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FinalExamSolutions - So I fA h\or-;Y "'= Final...

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Unformatted text preview: So I fA h\or-;Y "'= Final Exam / Chemistry 4521/ Physical Chemistry for Engineers /2005 Helpful Information: PV=nRT 760 Torr ::: 1 atm 1 bar = 750 Torr 1.01 x 105Pa = 1 atm 1 Pa = 1 N m-2 R = 0.08206 atm dm3Klmorl R = 8.3145 J Kl morl kB=1.381x 10-23J Kl Avogadro's Number = 6.022 x 1023morl dm=O.lm dm3 = 1000 em3 = 1 Liter 1.0 A= 1.0X 10-10m 1 J = 1 kg m2 S-2 1 Nm = 1 J 1 eal = 4.184 J 1 amu = 1.66 x 10-27kg 1 amu x Avogadro's Number = Mass of mole in grams ZA = (2)1I2ndA2 <uA>NAN ZAA = 0.5 ndA2 <uA>NlN2 <UA> = (8RT/nM)ln = (8kT/nm)1I2 A = V/[(2//2n dA2NA] dN/N = 4n (m/2nkTin exp[-mu2/2kT] U2du L\U = q (heat absorbed by system) + w (work done on system) L\U = q- PL\V H= U +PV L\H = L\U+ L\(PV) L\(PV)= L\nRT qp=L\H q = mCL\T G=H -TS L\G = L\H- T L\S L\G < 0 is spontaneous ~Go= -RT In Kpor L\Go = -RT In Kc (Different standard states for these two L\Go equations) tIlZ = In2/k A(t) = A(O)exp(-kt) tIlZ = lI[A(O)k] lIA(t)- lIA(O) = kt Steady State Approximation, d[I]/dt = k = A exp[-EalRT] In k = (-Ea/R)(lIT) + In A In (kZ/kl) = (-Ea/R) (lIT Z- lIT 1) k = (kBT/h) exp[-d+GO/RT] d+Go= d+Ho - Td+So First-order unimoiecular gas reaction: Ea =d+Ho + RT First-order unimoiecular gas reaction: k = e(kBT/h)exp[d+So/R]exp[-Ea/RT] Second-order gas reaction: Ea =d+Ho + 2RT Second-order gas reaction: k = ez(kBT/h)exp[d+So/R]exp[-Ea/RT] e = 2.718 aZ + bz = CZ nA = 2d sinE> Cubic Lattice: dhkl = a/(hz + kz + e)IIz E> = K[A]/(l + K[A]) (Langmuir Adsorption Isotherm) (l/Na)[P/(PO-P)]= [(c-l)/(c A no)](PlPo)+ (l/(c A no) (BET Adsorption Isotherm) Various terms in BET Adsorption Isotherm: Na == Totalamountadsorbed Po == SaturationPressure 'c =='td'tz no ==Number of sites per cmz A == Total surface area (cm2) 1 eV = 1.602 x 10-19J C=YA c = 3.0 X 108 m S-1 dE = hY h = 6.626 X 10-34Js hY = (1I2)mvz + <I> A= hip p=mv Energy operator = i(h/2n)alat Momentum operator =-i(h/2n)a/Jx E = nzhz/Smaz mass of electron, m=9.109 x 10-31kg T=IIIo A = -log IIIo A= Eel exp[-i2nEtIh] = exp[-iwt] 2nv= w Ej = J(J+l)hz/SnzI Llli = 2(J+l)hz/SnzI For J-7 J+ 1 Rotational Transitions: v = 2(J+l)h/SnzI = 2(J+l)B B =h/SnzI vA= 1/1..= vie = 2(J+l)hJSnzIc = 2(J+l)BA BA=h/SnzIc z I = jlro jl = m1mz/(ml+mZ) Ev= (v+ll2) hvo For v -7 v+1 Vibrational Transistions: LlE = hvo Vo = (1/2n)(k/jl)lIz G(v) = vo(v + 1/2) -Xe(v+ 1/2)2 LlG(v-7v+l) = LlGv+l/2= vo[1-2Xe(v+l)] Do = }:LlGv+lIz BASICS & GASES 1. Hooke's law states that the force associated with extending a spring is linearly related to the spring constant, k, and the displacement, x, according to F= -kx. (a) Work is defined as the integration of force over distance: fXI Work = Jo F .dx Derivean expressionfor the workperformedto extendthe spring. x, k 2. / x, " w::: [-Ic~d)( ::- 2")( =- k)(, fJ () Z- (b) Force is the negative derivative of the potential energy, Ep....
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This note was uploaded on 02/26/2008 for the course CHEM 4521 taught by Professor Bierbaum during the Spring '03 term at Colorado.

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FinalExamSolutions - So I fA h\or-;Y "'= Final...

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