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Unformatted text preview: Chemistry 260 Today in Chemistry 260 • Spontaneity • Summary of the three laws of thermodynamics • Gibbs energy This Week in Chemistry 260 • reading: (Wed.) 13.7 (Fri.) Ch. 5 (A&D) • More on Gibbs Energy • Phase Equilibria • Mixtures • MS 8 and OWL Due Friday 11/11 Lecture 26 November 7, 2011 ConcepTest Which way will the wheel turn?
(A) Clockwise
(B) Counterclockwise
(C) Turn? Are you kidding me? An “entropic” spring Rubber band force constants increase
with increased temperature! 1 An “entropic” spring ΔSuniv is pathway dependent! k ∝ T ΔS → k (T ) ΔS ΔSsys = 22.5 J K 1 irreversible expansion Srelax w =  P2ΔV =  1.42 kJ M T P1 = 15 atm V1 = 1 L T = 298 K M reversible expansion ⎛V ⎞
⎜⎟
w = −nRT ln⎜ 2 ⎟ = −6.71 kJ
⎝ V1 ⎠ T2 < T1 298 K ΔSuniv = 17.7 J K 1 P1 = 15 atm, V1 = 1 L P2 = 1 atm V2 = 15 L T = 298 K Sext ΔSsurr =  4.8 J K 1 q =  w = 1.42 kJ ΔS surr = qactual = − 1.42 kJ qrev =  wrev = 6.71 kJ Pressure Rubber band force constants increase
with increased temperature! P2 = 1 atm, V2 = 15 L Volume ΔSsys = 22.5 J K 1 ΔSsurr =  22.5 J K 1 Second Law of Thermodynamics: Corollary: for an isolated system, ΔSSYS ≥ 0 number of molecules A gas will not spontaneously compress. ΔS=27.7 k spontaneous WLeft = (0.25)20 = 9.09×10 13 WRight = (1)20 = 1 will not happen ΔS= 27.7 k ΔSuniv = 0 J K 1 in a truly macroscopic system N α 1023 “The second law of thermodynamics has as much truth as saying that, if you poured a glass of water into the ocean, it would not be possible to get the same glass of water back again” James Clerk Maxwell (1831 1879) Heat will not 8low spontaneously from a cooler to a warmer object T2 T1 q? T1 > T2 q small T1, T2 ~ constant ΔS1 = qrev
T1 ΔSSYS = ΔS1 + ΔS2 = ΔS2 = − qrev
T2 ⎛ T − T1 ⎞
qrev − qrev
+
= q⎜ 2
<0
T1
T2
⎝ T1T2 ⎟
⎠ ΔSSYS < 0 violating the second law ∴ it will not happen spontaneously ∴ (requires work) Three Laws of Thermodynamics Atkins 1. ΔU = q + w Energy Conservation 2. ΔS ≥ 0 everything tends toward increasing disorder 3. S > 0 except for perfect crystals at T = 0 K 0. Moore The internal energy of an You can’t win, the isolated system is best you can do is constant break even The entropy of the universe tends to increase The entropy of a perfectly crystalline substance is zero at T = 0 K T T T You must play the game. There is a game 1. ΔU = q + w Energy Conservation You can’t win. You can only break even at absolute zero 2. ΔS ≥ 0 everything tends toward increasing disorder You must lose except if it’s very cold. You can never reach absolute zero 3. S > 0 except for perfect crystals at T = 0 K It doesn’t get that cold. Summary: The energy of the universe is constant; the entropy of the universe tends always toward a maximum. Rudolf Julius Clausius (1822 1888) Summary: The energy of the universe is constant; the entropy of the universe tends always toward a maximum. Rudolf Julius Clausius (1822 1888) 2 When will a chemical reaction occur spontaneously? Does the entropy of the universe increase? Endothermic, exothermic and energy neutral processes all may occur spontaneously. ∴ ΔHSYS and ΔUSYS do not control spontaneity. Consider the following reaction: Second Law ΔSSYS = ΔSr ΔSSURR = 3
O 2 ( g ) + 2Fe(s ) ⎯⎯ Fe 2O 3 (s )
→
2 a reaction is spontaneous if and only if ΔSUNIV > 0 ΔSUNIV = ΔSSYS + ΔSSURR ≥ 0 heat absorbed from or released to the surroundings ΔSUNIV =  275 J K 1 mol 1 + ΔSSURR ≥ 0 qP − ΔH r
=
T
T ΔSUNIV = ΔSr − ΔSUNIV = ΔSSYS + ΔSSURR ≥ 0 − ΔH r − (−842)
=
= 2.83 kJ K −1 mol −1
T
298 A reaction is spontaneous if and only if: ΔH r
≥0
T ΔSr ≥ ΔH r
T ΔSUNIV =  275 J K 1 mol 1 + 2830 J K 1 mol 1 ≥ 0 ΔSUNIV = 2.55 kJ K 1 mol 1 ≥ 0 This reaction is spontaneous! Can we dekine ΔSUNIV as a state function? When will a chemical reaction occur spontaneously? Enthalpy Entropy ΔHr > 0 ΔSr < 0 ΔHr < 0 ΔSr > 0 ΔHr > 0 ΔSr > 0 ΔHr < 0 ΔSr < 0 Energy must be conserved First Law Exothermic? Spontaneous? endothermic NO exothermic ΔSUNIV = ΔSSYS + ΔSSURR ≥ 0 YES “heat required” endothermic exothermic “heat released” but ... ΔSUNIV = ΔSr − ΔSUNIV > 0 “heat released” “heat required” ΔSUNIV < 0 ΔSr − ΔH r
IF ΔSr > T
entropy driven The second law expressed solely in terms of system state functions! T always >0 ∴ multiply by  T − TΔSr + ΔHr ≤ 0 ΔH r
> ΔS r
T
enthalpy driven IF ΔHr − TΔSr ≤ 0
For any spontaneous reaction the enthalpy of reaction – T times the change in entropy must be a negative quantity. Second Law Entropy Rules! The Gibb’s “free” energy The Gibb’s “free” energy G ≡ H  TS Every system seeks to achieve a minimum of Gibbs energy G ≡ H  TS ΔG = ΔH  TΔS Measure of the change in the total entropy of a system and its surroundings at constant T and P ΔH r
≥0
T ΔH r
T ΔG = ΔH  TΔS Josiah Willard Gibbs
Yale (18391903) “ A Mathematician may say anything he pleases, but a Physicist must be at least partially sane.” – J. W. Gibbs (from John Barrow “The Book of Nothing”) Measure of the change in
the total entropy of a system and its surroundings at constant T and P “Driving force” of a chemical reaction ΔG > 0: product favored in the reverse direction ΔG < 0: product favored in the forward direction ΔG = 0: system is at equilibrium 3 The Gibb’s “free” energy Every system seeks to achieve a minimum of Gibbs energy G ≡ H  TS ΔG = ΔH  TΔS Measure of the change in the total entropy of a system and its surroundings at constant T and P “Driving force” of a chemical reaction ΔG is a function of the system ΔSuniv is a property of system and surroundings The Gibb’s “free” energy Reaction Gibbs energy ΔGr = ∑ νΔGr (products) − ∑ νΔGr (reactants) Molar Standard Gibbs energy of Formation Indication of a compound’s stability relative to its constituent elements. Thermodynamic stability ΔG f H 2O 237 AgCl 110 N H3 16.0 HI + 2.00 NO2 + 51.0 C 6H 6 + 124 4 ...
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This note was uploaded on 01/19/2012 for the course CHEM 260 taught by Professor Staff during the Fall '08 term at University of Michigan.
 Fall '08
 STAFF
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