If we define If we define GGii = G= G°° ( P ( Pii = 1 = 1 atmatm ) then ) then where Pwhere Pff must be expressed in atmospheres. must be expressed in atmospheres.In general for 1 mole ideal gas In general for 1 mole ideal gas Shows how G depends on P at fixed T if know GShows how G depends on P at fixed T if know G°°(T).(T).To distinguish G for 1 mole, call it To distinguish G for 1 mole, call it mm (T, P) = (T, P) = mm°° (T) + RT (T) + RT lnln P Pmm is free energy/mole for an ideal gas at T and P. (Called chemicalis free energy/mole for an ideal gas at T and P. (Called chemicalpotential) potential) Consider now the Chemical reaction:Consider now the Chemical reaction:For n moles nFor n moles nmm = n = nmm°° + + nRT lnnRT ln P P DDG = G = cc[[mmCC°° + RT + RT lnln P PCC] + ] + dd[[mmDD°° + RT + RT ln ln PPDD] - ] - aa[[mmAA°° + RT + RT ln ln PPAA] - ] - bb[[mmBB°° + RT + RT ln ln PPBB]]Free Energy for 1 moleFree Energy for 1 moleof ideal gas D at a partialof ideal gas D at a partialpressure of Ppressure of PDDTrue for True for arbitraryarbitrary values of P values of PCC, P, PDD, P, PAA, P, PBBSince initial and final states are in Since initial and final states are in eqeq. . ∆∆G is not G is not negneg for either for either direction. direction. \\ ∆∆G = 0G = 0fifiDDG = G = DDGG°° + + ccRT lnRT ln P PCC + + ddRT ln RT ln PPDD - - aaRT ln RT ln PPAA - - bbRT ln RT ln PPBBBut But KKpp = = {({(PPCeqCeq))cc ((PPDeqDeq ) )dd/(/(PPAeqAeq))aa ((PPBeqBeq))bb}!}!Remarkably important formula relates free energy and Remarkably important formula relates free energy and KKpp. . ∆∆GG°° = -RT = -RT ln Kln Kpp∆∆GG°° > 0 > 0 ÆÆ exponent < 0 exponent < 0 KKpp < 1 < 1KKpp = e = e --∆∆GG°°/RT/RT = = 1010 --∆∆GG°°/2.303RT/2.303RTBonus * Bonus * Bonus * Bonus * Bonus * Bonus * Bonus * Bonus * BonusBonus * Bonus * BonusRemember old rule for shift in Remember old rule for shift in eqeq. with T. Equilibrium shifts. with T. Equilibrium shiftsto left for an exothermic reaction and to right for an to left for an exothermic reaction and to right for an endothermic reaction.endothermic reaction.Shift in Equilibrium with temperature:Shift in Equilibrium with temperature:∆∆HH°° < 0 means heat released (exothermic) < 0 means heat released (exothermic)A A ÆÆ B + heat B + heatThink of heat as a reagent that works like common ion effect:Think of heat as a reagent that works like common ion effect:A A ÆÆ B + heat B + heat ∆∆HH°° > 0 heat absorbed (endothermic) > 0 heat absorbed (endothermic)heat + A heat + A ÆÆ B B Increasing T causesIncreasing T causes ∆∆HH°°/RT/RT and henceand hence ee++∆∆HH°°/RT/RT to get smaller. to get smaller. KKp p increases and equilibrium shifts to right. increases and equilibrium shifts to right. KKpp = e = e --∆∆HH°°/RT/RT e e ∆∆SS°°/R/R ∆∆HH°° < 0 means heat released (exothermic) < 0 means heat released (exothermic)A A ÆÆ B + heat B + heatConnecting Kinetics and Connecting Kinetics and EquilibriaEquilibriaBy definition, By definition, kinetic processeskinetic processes are not are not equilibrium processesequilibrium processes..In fact, we may think of kinetic processes as the mechanismIn fact, we may think of kinetic processes as the mechanismthat nature uses to reach the that nature uses to reach the equlibriumequlibrium state. state.kkff[A][A]ee[B][B]ee==kkrr[C][C]ee[D][D]ee (Equilibrium condition) (Equilibrium condition)Where [A]Where [A]e e etc. are the equilibrium concentrationsetc. are the equilibrium concentrationsof [A] etc. of [A] etc.Using the Using the ArrheniusArrhenius form for the rate constants form for the rate constants kkff and and kkrrBut as we just learned (or you already knew from high school):But as we just learned (or you already knew from high school):Where Where DDHH0 0 is the enthalpy change for the reaction and is the enthalpy change for the reaction and DDSS00 is the is theentropy change for the reaction. entropy change for the reaction. DDGG0 0 is the Free Energy is the Free Energy kkff==AAffee-- E EAfAf//RTRTkkrr==AArree--EEArAr//RTRTEquating these two forms for the equilibrium constant allows usEquating these two forms for the equilibrium constant allows us to connect thermodynamics and kinetics! to connect thermodynamics and kinetics!A + BA + BActivated StateActivated StateEEAfAfEEArArC + DC + D++∆∆HHoo = = EEAfAf - - EEArAr((∆∆HHoo = Enthalpy = Enthalpy change for change forA+B A+B ÆÆC+D)C+D)}}((AAff//AArr) exp [-() exp [-(EEAfAf--EEArAr)/RT] =)/RT] = {e {e ((DDSS°°/R)/R)} } •• { e { e (-(-DDHH°°/RT)/RT)}}Chemical BondingChemical BondingHydrogen atom based atomic Hydrogen atom based atomic orbitalsorbitals a.k.a. hydrogen atom a.k.a. hydrogen atom wavefunctionswavefunctions: 1s, 2s, 2p, 3s, 3p, 3d, : 1s, 2s, 2p, 3s, 3p, 3d, …………..yy1s1s = 1/( = 1/(pp))1/21/2(1/a(1/a00))3/23/2 exp[-r/a exp[-r/a00], a], a00=Bohr Radius = 0.529 Angstroms=Bohr Radius = 0.529 Angstroms••xxyyzzNucleusNucleus••rrElectronElectron((xx,,yy,,zz))rr22==xx22++yy22++zz22OrbitalsOrbitals, , Wavefunctions Wavefunctions and Probabilitiesand ProbabilitiesThe orbital or The orbital or wavefunction wavefunction is just a mathematical function is just a mathematical function that can have a that can have a magnitudemagnitude and and signsign (e.g. + 0.1 or -0.2) at a (e.g. + 0.1 or -0.2) at a given point r in space.given point r in space.Probability of finding a 1s electron at a particular point in Probability of finding a 1s electron at a particular point in space is often not as interesting as finding the electron space is often not as interesting as finding the electron in a thin shell between r and r+in a thin shell between r and r+drdr..OrbitalsOrbitals, , Wavefunctions Wavefunctions and Probabilitiesand ProbabilitiesProbability of finding a 1s electron in thin shell Probability of finding a 1s electron in thin shell between r and r+between r and r+drdr::ProbProb(r,r+(r,r+drdr) ~ ) ~ yy1s1s yy1s1s [r [r22]]drdr•rrr+r+drdrVolume of shell of thickness Volume of shell of thickness drdr::[r>>>dr Æ 3r2dr>>> 3r(dr)2+(dr)3 ]dV = (4/3)p [(r)3+3r2dr+ 3r(dr)2+(dr)3 - r3]dVdV≈≈(4(4p)[r2dr]Bonding in Diatomic Molecules such as HBonding in Diatomic Molecules such as H22••••••••rr11rr22H Nucleus AH Nucleus AH Nucleus BH Nucleus Byy1s1s(A) = 1/((A) =