Final Exam ReviewFinal Exam Review

Exam 4:30 -7 PM, Monday, in Chem 142 Comprehensive with 7-8 questions

Should take ~ 1 ½ to 2 hoursShould take 1 ½ to 2 hoursReview session tonight, 7- 9 PM, Chem 142

Thermodynamics and KineticsThermodynamics and Kinetics

Some high points

Internal EnergyInternal Energy,Heat, and Work

If heat (q) is absorbed by the system,and work (w) is done on the system,the increase in internal energy (U) is

i n b :

U = q (heat absorbed by the system)

given by:

U = q (heat absorbed by the system)+ w (work done on the system)

Reversible and Irreversible WorkW

Enthalpy DefinedEnthalpy DefinedEnthalpy, H U + PV

At Constant P,

H = U + PV

U = q + w

H = U + PV

q= qP = U - w, w = -PV

q = U + PV= HqP = U + PV= H

At constant V, q = U = H

Comparing H and UComparing H and Uat constant PH = U + PV

1. Reactions that do not involve gasesV 0 and H U

2. Reactions in which ngas = 0V 0 d H UV 0 and H U

3 Reactions in which n 0 3. Reactions in which ngas 0 V 0 and H U

Endothermic & Exothermic Processes

H P

H = Hfinal - Hinitial

H Positive Positive amount of heat absorbed by the system

H N ti

Endothermic Process

H Negative Negative amount of heat absorbed(i e heat released by the system)(i.e. heat released by the system)

Exothermic Process

Th h i l E tiThermochemical Equations

CH4 (g) + 2 O2 (g) CO2 (g) + 2 H2O (l)

(a combustion reaction) cH = – 890 kJ

R ti t b b l d

Phases must be specified

Reaction must be balanced

H is an extensive property

Sign of H changes when reaction is reversed

Standard StateStandard State

The Standard State of an element is defined to The Standard State of an element is defined to be the form in which it is most stable at 25 °C and 1 bar pressureand 1 bar pressureSome Standard States of elements:

Hg (l) O2 (g) Cl2 (g) Ag (s) C (graphite)

The standard enthalpy of formation (fH°)of an element in its standard state is of an element in its standard state is defined to be zero.

Enthalpies of FormationEnthalpies of Formation

The standard enthalpy of formation ( H°)The standard enthalpy of formation ( f H )of a compound is the enthalpy change for the formation of one mole of compound from the f f f p felements in their standard state.

Designated by superscript o: H°Designated by superscript o: H

For example, CO2:

C (graphite) + O2 (g) CO2 (g)

H° = 393 5 kJ/mol Appendix DrxnH = -393.5 kJ/mol Appendix D

f H° CO2 (g) = -393.5 kJ/mol

E h l i f R iEnthalpies of Reaction

The enthalpy of reaction can be calculated f th th l i f f tifrom the enthalpies of formationof the reactants and products

rxnH° = fH°(Products) rxn f ( )

- fH°(Reactants)

Example: Find rxn H°(usin Standard Enthalpies f F rmati n)(using Standard Enthalpies of Formation)

CH (g) + 2 O (g) CO (g) + 2 H O (l)CH4 (g) + 2 O2 (g) CO2 (g) + 2 H2O (l)

f H° (from Appendix D, text):CH4 (g) -74.6 kJ/molO2 (g) 02 (g)CO2 (g) -393.5H2O (l) -285 8H2O (l) 285.8

rxnH° = -393.5 -2 (285.8) – 0 – (-74.6) kJ/mol

Therefore, rxnH° = -890.5 kJ/mol

S d LSecond Law

Statement of law

Spontaneity (system vs. surroundings)

Entropy definedEntropy defined

Applied to cyclic processesCarnot engine – valid for all reversible engines

Steps of Carnot CycleSteps of Carnot Cycleq=0

qh absorbed (+) from hot reservoir Th

d b ( )

w done on system (+)

w done by system (–)

q=0w done by system (–)

q discarded (–) into coldqc discarded ( ) into cold reservoir Tcw done on system (+)

Efficiency of Carnot EngineEfficiency of Carnot Engine

Efficiency, , of Engine:

= Work PerformedHeat AbsorbedHeat Absorbed

/ = w/qh

= Th - Tch c

Th

Entropy change in a general ith id l process with an ideal gas

V1, T1 V2, T21, 1 2, 2Make a two component reversible path:Isothermal (expan or compr) from V1, T1 to V2, T1Isochoric heating or cooling to V2 T2Isochoric heating or cooling to V2, T2

2 2ln lnV TS S S nR C

1 21 1

ln lnVS S S nR CV T

P

PPath 1

Path 2

P1

V

Path 2P2

V2V1

Exam 2Exam

Subject matter: Subject matter:Gibbs EnergyStandard ΔG for reactions Pr ssur d p nd nc f ΔG f r id l s s liquids Pressure dependence of ΔG for ideal gases, liquids, solidsChemical potential

