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Unformatted text preview: ENTROPY AND SPONTANEITY HYPOTHESIS: if S is positive, the reaction will be spontaneous TEST THIS HYPOTHESIS Which of these processes are spontaneous as written? H2O(l) (at 25) H2O(g) Ag+(aq) + Cl-(aq) AgCl(s) Mg(s) + O2(g) MgO(s) S S S MJ Bojan Chem 112 1 Determining ReacLon Spontaneity using S What is S for: Mg(s) + O2(g) MgO(s) 1 atm, 298 K Calculate using absolute entropy S= So (MgO) = 26.8 J/mol-K So (Mg) = 32.6 J/mol-K So (O2) = 205.0 J/mol-K Do you think this reacLon is spontaneous? Is this a contradicLon to the second law of thermodynamics? MJ Bojan Chem 112 2 Entropy considering surroundings The entropy change of Mg(s) + O2(g) MgO(s) is not the only entropy change which occurs. This is only Ssystem ! Remember the 2nd Law: How do I find Ssurroundings ? The surroundings will absorb a quanLty of heat, qsurr equal to the heat energy given off by the reacLon: qsurr = -qsys = -Hsys (at constant T and atmospheric P) Ssurr = MJ Bojan Chem 112 3 Entropy considering surroundings Calculate (or look up) H for the reacLon: Mg(s) + O2(g) MgO(s) Hf (MgO) = 601.8 kJ/mol This reacLon is EXOTHERMIC Ssurroundings = Hsys / T = Suniverse = Ssystem + Ssurroundings > 0 The second law of thermodynamics is obeyed! MJ Bojan Chem 112 4 CRITERIA FOR SPONTANEITY H S Exothermic reactions (H <0) are usually spontaneous. Spontaneous if Ssystem + Ssurroundings > 0 We need a new state function that can predict spontaneity. This is called the Free Energy: G = H - TS T is absolute temperature (in K). G refers to a reaction at constant T and P. Criteria for spontaneity G < 0 Spontaneous G > 0 Not spontaneous G = 0 System at equilibrium. MJ Bojan Chem 112 5 Gibb's Cute Trick Second Law of Thermodynamics: Suniv = Ssystem + Ssurroundings > 0 (spontaneous) At constant temperature and pressure: Ssurroundings = qsys/T = Hsystem / T So now: Suniv = Ssystem Hsystem / T MulLply both sides by (T): TSuniv = Hsystem TSsystem By Gibb's definiLon: Gsystem = Hsystem TSsystem Therefore, at constant Temperature and Pressure: Gsystem = TSuniv MJ Bojan Chem 112 6 PotenLal Energy and Free Energy MJ Bojan Chem 112 7 STANDARD FREE ENERGY OF FORMATION Gf Free energy change in forming one mole of a compound from its elements each in their standard states. Standard States: Solid Liquid Gas Solution Elements Temperature Pure solid Pure liquid 1 atm pressure 1M solution Gf = 0 Usually 25C Units: Gf: kJ/mole Hf: kJ/mole S: J/mole-K MJ Bojan Chem 112 8 STANDARD FREE ENERGY STANDARD FREE ENERGY OF REACTION: Use tables of Gf at 298K. Grxn = Gf(prods) - Gf(reactants) Example What is Grxn for: AgCl(s) Ag+(aq) + Cl-(aq) Gfo -109.7 +77.1 -131.2 (kJ/mol) from Appendix C MJ Bojan Chem 112 9 STANDARD FREE ENERGY For other temperatures: Grxn Hrxn - TSrxn H and S do not vary much with T, BUT G does!!! Use tables of Hf and S to find Hrxn and Srxn and plug in to Grxn at a specific T. MJ Bojan Chem 112 10 EFFECT OF TEMPERATURE ON FREE ENERGY G = H - TS H and S do not change substantially with temperature, but G does. H S G Spontaneous? MJ Bojan Chem 112 11 Is it Spontaneous? 1. 2C8H18 + 25O2 16CO2+ 18H2O Burning gasoline + G 0 Ho So 2. Heat + CaCO3 (s) CaO (s) + CO2 (g) limestone lime - + G 0 Ho So - Chem 112 12 MJ Bojan Is it Spontaneous? 3. 2 H2(g) + O2 (g) 2H2O (g) Fuel cell + G 0 Ho So - ozone 4. 