Chemistry 163B Absolute Entropies and Entropy of Mixing
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1 Chemstry 163 Wnter 1 Hndouts for hrd Lw nd Entropy of Mxng (del gs, dstngushle molecules) PPENDIX : H f, G f, U S (no Δ, no su f ) Chemstry 163 solute Entropes nd Entropy of Mxng Hº f Gº f Sº 1 hrd Lw of hermodynmcs to clculte solute entropy from mesurements (E&R pp , Fgs ) he entropy of ny perfect crystllne sustnce pproches s ô K S=k ln W SC,,, DE, CP 1 H S C,,, DE, d C D E for perfectly ordered crystllne sustnce W ô 1 s ô K S ô 3 S III II S III S I S g S S K S ( ) + + S 3.66 IIIII t 3.66K S + S + C I t 54.39K + S D S S III t 43.76K S + g t 9.K + S E full clculton of Sº 98 for O (g) (Exmple Prolem 5.9, E&R pp13-14 [96-97] nd) S recton from solute entropes S J K mol 1 1 S( K ) S S III II t 3.66K S S II I t 43.76K SC S I t 54.39K SD S g t 9.K SE totl 4.9 J K -1 mol -1 5 n + n ôn C C + n D D t 98K S n S n S n S n S recton C C D D S ( 98K) S S recton rd re 3 Lw entropes (e.g. ppendx ) 6 1
2 Chemstry 163 Wnter 1 Hndouts for hrd Lw nd Entropy of Mxng (del gs, dstngushle molecules) qulttve fctors ffectng moleculr entropy Hgher Hgher S S C P P S Hgher P Lower S P P usully Phse S(g) vs > S() vs> S(s) (n recton the sde wth the greter numer of moles of gs generlly hs hgher S) Mxng or dssolvng of components (+), (s+s), (+s), (g+g) solutons Hgher S (g + ) or (g + s) soluton Lower S more qulttve fctors ffectng moleculr entropy sustnces wth hgher mss hve hgher S F (g) < Cl (g) < r (g) < I (g) Sº J K -1 mol -1 (more closely spced rottonl nd vrtonl levels) more rgd sustnces hve lower S C(gr) C(d) Sº J K -1 mol -1 more complex sustnces hve hgher S HF (g) H O (g) D O(g) MW 18 mu Sº J K -1 mol clcultng entropy (see summry on revew hndout) HW#5 Pro 31 Lecture 9, slde 3 nlogous to 31 Smple mdterm the reltonshps do some exmples: defntons: dfferentls of stte functons: U ª nternl energy du= dspd H ª U + P dh= ds+dp ª U S d= SdPd G ª H S dg= Sd+dP het nd temperture: dq nc d dq nc d P P du dq dw dq Pd dqrev ds dq ds S nc S ncp P 11 HW#5 Pro 31: derve E&R equton 3.19 LER s NOW U??? n terms of P,, nd ther dervtves technque pples to HW#6 Pro: 31e 1
3 Chemstry 163 Wnter 1 Hndouts for hrd Lw nd Entropy of Mxng (del gs, dstngushle molecules) do nother exmple: One mole of CO (g) s expnded sothermlly nd reversly from 1 to.usng the vn der Wls equton of stte P R to descre CO (g) clculte w, U, q, nd S n terms of 1 nd nd the vn der Wls constnts nd. Entropy of Mxng of Idel Gsses (EXR) E&Rº Sec Entropy of mxng for del gs (dstngushle prtcles) reversle sotherml expnson to totl volume S nrln fnl ntl solted from surroundngs q sys = q surr = w= ΔS surr = Δ S unverse > S n ln R S n ln R Δ S sys > =??? R P=n P=n + R reversle recomnng of volumes some rthmetc permele to not permele to permele to not permele to note flp leds to -ln S n Rln n Rln totl (only sotherml expnson steps contrute) n prtl pressure : P P n mole frcton : X ntotl totl ntotl note flp leds to -ln del gs : t strt P nr ; P nr t end P( ) ( n n) R dvde y const ΔU= P ext = w= q rev = ΔS= const ΔU= P ext = w= q rev = ΔS= 17 n X n X n n n n S nrln X nrln X nd per mole S S X Rln X X Rln X ntotl S R X ln X mxng S n R X ln X mxng totl 18 3
4 Chemstry 163 Wnter 1 Hndouts for hrd Lw nd Entropy of Mxng (del gs, dstngushle molecules) clcultng entropy (see summry on revew hndout) Wht formuls I hve to memorze for mdterm nd fnl? 19 G s Prdox: dstngushle vs dentcl (don t fret) G s Prdox: dstngushle vs dentcl (don t fret) n dentcl to n = sttstcs, Chemstry 163C n =n = Some references: Stotl n Rln S totl Stotl n Rln n Rln CORREC CORREC OO 1 oservtons: thermo het where we hve een Count Rumford, 1799 oserved wter turnng nto stem when cnon rrel ws ored work het nd wht s next 3 4 4
5 Chemstry 163 Wnter 1 Hndouts for hrd Lw nd Entropy of Mxng (del gs, dstngushle molecules) oservtons: mechncl effcency of stem engne gudng prncples Sd Crnot, 184 effcency of engnes Conservton of het nd work (Joule, 1845) 1st LW OF HERMODYNMICS Clusus, 186 Entropy nd LW OF HERMODYNMICS 5 oltzmnn, lte 19 th century, moleculr pcture of entropy Clusus the thermodynmc functons U, H, nd S (1 st nd nd lws) oltzmnn 6 pplctons How does knowledge out effcences of stem engnes, mechncl systems, etc, relte to processes n chemcl, ologcl, nd geologcl systems? NSWERED Y: End of Lecture J. W. Gs- rguly the frst gret mercn scentst who comned the concepts of het nd entropy nd proposed [Gs] Free Energy, G, thermodynmc stte functon tht leds to whole spectrum of pplctons
Chemistry 163B Absolute Entropies and Entropy of Mixing
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