advertisement

CHE 3190 Survey of Physical Chemistry (Fall 2013) G.Lind STUDY GUIDE FOR FINAL EXAM The First Part of the Exam covers Chapters 1, 2, 3, 6 , 7, 10 from House , Fundamentals of Quantum Chemistry , 2nd. ed. The Second Part covers Chapters 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13 from Fenn , Engines, Energy and Entropy Most of this Study Guide is identical to the Study Guides for Exams 1, 2, and 3 PART 1 : QUANTUM CHEMISTRY House CH 1 : The Early Days All All assigned End of Chapter Problems All Practice Exercises (PE), all daily quizzes (DQ) 1.1 Blackbody Radiation Interpret the graph f( v ) versus v Use lmax ×T = const to determine the temperature of a star given relevant data You don't need to know or interpret the formulas by Wien, Rayleigh, Rayleigh-Jeans, Planck Calculations using E = hv ; lv = c ; v= v ; c = h 2p 1.2 The Line Spectrum of Atomic Hydrogen Recognize the Series (Lyman, Balmer, Paschen, Brackett, Pfund) Balmer's Formula , Rydberg constant Continuous Spectrum , Line Spectra 1.3 The Bohr Model for the Hydrogen Atom Don't need to derive the formulas n = principal QN Reduced Mass : DE = hv = m= m1m2 m1 + m2 hc l Ground State, Exited State , Ionization Energy 1.4 The Photoelectric Effect Difference between the classical and the quantum mechanical understanding of electromagnetic radiation Photon E = hv - w E= ; Unit conversions mu 2 p 2 = 2 2m 1.5 Particle-Wave Duality De Broglie Wavelength l= h h h = = mu p 2mE 1.6 The Heisenberg Uncertainty Principle DxDp ³ h ; DxDu ³ h ; m DtDE ³ h House CH 2 : The Quantum Mechanical Way of Doing Things Handout : Lecture Notes for CH 2 All assigned End of Chapter Problems All Practice Exercises (PE), all daily quizzes (DQ) We will use one dimensional time-independent systems y (x) = state function (wave function) of a one dimensional time-independent system y (x) maybe a complex function Know how to work with complex numbers y *y = probability density ò y y dx ; * = probability b ò y (x)y (x)dx * = probability of finding the system between a and b a ¥ ò y (x)y (x)dx =1 Normalization Condition ò f (x)f (x)dx ¹1 Function * -¥ ¥ * f is not normalized -¥ ¥ N 2 ò f * (x)f (x)dx =1 with y = Nf Normalization : Find N , so that -¥ ¥ ò f (x)f (x)dx =1 means f1andf2 are normal ò f (x)f (x)dx = 0 means f1andf2 are orthogonal * 1 2 -¥ ¥ * 1 2 -¥ A state funcion has to be "well behaved" means it has to be FINITE, SINGLE VALUED, and CONTINUOUS Know how to normalize a function Know how to work with OPERATORS Know the operators , p̂x p̂x2 , Ĥ , x̂ , V̂(x) Know what an EIGENVALUE-EQUATION is Determine whether a function is an EF of an operator, determine the EV What is measered when Âf = af , What is measered when Determine the average value of an observable A table of integrals will be provided. Know how to use them House CH 3 : Particles in Boxes 3.1 The Particle in a One-Dimensional Box All assigned End of Chapter Problems All Practice Exercises (PE), all daily quizzes (DQ) 1 æ 2 ö 2 np yn (x) = ç ÷ sin x èaø a ; En = n2h2 8ma 2 Interpretation Term Diagram Application to conjugated dyes Calculate the absorption wavelength of a dye House CH 6 : Vibrations and the Harmonic Oscillator Study the Lecture Notes As discussed in class Âf ¹ af House CH 7 : Molecular Rotation and Spectroscopy Study the Lecture Notes As discussed in class House CH 10 : Symmetry 10.1 What Symmetry Means Read 10.2 Symmetry Elements Find all symmetry elements of a given molecule (ion) You need to be able to draw a correct Lewis structure including all bonding pairs and all lone pairs You need to be able to determine the molecular geometry (shape) of the molecule (ion) 10.1 What Point Group Is It ? Using the flow chart provided you need to be able to determine the point group of a molecule (ion) List your answers (no, yes, ........) PART 2 : THERMODYNAMICS