17.3 Free Energy and Spontaneity

Transcription

1 17.3 Free Energy and Spontaneity To Be Or Not To Be...spontaneous Dr. Fred Omega Garces Chemistry 201 Miramar College 1 Free Energy and Spontaneity

2 Relationship Between ΔS surr & H A + B (system) Water ΔS Surr q ΔS surr affected by heat transfer into or out of closed system Entropy of the surroundings will be affected only by the heat transferred into or out of any closed system. Heat added to surroundings: K.E. surr increases; Molecules are moving faster. Disorder increases since there is more randomness Entropy increases. Note: q p = - ΔH sys ΔS surr 2 Free Energy and Spontaneity

3 Heat flow; Temperature Dependent Remember that heat transfer is temperature dependent. Heat will transfer more efficiently with changes at low temperature than at high temperature. i.e., 100$ is worth more to a starving college student than to Bill High temperature, molecules are already moving fast, an extra 10 C will not increase the u rms as much as molecules at very low temperature. -Δ H sys = Δ S surr units: J. T mol K Therefore since: ΔS univ = ΔS sys + ΔS surr ΔS univ = ΔS sys - ΔH sys T 3 Free Energy and Spontaneity

4 ΔS univ and Spontaneity Criteria for Spontaneity in terms of the system: ΔS univ = ΔS sys + ΔS surr ΔS univ = ΔS sys - ΔH sys T ΔS univ ΔH sys (-) (+) Spontaneous ΔS sys (+) Spontaneous 4 Free Energy and Spontaneity

5 Spontaneity in terms of T ΔS univ Criteria for Spontaneity in terms of the system: ΔS sys + ΔS surr = ΔS univ (1) ΔS sys - ΔH sys = ΔS univ (2) T Note rearranging eqn. 2 -TΔS sys + ΔH sys = -T ΔS univ J. Willard Gibbs realized that -T ΔS univ can be defined as a new function provided that ΔT = 0 5 Free Energy and Spontaneity

6 J. Willard Gibbs J. Willard Gibbs ( ) was not particularly well known in his day, nor is his name widely recognized today, yet he is considered by some to be among the greatest scientists ever born in America. He was awarded the first doctorate in engineering granted in the U.S., by Yale University. Gibbs became a professor of mathematical physics at Yale when he was 32 years old and began to publish a series of papers related to thermodynamics and equilibrium. Perhaps because his work was so theoretical, it was largely unappreciated at the time, though its great value was recognized by James Clerk Maxwell. Gibb s work, if not his name, remains current and vital to this day. The Free Energy change (ΔG) is a measure of spontaneity of a process and of the useful energy available from such a process. 6 Free Energy and Spontaneity

7 ΔG and Spontaneity Defining a new State function ΔG: -T ΔS univ = ΔT, ΔP= 0 Consider ΔG = - T ΔS univ ΔG < 0 Spontaneous ΔS univ > 0 ΔG = equilibrium ΔS univ = 0 ΔG > 0 nonspontaneous ΔS univ < 0 (rev is spontaneous) 7 Free Energy and Spontaneity

8 ΔG: Pictorial View Forward reaction occur Spontaneous in forward direction ΔG < 0 ΔG = 0 ΔG > equilb Reverse reaction occur nonspontaneous in forward direction See later that : ΔG g Keq or Q ΔG < 0 ΔG > 0 Gibbs Free Energy can be defined in terms of the enthalpy of the system (ΔH sys ) and the entropy of the system (ΔS sys ) -T ΔS univ = ΔH sys - TΔS sys = ΔG ΔG = ΔH - T ΔS 8 Free Energy and Spontaneity

9 ΔG: Equations of Free Energy Gibbs Free Energy can be used to determine the Standard free energy ( ) of formation ΔG = ΔH - T ΔS ΔG f = ΔH f - T ΔS f Standard State f -formation from elements If data is not for formation process, then equation is slightly adjusted according to: ΔG = ΔH - T ΔS Or from tabulated thermodynamic data: ΔG rxn = Σ n Δ G f (prod) - Σ n Δ G f (react) 9 Free Energy and Spontaneity

