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Spontaneity

Spontaneity. I am a sleepless Slowfaring eater Maker of rust and rot In your bastioned fastenings, I am the crumbler: tomorrow Carl Sandburg. Spontaneity, Entropy & Free Energy. First Law of Thermodynamics Basically the law of conservation of energy

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Spontaneity

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  1. Spontaneity I am a sleepless Slowfaring eater Maker of rust and rot In your bastioned fastenings, I am the crumbler: tomorrow Carl Sandburg

  2. Spontaneity, Entropy & Free Energy • First Law of Thermodynamics • Basically the law of conservation of energy • energy can be neither created nor destroyed • i.e., the energy of the universe is constant • the total energy is constant • energy can be interchanged • e.g. potential energy (stored in chemical bonds) can be converted to thermal energy in a chemical reaction • CH4 + O2 --> CO2 + H2O + energy • Doesn’t tell us why a reaction proceeds in a particular direction

  3. Spontaneity, Entropy & Free Energy • Spontaneous Processes and Entropy • Spontaneous processes occurs without outside intervention • Spontaneous processes can be fast or slow

  4. Spontaneity, Entropy & Free Energy • Thermodynamics • lets us predict whether a process will occur • tells us the direction a reaction will go • only considers the initial and final states • does not require knowledge of the pathway taken for a reaction

  5. Spontaneity, Entropy & Free Energy • Kinetics • depends on the pathway taken • tells us the speed of the process • depends on • activation energy • temperature • concentration • catalysts

  6. Spontaneity, Entropy & Free Energy • Spontaneous Processes • a ball rolls downhill, but the ball never spontaneously rolls uphill • steel rusts, but the rust never spontaneously forms iron and oxygen • a gas fills its container, but a gas will never spontaneously collect in one corner of the container. • Water spontaneously freezes at temperatures below 0o C

  7. Spontaneity, Entropy & Free Energy • What thermodynamic principle explains why these processes occur in one direction? • The driving force for a spontaneous reaction is an increase in the entropy of the universe

  8. Spontaneity, Entropy & Free Energy • Entropy • Symbol: S • A measure of randomness or disorder • The natural progression is from order to disorder • It is natural for disorder to increase • Entropy is a thermodynamic function • Describes the number of arrangements that are available to a system in a given state

  9. Spontaneity, Entropy & Free Energy • Entropy • The greater the number of possible arrangements, the greater the entropy of a system, i.e., there is a large positional probability. • The positional probability or the entropy increases as a solid changes from a liquid or as a liquid changes to a gas

  10. Spontaneity, Entropy & Free Energy • Ssolid < Sliquid < Sgas • Choose the substance with the higher positional entropy: • CO2(s) or CO2(g)? • N2(g) at 1 atm and 25oC or N2(g) at .010 atm and 25oC?

  11. Spontaneity, Entropy & Free Energy • Predict the sign of the entropy change • solid sugar is added to water • iodine vapor condenses onto a cold surface forming crystals

  12. Spontaneity, Entropy & Free Energy • Second Law of Thermodynamics • The entropy of the universe is increasing • The universe is made up of the system and the surroundings • DSuniverse = DSsystem + DSsurroundings

  13. Spontaneity, Entropy & Free Energy • A process is spontaneous if the DSuniverse is positive • If the DSuniverse is zero, there is no tendency for the reaction to occur

  14. Spontaneity, Entropy & Free Energy • The effect of temperature on spontaneity • H2O(l) --> H2O(g) • water is the system, everything else is the surroundings • DSsystem increases, i.e. DSsystem is positive, because there are more positions for the water molecules in the gas state than in the liquid state

  15. Spontaneity, Entropy & Free Energy • What happens to the surrounding? • Heat leaves the surroundings, entering the system to cause the liquid molecules to vaporize • When heat leaves the surroundings, the motion of the molecules of the surroundings decrease, which results in a decrease in the entropy of the surroundings • DSsurroundings is negative

  16. Spontaneity, Entropy & Free Energy • Sign of DS depends on the heat flow • Exothermic Rxn: DSsurr >0 • Endothermic Rxn: DSsurr< 0 • Magnitude of DS is determined by the temperature • DSsurr = - DH T

