Entropy Gibbs Free Energy

Transcription

1 Entropy Gibbs Free Energy 1 Prof. Zvi C. Koren

2 Reaction Spontaneity What is the criterion for spontaneity? Observations about Nature: - bottles drop from our hands - rain falls - avalanche - waterfalls What happened? 1. Force of gravity acts on objects: 2. P.E. decreases, K.E. increases (until it hits the ground), 3. hen K.E. w (breaking of bottle) AND (heat when object hits ground) So, is the criterion for spontaneity one where (P.E.) <??? Yes, for Mechanical Systems only! But, what about Chemical Systems??? (read on) 2 Prof. Zvi C. Koren

3 Spontaneous Chemical Reactions: H 2 (g) + ½ O 2 (g) H 2 O(l), H rxn = H f = (By the way, does this rxn really occur???) C 8 H 18 (g) + 12½O 2 (g) 8CO 2 (g) + 9H 2 O(l), H rxn = H comb = 2NO 2 (g) N 2 O 4 (g), H rxn = H dimerization = So, for spontaneity, must the rxn be exothermic???? Seems logical, no? Other Spontaneous Chemical and Physical Reactions: H 2 O(l) H 2 O(g), H phys = H vaporization = + (that is, leave an uncovered cup of water at room temp and see what will happen) NH 4 NO 3 (s) H 2O NH4 NO 3 (a), H phys = H hydration = + Also, many chemical rxns. : So, it can t just be an energy factor alone that decides whether a rxn is spontaneous or not. (continued) 3 Prof. Zvi C. Koren

4 (continued) So what is happening here? What is the missing link for the determination of spontaneity? Let s review the previous spontaneous rxns that were not energetically favored, i.e., those with H > : H 2 O(l) H 2 O(g), H vap = + NH 4 NO 3 (s) H 2O NH 4 NO 3 (a), H hyd = + Note that in all of these spontaneous processes, disorder increases!!! Boltzmann Euation: S = k logw W = Ways, # of ways of arranging a system. k = Boltzmann constant = R/N A. Note: Lowest value of S is. herefore, S is a measure of the system s Probability of existence, disorder, chaos, randomness, tohu-vavohu, balagan, samatucha, etc. hus there are WO factors that determine whether a process is spontaneous: ENERGY (E or H) AND ENROPY (S)!!! 4 Prof. Zvi C. Koren

5 Directionality of Reactions: Matter & Energy Dispersal Matter DISPERSAL ( Disorder ) Energy DISPERSAL Matter dispersal favors spontaneity: Dispersing matter from a small volume ( order ) to a larger one ( disorder ) is more probable. Surroundings Potential Energy of System Exothermic rxns favor spontaneity. Why? 1. E stored in a small uantity of substances (reactants) released to a much larger uantity (surroundings). 2. Products have less E than reactants. E of system has been lowered and thus stabilized (with regards to E). 5 Prof. Zvi C. Koren

6 Matter Dispersal (Disorder) Spontaneous Processes Energy Dispersal (Disorder) Surroundings System combustion vaporization H H 2 O(l) H 2 O(g) 2 (g) + ½O 2 (g) H 2 O(l) S = H = + BU H = BU S = + enthalpy-driven entropy-driven or energy-driven 6 Prof. Zvi C. Koren

7 State of Matter (Phase) H 2 O: Solid, o C H 2 O: Liuid, 25 o C H 2 O: Vapor, 25 o C Entropy Properties: S = f(disorder) S: Gases >> Liuids > Solids solid liuid gas S = f(): vaporization, S vap : S o (J/Kmol) S = f(complexity of the molecule) Substance CH 4, methane CH 3 CH 3, ethane CH 3 CH 2 CH 3, propane S o (J/Kmol), 1 K fusion, S fus : liuid gas S (ionic solid): f(coulombic attraction) Ionic Solid MgO NaF S o (J/Kmol) solid f b S increases upon dissolution: A(s) A(a), S > Prof. Zvi C. Koren

8 hird Law of hermodynamics Absolute entropy (S) of a pure and perfect crystalline substance at absolute zero is zero: S K (pure, perfect crystal) =. Allows the calculation of the Absolute Entropy of any substance at any temperature. S (J/K mol) S vap gas liuid bp S fus solid mp 3 rd Law (K) 8 Prof. Zvi C. Koren