10 ΔG: Evaluation of Free Energy Consider the calculation for the following reaction: CH 3 OH (g) + O 2 (g) g CO 2 (g) + H 2 O (g) Determine ΔG rxn ΔH rxn ΔS rxn ΔG rxn 2 CH 3 OH (g) + 3 O 2 (g) g 2 CO 2 (g) + 4 H 2 O (g) Evaluate by: ΔG rxn = ΔH rxn - T ΔS rxn ΔX rxn = Σ n Δ X f (prod) - Σ n Δ X f (react) Or ΔG rxn = Σ n Δ G f (prod) - Σ n Δ G f (react) 10 Free Energy and Spontaneity

11 Temperature Affect on Free Energy Temperature influence on Free Energy and Spontaneity ΔG = ΔH - T ΔS both ΔH, ΔS (+) ie., (1000.0) (1.0) lg. # sm. # What is the sign of ΔG? Temperature will dictate outcome of ΔG. T low : Temperature small ΔH - T ΔS g ΔG (+) dominates negligible nonspontaneous T high : Temperature large ΔH - T ΔS g ΔG (-) negligible dominates spontaneous 12 Free Energy and Spontaneity

12 Phase Change Process What determines the spontaneity of a phase change? Endo ΔH(+) ΔH: s l g Exo ΔH(-) ΔS(+) ΔS: s l g ΔS(-) Two factors competing: Endo ΔH(+) Exo ΔH(-) ΔS(+) ΔS(-) Which factor dominates will determine phase change. Note: In a phase change: s D l is at equilib. or ΔG = 0 0 = ΔH - TΔS ΔH = TΔS With signs for ΔH & ΔS are the same T = ΔH ΔS 13 Free Energy and Spontaneity

13 Temperature Relationship and ΔG Consider Temperature affect on thermodynamic parameters ΔH -T ΔS T ΔG Spontaneity a - + all - spon: T not impt b + - all + nonspon: T not impt c - - low - spon: ΔH impt d - - high + nonspon: ΔS impt e + + low + nonspon: ΔH impt f + + high - spon: ΔS impt From this table, a spontaneous process can be made nonspontaneous i.e., c & d by increasing Temperature. 14 Free Energy and Spontaneity

14 Spontaneity: Example Example 19.35c B&L: (c) E + N 2 F 4(g) g 2NF 2 (g) ΔH - T ΔS ΔG 85 kj 198 J/K Example 12.8 Reger: (c) What temp will spontaneity switch for the rxn: N 2 (g) + 3H 2(g) D 2NH 3 (g) + E ΔH - T ΔS ΔG - 92 kj J/K To go from spontaneous to nonspontaneous, ΔG = 0 T = - 92kJ = K below spontaneous kj / K above, nonspontaneous 15 Free Energy and Spontaneity

15 Free Energy and work Science and Technology use physical and or chemical processes because these can do work. Economics: To make money $, the work to be preformed must be possibe and efficient. ΔG provides information on spontaneity: ΔG (+) or (-) provides information on the spontaneity of the ΔP, ΔT = 0 Wasting time: ΔG is useful because it prevents the wasted effort on process with no inherent tendency to occur. ΔG isn t whole story, Kinetics also important: Note that thermodynamically favorable process may still not occur to any appreciable extent because of the Kinetics. (That is why many reactions are carried out at high temperatures even if it is not necessary) - It makes sense to find a catalyst to speed up the reaction. - Prevents wasting time and resource of seeking a catalyst on a reaction that won t even work. 17 Free Energy and Spontaneity

16 ΔG indicator of efficiency In addition, ΔG yields how much work can be done by a given process. ΔG = w ΔP, ΔT = 0 : In fact the maximum possible useful work when ΔP, ΔT = 0, equals the change in free energy ΔG for that system Note: w max = ΔG = ΔH - TΔS ΔG : For spontaneous process, this represents the energy free to do useful work ΔH : Internal energy and ΔP = 0 TΔS: Less energy available due to Entropy On the other hand, for nonspontaneous process, ΔG provides information on the minimum amount of work that must be expended to make the process occur. ΔG c Indicator of how close the process is to 100% efficiency. Consider: Gasoline burning- C 8 H 18 (l) + 25/2 O 2 (g) g 8CO 2 (g) + 9 H 2 O (g) ΔH sys < 0 and ΔS sys > 0 Portion of gasoline which does work is ΔG less that 30% of the gasoline internal energy is ΔG. Why? 18 Free Energy and Spontaneity

