Chemistry C2407x Formulas for Exams, Study notes of Thermodynamics

Download Chemistry C2407x Formulas for Exams and more Study notes Thermodynamics in PDF only on Docsity! Chemistry C2407x Some Free Formulas for Exams Kinetic Theory of Gases Impacts/sec = (1/6) (N/V) Ac {Impacts/sec = (1/4) (N/V) Ac} Force = [2mc] [(1/6) (N/V) Ac]=(1/3) (N/V) mc2A Pressure=Force/A= (1/3) (N/V) mc2 = [(2/3)] [(1/2) mc2] [N/V] pV=nRT=(N/N0)RT=(N/N0)(N0k)T=NkT m/k=M/R [(1/2) mc2]=(3/2) kT [(1/2) Mc2]= (3/2)RT crms=(3kT/m)1/2= (3RT/M)1/2 cavge=(8kT/π m)1/2= (8RT/π M)1/2 cmp=(2kT/m)1/2 =(2RT/M)1/2 crms=1.37x105 cm/sec = 1.37x103 meter/sec (for He at 300 K) Effusion Rate: R=(1/6) (N/V) Ac {R=(1/4) (N/V) Ac} dw=-pdV dE=dQ+dw Cp=(dQ/dT)p CV=(dQ/dT)V CV=(3/2)R Cp=(3/2)R+R (Atoms) CV=(5/2)R Cp=(5/2)R+R (Linear molecules) z=πρ2c (N/V) {z=(2)1/2πρ2cavge (N/V)} λ=c/z= [πρ2 (N/V)]-1=[πρ2 (pN0/RT)]-1 {λ=cavge/z= [(2)1/2πρ2 (N/V)]-1=[(2)1/2πρ2 (pN0/RT)]-1} ∆N/N = (4π)(m/2πkT)3/2 c2 exp[-mc2/2kT] ∆c Binary Collision Model <urel>= (8kT/πµ)1/2, µ = ma mb/(ma + mb) z=π(σΑΒ) 2<urel>(N/V) ZAB=π(σΑΒ) 2<urel>(NA/V)(NB/V) ZAA=(1/2)π(σΑΑ) 2<urel>(NA/V)(NA/V) ZAA=(1/2)(2) 1/2 π(σΑΑ) 2 (8kT/πmA) 1/2 (NA/V) 2 All or Nothing Model PR=0 when E<EA; PR=1 when E≥EA Arrhenius Model PR=0 when E<EA; PR=(1-EA/E) when E≥EA R=kR(NA/V)(NB/V)=PZAB exp[-EA/RT] {P is the steric factor} kR= Pπ(σΑΒ) 2<urel> exp[-EA/RT]=A exp[-EA/RT] (Arrhenius Model) kR= (Ν0/1000) Pπ(σΑΒ) 2<urel> exp[-EA/RT] (molar units) -dC/dt=kC, C=C0 exp(-kt), t1/2=(0.693/k) -dC/dt=kC2, 1/C=[1/C0 ] + kt, t1/2=(1/kC0) k(T2)/k(T1)=exp[-(EA/R)(1/T2-1/T1)] A+A → A+A*, k1 A*+A → A+A, k-1 A* → P, k2 kuni = k2 k1 (A)/[k-1 (A) + k2], dP/dt=[A]kuni E+S → ES, k1 ES → E+S, k-1ES → P, k2 dP/dt=vi= k2(E0)/[1+KM/(S)], KM =[k-1+k2]/k1 (1/v)=(1/vmax) + (KM/vmax)(1/[S]) dlnkA/dT=EA/RT 2 dlnkBC/dT=εA/RT 2 εA=(1/2)RT+EA (kA is the Arrhenius rate constant and kBC is the binary collision rate constant)