Formulas and constants, 12/15/2009 R = 8.3145 J/K·mol = 0.08205 L·atm/K·mol = 1.987 cal/K·mol F = 96,500 J/mol·V e = 1.060 × 10-19 C kB = 1.38 × 10-23 J/K h = 6.626 × 10-34 J·sec c = 3.0 × 108 m/sec me = 9.11 × 10-31 kg mp = 1.67 × 10-27 kg 1 J = 1 N⋅m = 1 kg⋅m2/s2 = 0.239 cal = 9.87 × 10-3 L·atm 1 cal/K = 1 eu 1 atm = 1.01 × 105 Pa = 760 torr xxe303.210 =, xx log303.2ln = fTkDB= afsphereπη6= K,,TPwVv⎟⎠⎞⎜⎝⎛∂∂= mvVeff⎟⎠⎞⎜⎝⎛+=ρδ ()fmvrustρω−==12 dtrds212log303.2ω= ()ρvDRTsM−=1 ()()2022021ln rrRTvMcc−−=ωρ v = dc/dt = f([A], [B], [C], …) [A] = [A0] – k0t ln[A] = ln[A0] – k1t tkAA20][1][1+= 1,])[1(1])[1(1101≠+−=−−−ntkAnAnnnn12/12lnkt = ][1022/1Akt = 1012/1][)1(12−−−−=nnnAknt Keq = kf/kr ()RTHRSBRTEeehTkAekAmmΔ−Δ−==⎟⎟⎠⎞⎜⎜⎝⎛−−=121211lnTTREkkA ()ABANDDrk+=0max4π K.E. = ½ mu2 = hν - Φ λ = h/p = h/mu ννλncc== λνhchE == 2,2hh≥ΔΔ≥ΔΔ tEpx Ψ=Ψ+Ψ∇− EUm222h ∫Ψ= dVP2 ⎟⎠⎞⎜⎝⎛=Ψ xananπsin2 2228manhEn= Ψ=Ψ−Ψ∇− ErZemhe22228π ),()(),,(φθφθYrRr=Ψ atomJnRZnZeEn2222242−=−=hμatomJnZ21821018.2−×−= lceItIα−=0)( ll ccIIεα−=−=303.2log0 0IIT = A = εcℓ TA log−= ][][ GkQkkkkkeQptf++++=k1=τ τtiniteEE−= *][*][ absorbedphotonsemittedphotonsEQf # #.. ==φ fffkkττφ== DADdTTFRETkkkEφφ+−=+= 1 606601rrrDAD+=−=+ττ ⎟⎟⎠⎞⎜⎜⎝⎛−Δ−=1201211lnTTRHKK ΔG = -neFε QFnRTeln0−=εε eqeKFnRTln0=ε ⎟⎟⎠⎞⎜⎜⎝⎛−Δ−=121211lnTTRHPPvap Psolvent=asolventPsolvent,pure Π = cRT Π=wRTM freezefreexesolvfreezemKmHRTMTT =Δ=−1000200boilvapsolvboilmKmHRTMTT =Δ=−1000200 ΔΦ+=Δ zFaaRTinAoutAA,,lnμ inAoutAinouteqaazFRT,,ln−=Φ−Φ=ΔΦ2,1,01,02,0lnsolvsolvaaAaaRT=−=Δμμμ totbndPL][][=ν][][][1][LKLNLKLNKDAA+=+=ν ][][][1][LKLLKLKfDAA+=+= ννAAKNKL−=][ fKKLfAA−=][ nAnALKLKf][1][+= AKLnfflog]log[)1(log +=−Formulas and constants, 12/15/2009 ()∑∑==++=>=<NiiiiNiizyxNdNd122212211 <xo2> = 2Dτ <d2> = 2Dt, 4Dt or 6Dt DtxeDtcc4024−=π ∑=−−=NjTkUjTkUiiBjBiegegP1 TkmuBBeuTkmuF222324)(−⎟⎟⎠⎞⎜⎜⎝⎛=ππ K.E. = ½ mu2 TkNRTEKBA2323.. == mTkuBpm2..= mTkuBavπ8= mTkuBrms3= MRTVNz24σπ= MRTVNZtot222σπ= 221σπ⎟⎠⎞⎜⎝⎛=><=VNzul PV = nRT nRTE23= ΔE = q + w ∫∫∫===212121TTnTTmTTdTCndTCmCdTq nmLnLmq == ∫∫−==2121xxVVPdVfdxw xfw Δ= VPwPΔ−= ; ifTVVnRTwln−= H = E + PV TCdTCHPTTPPΔ==Δ∫21 TCdTCEVTTVVΔ==Δ∫21 ∑∑==Δ−Δ=ΔreacjjfjprodiifirxnHnHnH0,0,0 dS = dqrev/T TqST=Δ 12,ln21TTCdTTCSconstPTTPP==Δ∫ hotcoldTTe −=1 WkS ln= G = H – TS dG = dwnon-PV + VdP – SdT ∑∑==Δ−Δ=ΔreacjjfjprodiifirxnGnGnG0,0,0∑∑==−=ΔreacjjfjprodiifirxnSnSnS0,0,0 12,ln21TTCdTTCSconstPTTPrxn=Δ=ΔΔ∫ ifgasrxnPPRnSlnΔ−=ΔΔ TSGrxnrxnΔΔ−=ΔΔ ⎟⎟⎠⎞⎜⎜⎝⎛−Δ=Δ−Δ12112211)()(TTHTTGTTG 12lnPPnRTGrxnΔ=ΔΔ dG = VdP – SdT + μAdnA + μBdnB + μCdnC + … ,...,,,CBnnPTAAnG⎟⎟⎠⎞⎜⎜⎝⎛∂∂=μ μA = μ0A + RTlnaA agas = γgasPgas/1 atm asolvent = γsolventXsolvent asolute = γsolutecsolute/1 M L+++=CBAAAnnnnX ΔG = ΔG0 + RTlnQ bBaAdDcCaaaaQ)()()()(= ΔG0 = -RT