9 S for a Chemical Reaction S rxn Recall: H rxn S Products H Products f Reactants S Reactants H f,, H f S ( element) ( element) For example, for: C 8 H 18 (g) + 12½O 2 (g) 8CO 2 (g) + 9H 2 O(l), S o rxn = 8 S o (CO 2 ) + 9 S o (H 2 O) - S o (C 8 H 18 ) - 12½ S o (O 2 ) and for H o rxn : H o rxn = 8 H o f(co 2 ) + 9 H o f(h 2 O) - H o f(c 8 H 18 ) - 12½ H o f(o 2 ) 9 Prof. Zvi C. Koren

10 Definition of Entropy Change Introduction to Second Law Rudolph Clausius invented entropy : For an euilibrium process at a constant : chemical rxn at euil., physical transformation (fusion, vaporization, sublimation, transition) infinitely slow expansion/compression: S e (system at euil absorbs to reach a new euil) (units are cal/k or J/K) e E we E ( PV ) E PV S difference in statefunctions So, if S is related to a difference in state functions, then S itself is a state function: Important note: For spontaneous vs. euilibrium (non-spontaneous) processes, it can be shown that: euil > spont S A C B 1 2 e spont S A = S B = S C = S spont = S euil = S spont (continued) 1 Prof. Zvi C. Koren

11 SYSEM (rxn.) A+B C+D S system =? (continued) [] S system vs. S surroundings S S SURROUNDINGS surroundings = - system( Surroundings are so big that any flowing into or out does not affect the euilibrium in the surroundings: does not change. herefore, the surroundings are always in euilibrium No matter how the system rxn proceeds (euil or spont), surroundings always absorb the from the system rxn in an euilibrium manner. for the surroundings is an euilibrium one: So, since surr S surr euil. surroundin gs,, P e H, we have: system process( rxn [ P], H H P 11 Prof. Zvi C. Koren rxn

12 S system =? For a system at euil., since: S S S e system( [ P ], P H system(,, P euil. sys process( H euil. rxn H euil. rxn For a spontaneous system, From before: S S [ P], P H S system( system( system(,, P spont spont. system process( H H spont. rxn spont. rxn 12 Prof. Zvi C. Koren

13 he Second Law of hermodynamics S total(universe) = S system + S surroundings At euilibrium, []: S total ( universe ) euil. system process( For a spontaneous rxn, []: S total ( universe ) " " " euil. system process( " euil. surroundin gs process the system process( euilibrium system process( euil. surroundin gs process the system process( spontaneous system process( (since euil > spont ) (continued) 13 Prof. Zvi C. Koren

14 he Second Law of hermodynamics (continued) S total (universe) spontaneous euilibrium Spontanoeus = Natural = Irreversible Euilibrium = Reversible A criterion for spontaneity: If S total >, (NO just S sys( ) then rxn is spontaneous! Not the most convenient of criteria, but a criterion nevertheless. So, to determine if a rxn is spontaneous calculate S total according to: For [,P]: S total S Products S sys( If S total >, then rxn is spontaneous! S Reactants S surr H rxn 14 Prof. Zvi C. Koren

15 he Second Law of hermodynamics (continued) S total (universe) = S sys ( + S surroundings Examples of Spontaneous Processes spontaneous euilibrium combustion H 2 (g) + ½O 2 (g) H 2 O(l) S sys ( = BU S surroundings = + NH 4 NO 3 (s) H 2O NH 4 NO 3 (a) S surroundings = + BU S sys ( = 15 Prof. Zvi C. Koren

16 S for a Physical Process Physical Processes occur at [,P]: Fusion: s l, H fus Sublimation: s g, H sub Vaporization: l g, H vap ransition: s(i) s(ii), H trans e.g., C(diamond) C(graphite) For a physical process at euilibrium, both phases are present. he physical process is at euilibrium at a specific pressure at the euilibrium temp. hat is, not all physical processes are at euilibrium. For example, at 1 atm: Euilibrium physical process: H 2 O(s) H 2 O(l), o C Non-euilibrium (spontaneous) physical process: H 2 O(s) H 2 O(l), -1 o C supercooled water So, recalling Clausius s definition for S, S = e / : e. H [ P], phys P H S H phys For an euilibrium physical process: S phys 16 Prof. Zvi C. Koren

17 Objective: o find a more convenient criterion for spontaneity. Recall: S total = S rxn(system) + S surroundings, If S of OAL >, then REACION is spontaneous. Wanted: X of the REACION itself, not of the total. Enter: G Gibbs Free Energy H S. otal enthalpy ( energy ) ied-up energy and G = H - (S) G = H - S, [] Gibbs Free Energy, G 17 Prof. Zvi C. Koren

