Chemistry 163B Absolute Entropies and Entropy of Mixing

Transcription

1 Chemistry 163B Absolute Entropies and Entropy of Mixing 1

2 APPENDIX A: H f, G f, BUT S (no Δ, no sub f ) Hº f Gº f Sº 2

3 Third Law of Thermodynamics The entropy of any perfect crystalline substance approaches 0 as T 0K S=k ln W for perfectly ordered crystalline substance W 1 as T 0K S 0 3

4 to calculate absolute entropy from measurements (E&R pp , Figs ) S A, B, C, D, E T2 T 1 C P A, B, C, D, E T dt S H T A B C D E S S S III II II I I S g 0 S S K (0 ) S + + A S IIIII at 23.66K + S B S III at 43.76K + S C S I at 54.39K + S D S g at 90.20K + S E

5 full calculation of Sº 298 for O 2 (g) (Example Problem 5.9, E&R pp [96-97] 2nd ) S(0 K) S A S III II at 23.66K B S S II I at 43.76K S C S I at 54.39K S D S g at 90.20K S E S J K mol 1 1 total J K -1 mol -1 5

6 S reaction from absolute entropies n A A + n B B n C C + n D D at 298K S n S n S n S n S reaction C C D D A A B B S ( 298K ) S S 0 0 reaction i 298 i i i 6

7 qualitative factors affecting molecular entropy Higher T Higher S S T P C T P 0 Higher P Lower S vs usually S V P T vs Phase S(g) > S() > S(s) T P 0 (in a reaction the side with the greater number of moles of gas generally has higher S) Mixing or dissolving of components (+), (s+s), (+s), (g+g) solutions Higher S (g + ) or (g + s) solution Lower S 7

8 more qualitative factors affecting molecular entropy substances with higher mass have higher S F 2 (g) < Cl 2 (g) < Br 2 (g) < I 2 (g) Sº J K -1 mol -1 (more closely spaced rotational and vibrational levels) more rigid substances have lower S C(gr) C(dia) Sº J K -1 mol -1 more complex substances have higher S HF (g) H 2 O (g) D 2 O(g) MW amu Sº J K -1 mol -1 8

9 calculating entropy (see summary on review handout) Lecture 9, slide 3 9

10 HW#5 Prob 31 Sample midterm 3a analogous to 31a 10

11 the relationships definitions: U internal energy H U + PV A U TS G H TS differentials of state functions: du= TdSPdV dh= TdS+VdP da= SdTPdV dg= SdT+VdP heat and temperature: _ dq nc dt dq nc dt V V P P du dq dw dq PdV dq rev ds dq Tds T _ S ncv S nc T T T T V P P 11

12 do some examples: HW#5 Prob 31a: derive E&R equation 3.19 LATER is NOW U V T??? in terms of P, V, T and their derivatives technique applies to HW#6 Prob: 31e 12

13 do another example: One mole of CO 2 (g) is expanded isothermally and reversibly from V 1 to V 2.Using the van der Waals equation of state a P V b RT 2 V to describe CO 2 (g) calculate w, U, q, and S in terms of V 1 and V 2 and the van der Waals constants a and b. 13

14 Entropy of Mixing of Ideal Gasses (EXTRA) E&R Sec

15 Entropy of mixing for ideal gas (distinguishable particles) isolated from surroundings q sys = q surr =0 w=0 ΔS surr =0 Δ S universe >0 Δ S sys >0 =??? 15

16 reversible isothermal expansion to total volume ln final V S nr V initial V V V V S n ln a b a R S n ln a b br V V a b 16

17 reversible recombining of volumes permeable to b not permeable to a permeable to a not permeable to b T const ΔU=0 P ext =0 w=0 q rev =0 ΔS=0 T const ΔU=0 P ext =0 w=0 q rev =0 ΔS=0 17

18 some arithmetic note flip leads to ln V V V V Stotal na Rln nb Rln V V a b a b a (only isothermal expansion steps contribute) b note flip leads to ln ni partial pressure : Pi Ptotal mole fraction : X n total i n n i total ideal gas : at start PV n RT ; PV n RT a a b b at end P( V V ) ( n n ) RT a b a b divide by V n V n X V V n n V V n n a a b b a a b a b a b a b X b S n Rln X n Rln X and per mole a a b b S S X Rln X X Rln X n total a a b b S R X ln X mixing i i i S n R X ln X mixing total i i i 18

19 calculating entropy (see summary on review handout) 19

20 What formulas I have to memorize for midterm and final? 20

21 Gibb s Paradox: distinguishable vs identical (don t fret) n a identical to n b V a =V b S total n a =n b V a =V b 2n Rln2 a V V V V Stotal na Rln nb Rln V V a b a b a correct b S total 0 correct TOO 21

22 Gibb s Paradox: distinguishable vs identical (don t fret) statistics, Chemistry 163C Some references:

23 where we have been and what s next 23

24 observations: thermo heat Count Rumford, 1799 observed water turning into steam when canon barrel was bored work heat 24

25 observations: mechanical efficiency of steam engine Sadi Carnot, 1824 efficiency of engines 25

26 guiding principles Conservation of heat and work (Joule, 1845) 1st LAW OF THERMODYNAMICS Clausius, 1860 Entropy 2 nd LAW OF THERMODYNAMICS Boltzmann, late 19 th century, molecular picture of entropy Clausius the thermodynamic functions U, H, and S (1 st and 2 nd laws) Boltzmann 26

27 Applications How does knowledge about efficiencies of steam engines, mechanical systems, etc, relate to processes in chemical, biological, and geological systems? ANSWERED BY: J. W. Gibbs- arguably the frist great American scientist who combined the concepts of heat and entropy and proposed [Gibbs] Free Energy, G, a thermodynamic state function that leads to a whole spectrum of applications 27

28 End of Lecture 28

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