17 100% Efficiency is Never Attained 19 Free Energy and Spontaneity

18 Free Energy and The Laws of Thermodynamics 1. Conservation of Energy You can t win you can only break even 2. Entropy of the Universe is increasing You can t even break even 21 Free Energy and Spontaneity

19 Free Energy Physical Meaning ΔG or = Δ H - T Δ S ΔH = Δ G + T Δ S Work available (Internal Energy) Work that is useful Less the heat lost Gasoline internal Energy through chemical bonds Turn wheels and charge battery and so on Heat from engine and outside air leading to increase motion of the particles in the universe 22 Free Energy and Spontaneity

20 Wide Range of Energy Efficiency Engineers consider the efficiency of a device as that percentage of the energy input that results in a work output. The range of efficiencies is enormous in our society. Incandescent light bulb η = 5% of incoming electrical energy Large Electrical generator η = 99% Others Device η (efficiencies) Dry Cell battery 90% home oil furnace 65% hand-tool motor 63% Liquid fuel rocket 50% car engine <37% fluorescent lamp 20% solar cell 29% (limit) 23 Free Energy and Spontaneity

21 Application to Energy Crisis Why do we have an energy crisis? There should be no problem since there is an abundant supply from the sun and energy is conserve. All form of energy we receive is from one source Hydrodynamics, wind/weather, fossil fuel/coal - our sun. Main problem with our perception of the energy crisis is the availability of useful energy. Concentrated form is ultimately turning to dilute, useless form. The hierarchy of energy is sun, plant, oil, batteries, heat. When we use energy, we degrade its usefulness. We are rapidly consuming concentrated form of energy i.e., fossil fuel. 24 Free Energy and Spontaneity

22 In Planet Earth: USA utilization of Energy US represent 5% of the population yet consumes ~30% of world energy. 80% of our energy comes in the form of petroleum (fossil fuel) Hostage of our Addiction: In the 70 s and 80 s, USA was held hostage by our addition of black liquid gold. Fossil fuel is a nonrenewable resource and is being consumed 100,000 times faster than it can be formed. Origins of Fossil Fuel: Plants and animal are the main source. C m H n with some N,S & O Combustion of hydrocarbon yields Energy and CO 2 Other emission yield is SO 2, SO 3, NO, N x O y which contributes to acid rain. Catalytic converters are needed for automobile. Links: 1. Life after the oil crash The end of cheap oil Book review, War Politics and oil or Lack of it Oil Crisis Free Energy and Spontaneity

23 H 2 O (l) D H 2 O (g) Free Energy versus Evaporation of Water ΔG =? Key is the vapor pressure of water. 26 Free Energy and Spontaneity

24 Concentration and Free Energy For a system (substance) not at standard state Concentration must be considered - H 2 O (l) D H 2 O (g) ΔG > 0, yet water evaportate G = G + RT lnp Correction term G - Free energy of the substance G - Free energy in its standard state R - Gas constant (8.314 J /mol K) T - Absolute Temperature (K) P - Partial Pressure (Atm) For a reaction not at standard state: ΔG = ΔG + RT ln[prod x /React y ] Note: [P x /R y ] = Q (Reaction quotient) Therefore: ΔG rxn = ΔG rxn + RT ln Q 27 Free Energy and Spontaneity

25 Consider, H 2 O (l) D H 2 O (g) ΔG = ΔG + RT lnp Vaporization H 2 O standard condition, ph 2 O = 1.0 atm, ΔG = atm 3G=(+) ΔG = ΔG + RT ln [ 1.0 ] ΔG = 8.59 kj + RT ln[ 1.0 ] = 8.59 kj, ΔG >0, not 25 C, ph 2 O = atm (100 % humidity) 3G=(0) ΔG = ΔG + RT ln [ ] ΔG = 8.59 kj + (8.314 J/mol K) * K ln[ ] = 0 kj, 25 C, ph 2 O = atm (Dry air) 3G=(-) ΔG = ΔG + RT ln [ ] ΔG = 8.59 kj + (8.314 J/mol K) * K ln[ ] = -4.5 kj /mol 28 Free Energy and Spontaneity