  17. Spontaneity, Entropy & Free Energy Signs of Entropy Changes DSsysDSsurr DSunivSpontaneous? + + - - + - - +

  18. Spontaneity, Entropy & Free Energy • Free Energy • aka Gibbs Free Energy • G • another thermodynamic function • related to spontaneity • G = H - TS • for a process that occurs at constant temperature (i.e. for the system): DG = DH - TDS

  19. Spontaneity, Entropy & Free Energy • How does the free energy related to spontaneity? DG = DH - TDS - DG = - DH + DS (remember, - DH = DSsurr ) T T T -DG = DSsurr + DSsys (remember, DSsurr + DSsys = DSuniv) T -DG = DSuniv T

  20. Spontaneity, Entropy & Free Energy • DSuniv > 0 for a spontaneous reaction • DG < 0 for a spontaneous reaction • DG > 0 for a nonspontaneous reaction • Useful to look at DG because many chemical reactions take place under constant pressure and temperature

  21. Spontaneity, Entropy & Free Energy • H2O(s) --> H2O(l) • DHo = 6.03 x 103J/mole • DSo = 22.1 J/K.mole • Calculate DG, DSsurr, and DSuniv at -10oC, 0oC, and 10oC

  22. Spontaneity, Entropy & Free Energy • For the melting of ice • DSsys and DSsurr oppose each other • spontaneity will depend on temperature • DSo is positive because of the increase in positional entropy when the ice melts • DSsurr is negative because the reaction is endothermic

  23. Spontaneity, Entropy & Free Energy • At what temperatures is Br2(l) --> Br2(g) spontaneous? • What is the normal boiling point of Br2? DHo= 31.0 kJ/mol DSo = 93.0 J/K.mol

  24. Spontaneity, Entropy & Free Energy • Entropy Changes in Chemical Reactions • Just like physical changes, entropy changes in the surroundings are determined by heat flow • Entropy changes in the system are determined by positional entropy (the change in the number of possible arrangements)

  25. Spontaneity, Entropy & Free Energy • N2 (g) + 3 H2(g) --> 2 NH3 (g) • The entropy of the this system decreases because • four reactant molecules form two product molecules • there are less independent units in the system • less positional disorder, i.e. fewer possible configurations

  26. Spontaneity, Entropy & Free Energy • When a reaction involves gaseous molecules: • the change in positional entropy is determined by the relative numbers of molecules of gaseous reactants and products • I.e., if you have more product molecules than reactant molecules, DS will be positive

  27. Spontaneity, Entropy & Free Energy • In thermodynamics, the change in a function is usually what is important • usually we can’t assign an absolute value to a function like enthalpy or free energy • we can usually determine the change in enthalpy and free energy

  28. Spontaneity, Entropy & Free Energy • We can assign absolute entropy values, i.e., we can find S • A perfect crystal at 0 K, while unattainable, represents a standard • all molecular motion stops • all particles are in their place • the entropy of a perfect crystal at 0 K is zero = third law of thermodynamics

  29. Spontaneity, Entropy & Free Energy • Increase the temperature of our perfect crystal • molecular motion increases • disorder increases • entropy varies with temperature • See thermodynamic tables for So values (at 298 K and 1 atm)

  30. Spontaneity, Entropy & Free Energy • Entropy is a state function • entropy does not depend on the pathway taken • DSrxn = SnDSoproducts- SnDSoreactant

  31. Spontaneity, Entropy & Free Energy • Calculate DSo at 25oC for • 2NiS(s) + 3 O2(g) --> 2 SO2(g) + 2 NiO(s) Substance So(J/K.mol) SO2 248 NiO 38 O2 205 NiS 53

  32. Spontaneity, Entropy & Free Energy • Calculate DSo for Al2O3(s) + 3 H2(g) --> 2 Al(s) + 3 H2O(g) Substance So (J/K.mol) Al2O3 51 H2 131 Al 28 H2O 189

  33. Spontaneity, Entropy & Free Energy • What did you expect the DSo to be? • Why is it large and positive? • H2O is nonlinear and triatomic • H2O has many rotational and vibrational motions • H2 is linear and diatomic • H2 has less rotational and vibrational motions • The more complex the molecule, the higher the DSo