3 O2(g) 2 O3(g) oxygen + G 0 Ho So - Chem 112 13 MJ Bojan Q. Is this reaction spontaneous at 298 K? At 1100 oC? CaCO3(s) CaO(s) + CO2(g) So 92.88 39.75 213.6 (J/mol K) Hfo -1207.1 (kJ/mol) -635.3 -393.5 MJ Bojan Chem 112 14 CombusLon of Sucrose C12H22O11(s) + 8 KClO3(s) 12 CO2(g) + 11 H2O(l) + 8 KCl(s) Is this reac;on spontaneous? How does H2SO4 affect the reac;on? What are two possible reasons for using high T to carry out a reac;on? MJ Bojan Chem 112 15 Phase Changes During phase changes temperature is a constant. (Heat transfer is reversible qrev) Phase transfer S is always positive at melting or boiling. Disorder increases. G = ??? Entropy and heat: Strans = qrev = Htrans T T e.g., for melting ice, Sfus = Hfus/273 K (endothermic) + + m.p.= 0C MJ Bojan Chem 112 16 Free Energy at Equilibrium Calculate the boiling point of bromine. Hovap 31.0 (kJ/mol) Sovap 92.9 (J/mol-K) MJ Bojan Chem 112 17 Extent of reac;on So far we have considered only standard conditions and Ho, So, Go and how to estimate Go at different T. What happens under other conditions? G = G + RT ln Q G = G + 2.303 RT log10Q aA + bB cC + dD ! [C ] [ D] Q = [ A ] a [ B] b c d REACTION QUOTIENT MJ Bojan Chem 112 18 Extent of reac;on AgCl(s) Ag+(aq) + Cl-(aq) 1) Is this spontaneous under standard conditions? Grxn = +55.6 kJ/mol 2) What if [Ag+] = [Cl-] = 1 10-10M at 298K? Grxn = G + RT ln Q MJ Bojan Chem 112 19 Free Energy and the Equilibrium Constant AgCl(s) Ag+(aq) + Cl-(aq) 3) What if [Ag+] = [Cl-] = 1.34 10-5 M at 298K? G = G + RT ln Q MJ Bojan Chem 112 20 RELATIONSHIP BETWEEN G AND Keq G = G + RT ln Q At equilibrium, G = Q= G > 0 G < 0 G = 0 Keq < 1 Keq > 1 Keq = 1 MJ Bojan Chem 112 21 Free Energy and Equilibrium MJ Bojan Chem 112 22 ANALOGY BETWEEN POTENTIAL ENERGY AND FREE ENERGY Go slope = 0 At equilibrium point, G = 0 for interconverting reactants products Note: This does NOT mean Go = 0 RELATIONSHIP BETWEEN G AND G G = G + RT lnQ How do concentrations affect Q and G? Q Add more reactants Take away products Take away reactants Is this consistent with LeChatelier's Principle? MJ Bojan Chem 112 24 G rxn direction Equilibrium Constant Calculation What is the solubility product constant Keq of AgBr at 25oC? AgBr(s) Ag+(aq) + Br-(aq) Gfo Gfo Gfo Ag+ (aq) Br- (aq) AgBr (s) 77.1 kJ/mol -104 kJ/mol -96.9 kJ/mol MJ Bojan Chem 112 25 RELATIONSHIP BETWEEN G AND WORK For a spontaneous process, G = Wmax = The maximum work that can be obtained from a process at constant T and P. For a non-spontaneous process, G = Wmin = The minimum work that must be done to make a process go at constant T and P. What is "free" about Free Energy? G is how much work can be done by a process and is the portion of the energy change of a spontaneous reaction that is free to do useful work. But in actuality, not all of this "free energy" will be able to be used to do work. Some the energy enters the environment as heat. MJ Bojan Chem 112 26 Work done in a Combustion Reaction Calculate the maximum energy available from the oxidation of octane at 25 oC and 1 atm. C8H18(l) + 12.5 O2(g) 8CO2(g)+ 9H2O(l) Gfo 17.3 kJ/mol 0 -394.4 -237.2 MJ Bojan Chem 112 27 PredicLng The Sign of H 1) 2) 3) 4) 5) 6) Combustion (burning) = exo Breaking multiple bonds = endo Phase changes s l g = endo Opposite processes (g l s) = exo Measured T OR heat given off = exo Measured T OR heat added = endo Other than these cases, you must calculate H PredicLng The Sign of S S is positive (disorder increases) when: 1) # molecules of gas during a reaction 2) Phase changes s l g 3) Solid dissolves in solution 4) # particles during a reaction 5) # atoms in a molecule is larger 6) T increases MJ Bojan V increases Chem 112 7) 28 PredicLng The Sign of Grxn (Spontaneity) 1) If you can predict the signs of H and S, draw an energy diagram. Is G ALWAYS posiLve or negaLve? 2) If you can't predict the signs of Hrxn and Srxn, calculate them using Hof and Sof in the appendix. 3) Calculate Grxn using the calculated Hrxn and Srxn; is it posiLve or negaLve? 4) At equilibrium, Grxn=0. MJ Bojan Chem 112 29 ...
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