26 Free Energy and Equilibrium Constant to determine Spontaneity Both Free energy change and equilibrium constants can be used to determine direction of spontaneity. Spontaneity versus Product favored reaction Q < K eq K eq Q > K eq Q Neg ΔG(-) Forward Pos ΔG(+) Reverse ΔG ΔG = ΔG + RT ln [Q/K] Q ΔG Direction Rxn Q < K, [R](i ) [P](h ) decr Forward (-) Forward Q > K, [R](i ) [P](h ) incr Reverse (+) Reverse 31 Free Energy and Spontaneity

27 Relationship Between K eq and ΔG What is the relationship between Free Energy (ΔG) and a system at Equilibrium (K eq )? ΔG = ΔG + RT ln (Q) at equilibrium, Q = K eq and ΔG = 0 but ΔG 0 0 = ΔG + RT ln K eq therefore, ΔG = - RT ln K eq Rearranging for K eq K eq = Exp {-ΔG /RT} 32 Free Energy and Spontaneity

28 K eq & ΔG : Example Determine K p at 298 K for the reaction: 3 C 2 H 2 (g) D C 6 H 6 (g) ΔG(kJ/mol) K p = Exp -{[ ( )] / ( )} Exp {+201} = Free Energy and Spontaneity

29 Free Energy and Equilibrium Constant to determine Spontaneity Relationship between ΔG and K at 298 K ΔG = ΔG + RT ln [Q/K] ΔG K Significance e-36 Hardly any forward reaction e e e-1 Forward and reverse 0 1 proceed to same extent e e17 Forward reaction goes towards completion e35 hardly any reverse reaction 34 Free Energy and Spontaneity

30 In Class Exercise (or take home) In an equilibrium mixture the following reaction at 345 C occur: CO (g) + H 2 O (g) D CO 2 (g) + H 2 (g) The mole fraction of gases were found to be: χ CO 2 = χ H 2 = 0.320, χ CO = 0.133, and χ H 2O = 0.347, i) What is ΔG for the reaction at 345 C? ii) What is ΔG for the reaction? iii) In what direction will a net reaction occur if one brings together mol CO, mol H 2 O, mol CO 2 and mol H 2 and allows them to come to equilibrium? iv) What is the composition of the equilibrium mixture obtained by the reaction in (iii)? 35 Free Energy and Spontaneity

31 CO (g) + H 2O (g)! CO 2 (g) + H 2 (g) [e] K eq = (.320) 2 (.347) (.133) = 2.219, ΔG = - RTln (K eq) = - (8.314) ( 618) ln = J ΔG = 0 by definition when a reaction is at equilibrium. CO (g) + H 2 O! CO + H (g) 2 (g) 2 (g) [i] (.145) (.226) Q = (.085) (.112) = 3.96, Q > K eq, Rxn proceeds to left CO (g) + H 2 O! CO + H (g) 2 (g) 2 (g) [i] Δ - x - x + x + x [e] x x x x 2 ( x) ( x) x + x K eq = = = ( x) ( x) x + x ( x 2 ) = x + x x x2 = x + x x x = 0 x = , , real solution is Confirm results ( x) ( x) K eq = = ( ) ( ) = = ( x) ( x) ( ) ( ) In Class Exercise (or take home) In an equilibrium mixture the following reaction at 345 C occur: CO (g) + H 2 O (g) D CO 2 (g) + H 2 (g) The mole fraction of gases were found to be: χ CO 2 = χ H 2 = 0.320, χ CO = 0.133, and χ H 2O = 0.347, i) What is ΔG for the reaction at 345 C? ii) What is ΔG for the reaction? iii) In what direction will a net reaction occur if one brings together mol CO, mol H 2 O, mol CO 2 and mol H 2 and allows them to come to equilibrium? iv) What is the composition of the equilibrium mixture obtained by the reaction in (iii)? 36 Free Energy and Spontaneity

32 Temperature Dependent on K eq via Free Energy ΔG = -RT ln K ΔG = ΔH -T ΔS -RT ln K = ΔH -T ΔS ln K = - (ΔH /RT) + ( ΔS /R) lnk = ΔH rxn R $ & % 1 T ' ) + ΔS rxn ( R Plot of lnk vs 1/T yields ΔH and ΔS 37 Free Energy and Spontaneity

33 Summary of ThermoChemistry & Thermodynamics 38 Free Energy and Spontaneity

34 ΔG Equations ΔG - nfe ΔH - Τ ΔS - RT ln K eq Σ n ΔG prod - Σ n ΔG rxn ΔG - RT ln Q 39 Free Energy and Spontaneity