  34. Spontaneity, Entropy & Free Energy • Free Energy and Chemical Reactions • Standard Free Energy Change • DGo • the change in the free energy that occurs if the reactants in their standard states are changed to products in their standard states • can’t be measured directly • calculate from other values • allows us to predict the tendency for a reaction to go

  35. Spontaneity, Entropy & Free Energy • How do we calculate DGo? • DGo = DHo - TDSo (for a reaction carried out at constant temperature) • Use Hess’ Law • Use DGof (standard free energy of formation) • DGo = SnDGof (products) - SnDGof (reactants)

  36. Spontaneity, Entropy & Free Energy • Calculate DGo for the reaction at 25oC 2SO2(g) + O2(g) --> 2 SO3(g) SubstanceDHof(kJ/mol)DSo(J/K.mol) SO2(g) -297 248 SO3 -396 257 O2 0 205

  37. Spontaneity, Entropy & Free Energy • Calculate DGo for the reaction Cdia --> Cgr using the following data: Cdia + O2 --> CO2(g) DGo = -397 kJ Cgr + O2 --> CO2(g) DGo = -394 kJ

  38. Spontaneity, Entropy & Free Energy • Calculate DGo for the reaction 2CH3OH + 3 O2--> 2 CO2 + 4 H2O SubstanceDGof(kJ/mol) CH3OH -163 O2 0 CO2 -394 H2O -229

  39. Spontaneity, Entropy & Free Energy • The dependence of free energy on pressure • How does pressure affect enthalpy and entropy? • Pressure does not affect enthalpy • Pressure does affect entropy because pressure depends on the volume • 1 mole of a gas at 10.0 L has more positions available than 1 mole of a gas at 1.0 L • Slarge volume > Ssmall volume • Slow pressure > Shigh pressure

  40. Spontaneity, Entropy & Free Energy • Given that G = DGo + RTln(P) • where G is the free energy at some P (not necessarily 1 atm) • where DGo is the free energy at 1 atm • Ex: N2(g)+ 3 H2(g) --> 2 NH3(g) (lots of equations…lots of equations…) • DG = DGo + RT ln Q • Q is the reaction quotient (from the law of mass action) • T is the temperature in K • R is the gas constant, 8.3145 J/mol.K

  41. Spontaneity, Entropy & Free Energy • Calculate DG at 25o C for the reaction CO(g) + 2 H2(g) --> CH3OH where carbon monoxide is 5.0 atm and hydrogen gas at 3.0 atm are converted to liquid methanol. • What does the answer tell us about this reaction under these conditions?

  42. Spontaneity, Entropy & Free Energy • Free Energy and Equilibrium • Equilibrium occurs at the lowest value of free energy available to the reaction system, i.e., when DG = 0 • At equilibrium, DG = 0, Q = Keq so DG = 0 = DGo + RT ln Keq DGo = - RT ln Keq • Use this equation to find Keq given DGo, or to find DGogiven Keq

  43. Spontaneity, Entropy & Free Energy • Relationship between DGo and Keq • DGo Keq • = 0 1 • < 0 >1 • > 0 < 1

  44. Spontaneity, Entropy & Free Energy • For N2 + 3 H2 --> 2 NH3, DGo = - 33.3 kJ per mole of N2 consumed at 25oC. Predict the direction in which the reaction will shift to reach equilibrium a. PNH3 = 1.00 atm, PN2 = 1.47 atm, PH2 = 1.00 x 10-2 atm b. PNH3 = 1.00 atm, PN2 = 1.00 atm, PH2 = 1.00 atm

  45. Spontaneity, Entropy & Free Energy • 4Fe + 3 O2 <====> 2Fe2O3Calculate the equilibrium constant using the following information: Substance DHof (kJ/mol) So(J/K.mol) Fe2O3 -826 90 Fe 0 27 O2 0 205

  46. Spontaneity, Entropy & Free Energy • Keq and temperature • We used Le Chatelier’s Principle to determine how Keq would change when temperature changes • Use DG to determine the new Keq at a new temperature • DGo = -RT ln K = DHo - TDSo ln K = - DHo.1 + DSo R T R

  47. Spontaneity Chart ∆S Spontaneous At high temp Nonspontaneous ∆H Spontaneous At all temps Nonspontaneous

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