Cheat Sheet for Physical Chemistry II | CHEM 312, Study notes of Physical Chemistry

Download Cheat Sheet for Physical Chemistry II | CHEM 312 and more Study notes Physical Chemistry in PDF only on Docsity! 1 Chemistry 312 Spring 2008 Equation Guide Constants h = 6.626 x 10-34 J s h = h/2π NA = 6.022 x 1023 mol-1 m(electron) = 9.1094 x 10-31 kg m(proton) = 1.6726 x 10-27 kg m(neutron) = 1.6749 x 10-27 kg c (vacuum) = 2.9979 x108 ms-1 Charge of an electron, e = 1.602 x 10-19 C k = 1.381 x 10-23 J K-1 R = 8.314 J K-1 mol-1 = 0.08206 L atm K-1 mol-1 Pressure conversions: 1 atm = 1.01325 bar = 1.01325 x 105 Pa = 760 mm Hg = 760 torr Particle in a box E = h 2 8m nx 2 a2 + ny 2 b2 + z 2 n c2 ! " # $ % & nx, ny, nz = 1,2,3,... Rigid Rotor ! EJ = h 2 2I J(J +1) I = µre 2 gJ = 2J +1 µ = m 1 m 2 m 1 + m 2 J = 0,1,2,... Harmonic Oscillator Ev = hνvib(v+1/2) v = 0,1,2,... νvib = 1/2π (k/µ)1/2 Quantum Theory (Electronic levels and light) Ephoton = hν = hc/λ Gas Equations PV = nRT (ideal) ! P + an 2 V 2 " # $ $ % & ' ' V ( nb( ) = nRT (van der Waals) ! Z = PV RT Z = 1 +B’P + C’P2 + ... (virial with P) ! Z =1+ B V + C V 2 + ... (virial with V) 2 Kinetic molecular theory of Gases ! PV = 1 3 Nmv rms 2 P = 1 3 "v rms 2 v rms = 3kT m = 3RT MM Dalton’s Law of Partial Pressures Ptot = PA + PB + Pc + ... Mole fraction ! " A = n A n tot P A = " A P tot Distributions Number of arrangements, ! W = g 1 N 1g 2 N 2g 31 N 3 ...( ) N! N 1 !N 2 !N 3 !... probability =W 1 gi" # $ % % & ' ( ( N Boltzmann distribution ! Ni N j = gi g j exp " Ei " E j( ) kT # $ % % & ' ( ( Ni N = gi q exp " Ei " E0( ) kT # $ % & ' ( ! N = N i i " Partition functions ! q = gi i " exp # Ei # E0( ) kT $ % & ' ( ) qtrans(1d ) = * 2 kT h 2 /8ma 2 + , - . / 0 1 2 qtrans(3d ) = 2*mkT h 2 + , - . / 0 3 2 V qrot = 2IkT 1h 2 qvib = 1 1# exp(#x) ; x = hvvib kT Thermal Energy ! (U "Uo) = RT 2 q dq dT = RT 2 d(lnq) dT For ideal gases: (U − Uo)trans = 0.5 RT per degree of freedom (U − Uo)rot = 0.5 RT per degree of freedom ! (U "U o ) vib"mod e = RT x exp(x ) "1 # $ % % & ' ( ( ; x = hv vib kT 5 ! d(lnK P ) dT = "H o RT 2 d(lnK P ) d(1/T) = #"H o R [Temperature dependence] Free energy functions: ! Go "H 298 o T = H o "H 298 o T " S o G o "U 0 o T = "R ln q o NA Fugacity, f Activity coefficient, γ = f / P ! G 2 "G 1 = RT ln f 2 f 1 Inter-relation of thermodynamic properties ! "G "P # $ % & ' ( T =V ; "G "T # $ % & ' ( P = )S ; " *G T( ) "T # $ % % % & ' ( ( ( P = ) *H T 2 "S "P # $ % & ' ( T = ) "V "T # $ % & ' ( P Relation between CP and Cv ! Cp " Cv = "T #V #T $ % & ' ( ) P 2 #V #P $ % & ' ( ) T for van der Waals gas (ignoring high order terms) ! Cp " Cv = R 1+ 2a R 2 T 2 P # $ % & ' ( for liquids and solids ! Cp "Cv = # 2VT $ ; # = 1 V %V %T & ' ( ) * + P $ = " 1 V %V %P & ' ( ) * + T where α is the thermal expansivity and β is the isothermal compressibility Raoult’s Law: ! xi = PA PA o ; GA liq =GA o + RT ln xA for solvent A. ! "G mix = x A RT ln x A + x B RT ln x B for a binary solution A-B. Henry’s Law: ! P B = kx B = k 'm ; G B =G B o + RT lnm for solvent B, standard state m = 1 ! G B =G B o + RT ln "m where γ is the activity coefficient 6 Kinetics For the general reaction aA + bB → cC + dD Rate = ! " 1 a d[A] dt = " 1 b d[B] dt = 1 c d[C] dt = 1 d d[D] dt = k[A] m [B] n Integrated Rate Laws: Half-lives: Zeroth order: [A] = [A]0 – kt [A]0/2k First order: ln[A] = ln[A]0 – kt 0.693/k Second order: 1/[A] = 1/[A]0 + kt 1/(k[A]0) Equilibria & Rates: For the elementary equilibrium ! A k1" # " k$1 % " " B , ! d[A] dt = "k 1 [A]+ k"1[B] Temperature dependence ! k = A exp "E a RT # $ % & ' ( Steady state approximation: If [M] is constant, d[M]/dt = 0 Rate equation for Michaelis-Menten enzyme catalyzed reactions Rate = ! k 2 [E tot ][S] K M + [S] ; K M = k"1 + k2 k 1 = [E][S] [E • S] ! E + S k1" # " k$1 % " " E •S E • S k 2" # " E + products Rate equation for Lindemann mechanism for unimolecular gas phase reactions Rate = ! k 1 k 2 [A] 2 k"2[A]+ k1 ! ! A + A k2" # " k$2 % " " A + A * A * k 1" # " products