other ex: 1. S solid < S liquid << S gas 2. Formation of a solution entropy?

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 12 The Second Law of Thermodynamics...in any spontaneous process there is always an increase in the entropy of the universe.  S univ > 0 for a spontaneous process. (notice, unlike mass and energy, entropy is NOT conserved)

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 13 ∆S universe ∆S univ = ∆S system + ∆S surrounding ∆S univ + for spontaneous ∆S univ - spontaneous in opp direction ∆S univ 0 process no tendency to occur. We must know the entropy changes in both the sys and the surr.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 14 ∆S univ = ∆S system + ∆S surrounding Consider this process: H 2 O (l) → H 2 O (g) What happens to  S SYS here? What about  S SURR ?

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 15 ∆S surr ∆S surr mainly determined by heat flow to or from the sys. If system is exo, heat flows to surr and ∆S surr is pos If system is endo, heat flows out of surr and ∆S surr is neg Why?

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 16 ∆S univ = ∆S system + ∆S surrounding So for H 2 O (l) → H 2 O (g)  S SYS is +  S SURR is - and ∆S univ = ∆S system + ∆S surrounding So will this rxn occur. It depend on ____?

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 17 The Effect of Temperature on Spontaneity We know that if T > 100 ˚C, the process is spontaneous as written. If T < 100˚C, the process is spontaneous in the reverse direction.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 18 The Effect of Temperature on Spontaneity Why does T matter? Think exothermic rxn. Recall the $50 dollar bill story. So, the impact of a transfer of heat to or from the surroundings will be greater at lower temperatures.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 19 The Effect of Temperature on Spontaneity To summarize: entropy flow in the surroundings: The SIGN of  S SURR depends on the direction of heat flow. The MAGNITUDE of  S SURR depends on the temperature.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 20 The Effect of Temperature on Spontaneity Combining these concepts shows that for conditions of constant T and P,  S SURR = -  H T minus sign : we’re looking from the system’s POV, and this equation shows a property of the surroundings.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 21 ∆S univ = ∆S system + ∆S surrounding Finally for H 2 O (l) → H 2 O (g)  S SYS is +  S SURR is - and ∆S univ = ∆S system -  H T Sys favors sponteneous (positional), but surrounding do not (endo). The higher the T the better.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 22 One more thing ∆S surrounding = -  H T At low T, exothermicity will be most import. driving force For endothermic, higher T will minimize the neg effect on entropy (think vaporization example

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 23 The Effect of Temperature on Spontaneity See S/E 16.4, p. 802, and Table 16.3, p. 803.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 24 Free Energy  G =  H  T  S (from the standpoint of the system) A process (at constant T, P) is spontaneous in the direction in which free energy decreases:  G means +  S univ

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 25 Free Energy See Table Spend some time with this. Study it closely. Have your calculator out and run the numbers. Satisfy yourself that these numbers explain why ice melts at +10 ˚C, freezes at -10˚C, and is in equilibrium with liquid water at 0˚C.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 26 Effect of  H and  S on Spontaneity

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 27 The Third Law of Thermodynamics... the entropy of a perfect crystal at 0 K is zero. Because S is explicitly known (= 0) at 0 K, S values at other temps can be calculated.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 28 Figure 16.5 Entropy

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 29 Because Entropy is a State Function,  S ˚ RXN = Σn p S˚ products - Σn p S˚ reactants This time, we must include values for elements in their standard states, because we have a real “floor” value from which to compare them. See S/E 16.7, p. 809 and S/E 16.8, pp 809 – 810.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 30 Figure 16.6 H 2 O Molecule

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 31 Free Energy Change and Chemical Reactions  G  = standard free energy change that occurs if reactants in their standard state are converted to products in their standard state.  G  =  n p  G f  (products)   n r  G f  (reactants)

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 32 Figure 16.7 Schematic Representations of Balls Rolling Down into Two Types of Hills

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 33 Free Energy and Pressure  G =  G  + RT ln(Q) Q = reaction quotient from the law of mass action.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 34 Figure 16.8 The Dependence of Free Energy on Partial Pressure

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 35 Free Energy and Equilibrium  G  =  RT ln(K) K = equilibrium constant This is so because  G = 0 and Q = K at equilibrium.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 36 Figure 16.9 Free Energy and Equilibrium

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 37 Temperature Dependence of K y = mx + b (  H  and S   independent of temperature over a small temperature range)

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 38 Reversible v. 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).

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 39 Figure A Battery

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 40 The Effect of Temperature on Spontaneity Since  S SYS and  S SURR are opposed here, the temperature must have an effect on the relative importance of these two terms. The idea here is that entropy changes in the surroundings are determined by heat flow. So, exothermicity is an important driving force for spontaneity.