18 For a spontaneous process: S total = S surroundings + S rxn(system) >, = - H rxn / + S rxn(system), [,P] Multiply both sides by : -S total = H rxn - S rxn < But from before, at []: G rxn = H rxn - S rxn < he most convenient criterion for spontaneity is: G rxn <, [,P] (just need to calculate G for the reaction!) he Free (or available) Energy of the system is naturally lowered. For a non-spontaneous process: G rxn >, [,P] For an euilibrium process: G rxn =, [,P] 18 Prof. Zvi C. Koren

19 Reaction Spontaneity as a Function of H and S H S G = H - S Spont at all s - ( enthalpy-driven ) ( entropy-driven ) - - Spont at low s Spont at high s Non-spont at all s Examples of Spontaneous Processes: 2NO 2 (g) N 2 O 4 (g)+heat ( enthalpy-driven ) NH 4 NO 3 (s)+heat NH 4 NO 3 (a) ( entropy-driven ) Na 2 CO 3 (s)+2hcl(a) 2NaCl(a)+H 2 O(l)+CO 2 (g)+heat (enthalpy- and entropy-driven) 19 Prof. Zvi C. Koren

20 G for a Chemical Rxn 1. Recall: G H rxn rxn Products Products G f H f Reactants G Re actants f H, f, G f H ( element) f ( element) S rxn S Products S Re actants, S ( element) For example, for: C 8 H 18 (g) + 12½O 2 (g) 8CO 2 (g) + 9H 2 O(l), G o rxn = 8 Go f (CO 2) + 9 G o f (H 2O) - G o f (C 8H 18 ) - 12½ G o f (O 2) 2. G o rxn = Ho rxn - So rxn 2 Prof. Zvi C. Koren

21 Industrial Application of Gibbs Free Energy An Example of a Practical Industrial Application of G G o rxn = Ho rxn - So rxn Goal: o reduce the Fe 2 O 3 ore to Fe Method 1: Decomposition by Heating Fe 2 O 3 (s) 2Fe(s) O 2 (g) At what will this rxn be spontaneous? H o rxn = - Ho f (Fe 2 O 3 ) = kj (not so good ) S o rxn = P So - r S o = +275 J/K (pretty good ) Blast furnace At what will this rxn be spontaneous (i.e., G o = -)? According to G o rxn = Ho rxn - So rxn (and don t forget kj J): G o = at > 2,997 K. oo high! echnically and economically not feasible. (continued) 21 Prof. Zvi C. Koren

22 Method 2: Reduction by Aluminum (aluminium) hermite rxn is started with a fuse of burning Mg wire: Fe 2 O 3 (s) + 2Al(s) 2Fe(s) + Al 2 O 3 (s) At what will this rxn be spontaneous? H o rxn = P Ho f - r H o f = -852 kj (pretty good ) S o rxn = P So - r S o = + 39 J/K (also good ) Rxn is spontaneous at all s. BU, the cost of producing Al(s) is MORE than the value of the Fe(s) produced. So, this process is not economically feasible. Method 3: Reduction by Carbon (graphite, of course) 2Fe 2 O 3 (s) + 3C(s) 4Fe(s) + 3CO 2 (g) At what will this rxn be spontaneous? H o rxn = kj (not so good ) = J/K (pretty good ) S o rxn At what will this rxn be spontaneous (i.e., G o = -)? According to G o rxn = Ho rxn - So rxn (and don t forget kj J): G o = - at > 835 K (562 o C). Fine! Easy for industrial furnaces. 22 Prof. Zvi C. Koren

23 hermodynamics and the Euilibrium Constant G o rxn K e For the general rxn: aa + bb cc + dd According to Lewis: G rxn = G o rxn + R lnq When substances are NO in their standard states: Gases NO at 1 atm (or 1 bar), Solutes NO at 1 M. When substances ARE in their standard states: Gases at 1 atm (or 1 bar), Solutes at 1 M. Reaction Isotherm Q = Reaction Quotient = [C] c [D] d / [A] a [B] b for aueous solutions (or for gas-phase system) = P Cc P D d / P Aa P B b for gas-phase system But at euilibrium: G =, [,P] = G o + R lnq e and G o = -R lnk, K P for gases & K C for aueous solution R = 8.31 J/K mol If K > 1, G o = -: If K < 1, G o = +: If K = 1, G o = : 23 Prof. Zvi C. Koren

24 he hree Laws of hermodynamics A Summary he First Law he Energy of the universe is constant (Law of the Conservation of Energy) he Second Law he Entropy of the universe is increasing (S universe > for spontaneous, i.e., natural, processes) he hird Law he absolute Entropy of a pure crystalline substance at K is zero. (S K = ) 24 Prof. Zvi C. Koren