Chemistry 163B Absolute Entropies and Entropy of Mixing

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1 Chemistry 163B Absolute Entropies and Entropy of Mixing 1 APPENDIX A: H f, G f, BU S (no Δ, no sub f ) Hº f Gº f Sº 2 1

2 hird Law of hermodynamics he entropy of any perfect crystalline substance approaches 0 as ô 0K S=k ln W for perfectly ordered crystalline substance W ô 1 as ô 0K S ô 0 3 to calculate absolute entropy from measurements (E&R pp , Figs ) S ABCDE,,,, 2 1 C P ABCDE,,,, d H S A B C D E S S III II III I S 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

3 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 C S S I at 54.39K D S S g at 90.20K S E S J K mol total J K -1 mol -1 5 S reaction from absolute entropies n A A + n B B ôn 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 0 0 reaction i 298 i i i S rd are 3 Law entropies (e.g. Appendix A) 6 3

4 qualitative factors affecting molecular entropy Higher Higher S S P CP 0 Higher P Lower S usually S P Phase S(g) vs > S() vs> S(s) 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 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

5 calculating entropy (see summary on review handout) Lecture 9, slide 3 9 HW#5 Prob 31 Sample midterm 3a analogous to 31a 10 5

6 the relationships definitions: U ª internal energy H ª U + P A ª U S G ª H S differentials of state functions: du= dspd dh= ds+dp da= SdPd dg= Sd+dP heat and temperature: dq nc d dq nc d P P du dq dw dq Pd dqrev ds dq ds S nc S nc P P 11 do some examples: HW#5 Prob 31a: derive E&R equation 3.19 LAER is NOW U??? in terms of P,, and their derivatives technique applies to HW#6 Prob: 31e 12 6

7 do another example: One mole of CO 2 (g) is expanded isothermally and reversibly from 1 to 2.Using the van der Waals equation of state a P 2 b R to describe CO 2 (g) calculate w, U, q, and S in terms of 1 and 2 and the van der Waals constants a and b. 13 Entropy of Mixing of Ideal Gasses (EXRA) E&Rº Sec

8 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 reversible isothermal expansion to total volume S nrln final initial S n ln a b a R S n ln a b br a b R P=n a a P=n b b + a b R + a b 16 8

9 reversible recombining of volumes permeable to b not permeable to a permeable to a not permeable to b const ΔU=0 P ext =0 w=0 q rev =0 ΔS=0 const ΔU=0 P ext =0 w=0 q rev =0 ΔS=0 17 some arithmetic note flip leads to -ln a b a b Stotal na Rln nb Rln a (only isothermal expansion steps contribute) b note flip leads to -ln ni partial pressure : Pi Ptotal mole fraction : X i n total ideal gas : at start Pa nar ; Pb nbr at end P( ) ( n n ) R a b a b ni n total divide by n n X X n n n n a a b b a a b a b a b a 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 b S R X ln X mixing i i i S n R X ln X mixing total i i i 18 9

10 calculating entropy (see summary on review handout) 19 What formulas I have to memorize for midterm and final? 20 10

11 Gibb s Paradox: distinguishable vs identical (don t fret) n a identical to n b a = b S total n a =n b a = b 2n Rln 2 a Stotal na Rln nb Rln a b CORREC a b a b S total 0 CORREC OO 21 Gibb s Paradox: distinguishable vs identical (don t fret) statistics, Chemistry 163C Some references:

12 where we have been and what s next 23 observations: thermo heat Count Rumford, 1799 observed water turning into steam when canon barrel was bored work heat 24 12

13 observations: mechanical efficiency of steam engine Sadi Carnot, 1824 efficiency of engines 25 guiding principles Conservation of heat and work (Joule, 1845) 1st LAW OF HERMODYNAMICS Clausius, 1860 Entropy 2 nd LAW OF HERMODYNAMICS 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 13

14 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 End of Lecture 28 14

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