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Physical Chemistry Test (A)
Dalian University of Technology
Name
Course:
Physical Chemistry
Date: Jan 16, 2009
No.
Department
Standard Score
Test:
Total page: 8
(A)
Type: close book
I
II
III
IV
V
VI
VII
VIII
Total
10
16
18
10
12
10
16
8
100
Scoring
Grade:
Fundamental Constants:
Avogadro constant: L= 6.022  1023mol-1;
Class:
The mass of electron
I.
Plank constant h=6.626 10-34J s
m = 9.109×10-28g
True or False (10 points )
Direction: Write “T” in the bracket before the sentence, which you think to be correct, and “F” to be wrong.
[
] 1. Surfactants lower the surface tension of liquids in which they are dissolved.
[
] 2. All the particles have the characteristics classically ascribed to waves.
[
] 3. Milk is a water -in- oil emulsion of water in butterfat.
[
] 4. A saddle point is not maximum point on the potential energy surface.
[
] 5. The Born-Oppenheimer Approximation treats atoms as having fixed nuclei.
[
] 6. In quantum mechanics, the orbital is a mathematical expression, describing the
probability of finding an electron at some point near the nucleus.
[
] 7. General speaking, the energies of particles cannot be varied continuously.
[
] 8.
When the labels of any two identical fermions are exchanged, the total wavefunction changes sign.
[
] 9. Due to surface tension, liquids try to have the minimum surface.
[
] 10. It is impossible to specify simultaneously, with arbitrary precision, both the
momentum and the position of a quantum particle.
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Physical Chemistry Test (A)
II. Selection (16 points)
Direction: Choose the best answer for each question and write the letter of your selection in the corresponding brackets.
[
] 1. The equation for the "electronic" Hamiltonian neglects which term in the
original equation?
(A) the term to calculate the kinetic energy of the electrons
(B) the term for kinetic energy for nuclei
(C) the term to describe the repulsive force of an electron on another electron
(D) the term to calculate the repulsive force of a nucleus on another nucleus
[
] 2. A silver iodide sol was prepared by mixing KI and Ag NO3 solution with
the KI in slight excess, the silver iodide sol particle is
[
(A) Positively charged
(B) negatively charged
(C) electrically neutral
(D) uncertainty
] 3. The PCl5 molecule consists of the elements( multi-choice):
(A)C3
[
(B) 
(C)
C2
(D) i
] 4. If  is the fraction of the surface occupied by adsorbate molecules at
equilibrium, then, according to the Langmuir theory, the rate of adsorption is given by
(A) k (1– )
(B)
k
(C) k p
(D) k (1– ) p
where k is a constant.
[
] 5. The HCN molecule belong to the point group:
(A) C2v
[
] 6.
(B) Td
(C)
C∞v
The probability of locating an electron is calculated by the
(A) square of the Hamiltonian
(B) square of the wavefunction
(C) square of the energy of the system
[
] 7.
(D) D6h
The Schrödinger's Equation
(A) cannot be used to solve one-electron atoms
(B) can be solved exactly only for one-electron atoms
(C) is not used for large molecules
2
Physical Chemistry Test (A)
] 8. If a liquid of density  rises in a capillary of radius r to a height h cm, and  is
[
the contact angle, then the surface tension of the liquid is
(A)
1
rhg cos 
2
(B)
r gρ
h
2 cos θ
(C)
2 cosθ
rhρh
(D)
2rh g
cos
III Fill in the blanks (18 points)
1 Write down the Hamiltonion of a rigid rotor.
2 In a case of a particle moving in a cubic box of edge a, calculate the degeneracy corresponding to energy (E) equal to 14h2/8ma2.
( E nx , n y , nz 
2
h 2 n x2 n y n z2
( 2  2  2) )
8m a
a
a
3 Write down the Hamiltonion of a harmonic oscillator.
.
4 The assumptions of ab initio quantum chemistry are:
,
and
.
5 Does the vibration of a homonuclear diatomic molecule (e.g. O2, N2, etc.) result in infrared absorption and why?
.
6 Distinguish between a fermion and a boson.
.
7 Identify the point groups to which the following objects belong:
(a) a sphere
, (b) an isosceles triangle
,
(c) an equilateral triangle
, (d) an unsharpened cylindrical pencil
.
8 The Langmuir adsorption isotherm is based on the following assumptions:
(i)
;
(ii)
;
(iii)
;
(iv)
.
9 Please indicate the direction of excess pressure p of the curved surface with arrow on
the following diagram:
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Physical Chemistry Test (A)
IV (10 points) The following data for the gas – phase decomposition reaction
2A (g)  2Y (g) +
Z (g) were obtained.
Reaction Temperature
Initial pressure of A
Half-life period
T/K
PA,0/kPa
t1/2/s
950
39.4
1520
950
157.6
380
1020
7.8
1378
1020
50.7
212
The rate law can be expressed as 
dpA
 k A pAn .
dt
(a) Determine the reaction order n.
(b) Calculate the rate coefficient kA (950K) and kA (1020K).
(c) Calculate the activation energy Ea.
4
Physical Chemistry Test (A)
V (12points) Answer the following questions:
1 What are the assumptions of quantum mechanics?
2 Discuss the approximations built into the Hückel method(HMO).
3 How to convert physical observables into their operators in quantum mechanics?
5
Physical Chemistry Test (A)
4 Discuss the steps involved in the calculation of the energy of a system by using the
variation principle.
VI (10points) Derive the rate law for the decomposition of ozone in the reaction,
2O3(g) → 3O2(g), on the basis of the following proposed mechanism:
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Physical Chemistry Test (A)
VII (16 points) (1)Calculate the following partition function of 1mole N2 at 25℃
and 100 kPa. For N2, the moment of inertia I=1.394 10
frequency v = 7.705 10 –13 s –1
(a) translational partition function qt;
(b) rotational partition function qr;
(c) vibrational partition function qv.
7
–46
kg m2, the vibration
Physical Chemistry Test (A)
(2) Write down the Schrödinger equation of He, calculate the orbital energy, the angle between the orbital angular momentum and z axis, and the angle between the
spin angular momentum and z axis of 4,3,1,1/2 (He+).
VIII (8 points) List the symmetry elements of NO2 molecule, construct the group multiplication table, name the point group to which it belongs, point out the normal subgoups
and check up the table by multiplication table rule.
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