1Week 15 CHEM 1310 - Sections L and M 1Entropy & Physical Changes Entropy is dependent on temperatureS = kB ln Ω∆ S = qrev / T1 21 22121ln at constant Pressureln at constant VolumeT T pT T VTS nCTTS nCTÆÆÊ ˆD =Á ˜Ë ¯Ê ˆD =Á ˜Ë ¯Show explanation on board:Week 15 CHEM 1310 - Sections L and M 2Entropy & Physical Changes Entropy changes are also associated withchanges in phasefusrevHqST TDD = =Calculate the change in entropy that occurs when asample containing 1.00 mol of ice is heated from–20°C to +20°C at 1 atm pressure.The molar heat capacities of H2O(s) and H2O(l) are38.1 JK-1mol-1 and 75.3 J K-1mol-1 respectively and theenthalpy of fusion (melting) is 6.01 kJ mol-1 at 0°C.Show on boardWeek 15 CHEM 1310 - Sections L and M 3• Use calorimetry• Measure cp vs T• Deduce molar absoluteentropy – J K-1 mol-1• If phase change occursfrom 0  T, then add ΔSof phase transitionΔ Svap = Δ HvapTbExampleMeasuring Entropy2Week 15 CHEM 1310 - Sections L and M 4Sº increases are you read down a Group.Sº is similar across a Period.Ssolid < S liquid < SgasKnow this!Standard Molar EntropiesWeek 15 CHEM 1310 - Sections L and M 5Δ Sreaction = Sproducts - SreactantsΔSrxn° = ΣS°products – ΣS°reactantsa A + b B → c C + d DStandard molar entropy valuesS° in units JK-1mol-1Entropy of a ReactionWeek 15 CHEM 1310 - Sections L and M 6• 1st Law of Thermodynamics– In any process, the total energy of the universe remainsunchanged: energy is conserved• 2nd Law of Thermodynamics– S, the entropy of a universe, must increase– Δ Suniv = (Δ Ssys + Δ Ssurroundings) > 0Laws of ThermodynamicsΔSuniv > 0 SpontaneousΔSuniv = 0 EquilibriumΔSuniv < 0 Non-spontaneous3Week 15 CHEM 1310 - Sections L and M 7Entropy & SpontaneityWeek 15 CHEM 1310 - Sections L and M 8Gibbs’ Free Energy How are Enthalpy and Entropy related?G = H - T•S G has several names1. Gibbs function2. Gibbs free energy3. Free Enthalpy For the change in the Gibbs Energy of system, atconstant Temperature and PressureΔGsys = ΔHsys - T·ΔSsysWeek 15 CHEM 1310 - Sections L and M 9Recall the 2nd Law of ThermodynamicsΔSuniverse > 0 (spontaneous process)ΔSuniverse = ΔSsystem + ΔSsurroundingsThus, ΔSsystem + ΔSsurroundings > 0Gibbs’ Free Energy4Week 15 CHEM 1310 - Sections L and M 10ΔSsys - ΔHsysT> 0 Recall the 1st Law of ThermodynamicsΔHsurroundings = - ΔHsysΔSsystem + ΔSsurroundings > 0ΔHsurroundingsΔSsurroundings =Energy is conserved!T=- ΔHsystemTThus…Gibbs’ Free EnergyWeek 15 CHEM 1310 - Sections L and M 11Gibbs’ Free Energy ExpressionΔGsys = ΔHsys – Tsys ΔSsysΔSsys - ΔHsysT> 0 Multiply by T: TΔSsys - ΔHsys > 0 Multiply by -1: ΔHsys - TΔSsys < 0 Gibbs’ Free EnergyWeek 15 CHEM 1310 - Sections L and M 12Gibbs’ Free Energy ExpressionΔGsys = ΔHsys – Tsys ΔSsysIf ΔGsys < 0, then rxn is spontaneousIf ΔGsys = 0, then rxn is at equilibriumIf ΔGsys > 0, then rxn is non-spontaneousFor constant T and P!Therefore, both Δ S and Δ G are indicative of reaction spontaneity. Gibbs’ Free Energy5Week 15 CHEM 1310 - Sections L and M 13ΔGreaction = Gproducts - GreactantsΔG°rxn = Δ H°rxn – T Δ S°rxna A + b B → c C + d DΔG°f = Δ H°f – T Δ S°fStandard GibbsEnergy of Reaction:Standard Molar GibbsEnergy of Formation:ΔG°rxn = cΔG°f, for C + dΔG°f, for D - aΔG°f, for A- bΔG°f, for BAppendix DGibbs’ Energy ExpressionsWeek 15 CHEM 1310 - Sections L and M 14Gibbs’ Energy and TempWeek 15 CHEM 1310 - Sections L and M 15Δ H is negativeΔ S is positiveΔ G is negativeΔG°rxn = Δ H°rxn – T Δ S°rxnSpontaneousReactionTemp & Gibbs’ Free Energy6Week 15 CHEM 1310 - Sections L and M 16Δ H is positiveΔ S is negativeΔ G is positiveΔG°rxn = Δ H°rxn – T Δ S°rxnNon-spontaneousReactionTemp & Gibbs’ Free EnergyWeek 15 CHEM 1310 - Sections L and M 17Δ H is positiveΔ S is positiveΔ G is negative,when T is big!ΔG°rxn = Δ H°rxn – T Δ S°rxnSpontaneousReactionTemp & Gibbs’ Free EnergyWeek 15 CHEM 1310 - Sections L and M 18Δ H is negativeΔ S is negativeΔ G is negative,when T is small!ΔG°rxn = Δ H°rxn – T Δ S°rxnSpontaneousReactionTemp & Gibbs’ Free