Fenn CH 1 : In the Beginning Definition of Force, F = ma , F = mg (earth) , units Definition of Work, w = FL , units Calculate force, work given values of mass, distance, g etc (move a mass from a to be etc) Sign convention ( + is in, - is out) w = won , q = qadd Fenn CH 2 : How Hot is Hot Thermometer, Temperature scales (oC, K, oF) Zeroth Law Constant volume Gas Thermometer Ttp = 273.16 K Fenn CH 3 : Systems, Properties, and States Ideal Gas Law : PV = nRT , P V = RT, P = dRT mRT P1V1 P2V2 , M= , = T1 T2 M PV What is an Ideal Gas PV graph, PVT graph Isotherm, Isobar, Isochore Van der Waals Equation with V and with PV graph, PVT graph Isotherm, Isobar, Isochore V ( a , b) Fenn CH 4 : Back to Work Study the lecture notes Calculate work for different paths, including geometrically (area under curve) Work going different ways on path (forward, backward) Fenn CH 5 : More in re Heat q = mc(Tf – Ti) = C D T c = specific heat C = cm = (specific) heat capacity C = molar heat capacity (units : Jmol-1 ) ; n m ; n = amount of substance (mol) ; n= M C = n C = m C ; C = MC C= C= C = specific heat capacity (units : Jg-1) m m = mass (g) ; M = molar mass (gmol -1) 1.0000 cal = 4.1845 J C increases with the complexity of the molecule : Equipartition Theorem : 1 1 1 Cu = Rftrans + Rfrot + 2 Rfvib = molar heat capacity at constant volume at high T 2 2 2 1 1 Cu = Rftrans + Rfrot = molar heat capacity at constant volume at low T 2 2 Total degrees of freedom (f) = 3N with N = number of atoms in molecule linear molecule : fvib = 3N - 5 ; nonlinear molecule : fvib = 3N - 6 C p = Cu + R Fenn CH 6 : The Origin of Cycle Analysis Carnot Cycle : Step I : isothermal , Step II : adiabatic : Step III : isothermal , Step IV : adiabatic ; Know how to calculate Pf , Vf , Tf , q , w , D U , D H for : (a) Isothermal change (b) Isochoric change (c) Isobaric change (d) Adiabatic change e= -w general qadd ; e(Carnot) = TH - TC TH only for Carnot cycle Fenn CH 7 : Heat is Work and Work is Heat. But Energy's the Difference First Law : dU = dq + dw DU = q + w Sign convention ( + is in, - is out) w = won , q = qadd Fenn CH 8 : Two Laws from One Dilemma dU = dq - PdV H = U + PV dqv = D U ; dqp = D H U = U(T) and H = H(T) for ideal gas dU = Cv dT and dH = Cp dT for ideal gas DU = n C u (Tf - Ti ) adiabatic change : ; DH = n C p (Tf PV g = const and - Ti ) TV g -1 = const D Ucycle = 0 Fenn CH 10 : HER Has Much to say Thermal Pollution by Power Plants TC qc general ; c(Carnot) = only for Carnot cycle TH - TC w TH -qH Heat pump : coefficient of performance b = general ; b (Carnot) = only for Carnot cycle TH - TC w Refrigerator : coefficient of performance c= Fenn CH 11 :HER Under the Hood Stirling Engine : be familiar with the cycle , q, w, D U, D S for each step, efficiency Otto Engine : be familiar with the cycle , q, w, D U, D S for each step, efficiency Compare both engines to a Carnot engine Fenn CH 12 : Enter Entropy Definition of Entropy Computation of Entropy changes : reversible phase change Processes : isothermal, isochoric, isobaric, adiabatic, general Reversible, irreversible changes Fenn CH 13 : Entropy is the End DSuniverse = DSsystem + DSsurroundings Second Law of Thermodynamics : DSuniverse ³ 0 all processes (> 0 for irreversible, = 0 for reversible) Microstates , macrostates Number of microstates Probability of macrostate Boltzmann's equation : S = k lnW CHEAT SHEETS: You should prepare TWO cheat sheets One page for Part 1 : Quantum Chemistry (8.5x11 in), both sides, everything handwritten (no copies), no answers to end of chapter problems or PEs or DQs. Your name must be on the sheet. One page for Part 2 : Thermodynamics (8.5x11 in), both sides, everything handwritten (no copies), no answers to end of chapter problems or PEs or DQs. Your name must be on the sheet. Both sheets have to be handed in with the exam.