EquilibriumEquilibrium constants, ideal gas equilibriaShifts of equilibrium at constant TShifts of equilibrium at constant TLe Chatelier PrincipleRelationship between standard Gibbs energy change and the equilibrium constantand the equilibrium constant

Exam 2Exam

KineticsKineticsRates, rate laws, mechanisms, method of initial ratesArrhenius rate law – physical interpretationReaction paths, potential energy surfacesMolecular basis of reactionsElementary reactions, composite reactionsElementary reactions, composite reactionsFast and slow rate approximations; steady state

rate determining steps; catalyzed reactions

Exam 2Exam

~ 6 problems (weights given) – budget your timep g g g yClosed book Don’t memorize formulas/constants

You will be given things you needYou will be given things you needStudy lecture material, examples, and homework!Exam will not be heavily numeric, but will emphasize concepts

Probably more numerical than last time (bring calculators)y gIf a problem seems lengthy, do another problem & come back later

Understanding homework will be useful

Exam 3 Review (1)

Some key concepts:Matter waves: = h/p – interference leads to quantized statesp f q Pre QM: photoelectric effect, Bohr atom, electron diffractionQM operators, eigenvalues, eigenfunctions, orthogonality, normalization Commuting operators; implies both properties can be measured without Commuting operators; implies both properties can be measured withoutdisturbing the other. Non-commuting, then, eg, x px > ℏEigenfunctions of a Hermitian operator form a complete, orthogonal set QM postulates – Schrödinger equation, acceptable state functions, boundaryp g q p yconditions, measurements, “sharp” quantities, expectation value, Particle in a box – showcase for developing intuitionSeparation of variables: if H can be written as a sum of single variables, qi,then E is also a sum and is a product of single coordinate (q ) then E is also a sum and is a product of single coordinate i(qi) Dimensionality and number of quantized properties. Nodal points, lines, surfaces (1D energies ordered by number of nodes) Zero point energies - - related to uncertainty issues

ll l l l Harmonic oscillator – model for molecular vibration Three dimensional motion

Exam 3 Review (2)Some key concepts:

Separation of variables2 and 3D boxes with several particles2 and 3D boxes with several particlesSepoaration ofcm motion from internal motion

Three dimensional motion- leads to angular momentum properties:

  2 2, ,, 1 ,

i h 0 1 2m mL Y Y

, ,

with 0,1,2,and the z-component of L given by

, ,with , 1, ,0, ,

z m mL Y m Ym

Central field -- for two particles, V = V(r) means that is separable in spherical polar coordinates (r,,) = R(r) Yℓ,m(,)H atom and one-electron ions – also rigid rotor, 3 D Harm oscEnergies orbitals properties nodes radial probability distribution

with , 1, ,0, ,m

Energies, orbitals, properties, nodes, radial probability distribution  2 2

2

2 2 2

ˆ2

13.6e

Zem rZ e ZE eV

2** ( ) ( )4dr R r R r r dr 2 2

081,2,3,

no

E eVn a n

n

, ,( ) ( )4n ndr R r R r r dr

Hydrogen Atom integrals

, , , ,

2 2

ˆn m n n mE

, , 2,1,0 , , 2 2,1,0ˆ 2 2n m n n mE E

2 2, , , ,1n m n mL

L m

2,0,0 0nL

L

, , , ,

2,1,0 210 2ˆ

z n m n mL m

E

3,2, 1 3,2, 1

2 1 0 2 0 0ˆ 0

zL

2,1,0 210 2

2,1,0 200ˆ 0

2,1,0 2,0.0

2,1,0 2,1,1ˆ 0

2,1,0 200 0zL

2,1,0 2,0,0 2,0,0 0zL

2 22,1,0 210 2L

2,1,0 2,1,0 0zL

Final Exam ReviewBasic Material will be provided, as on earlier exams 7-8 questions, comprehensive coverage

1 gas question 1-2 thermo questions 1 kinetics 1 gas question, 1-2 thermo questions, 1 kinetics1-2 quantum pre exam 3 1-2 qualitative molecular structure post exam 3

Should be about the length of 1 ½ regular examsP E Post Exam 3 conceptsBorn –Oppenheimer approximation- potential energy surfacesMolecular Hamiltonian and B-O simplificationsH2

+ as a molecular building block in analogy with H for atomsH2 as a molecular building block, in analogy with H for atomsLCAO – MO Variational calculations

Qualitative understanding and molecular building principlesSecular determinant Hü k l i ti ith h i l i f tHückel approximation with physical meaning of terms

Study homework and old exams!