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.