Chemistry
1st Midterm Exam
2010/11/5
Periodic Table of Elements
Formulae
E = hν
ν = ℜ(1/n12 – 1/n22), ℜ = 3.29x1015 Hz
= h/mv = h/p
En = n2h2/8mL2
1/2mev2 = hν - Φ
Constants
R = 8.314 J / mol K
= 0.0821 L atm / K mol
= 8.314 L kPa / K mol
Mass of e , me = 9.10939 × 10 -31 kg
Nature Exponential Base e = 2.71828
⎡ h2 2
⎤
∇ + V ( x, y , z ) ⎥ ψ ( x, y , z ) = E ψ ( x , y , z )
⎢−
⎣ 2m
⎦
Hψ = Eψ
1 atm = 760 Torr = 1.01x105 Pa
c = 2.99×108 m/s
h = 6.63×10-34 J⋅s
1
Suppose the electron is in a 1s-orbital of a H atom. What is the probability of finding
the electron in a small region a distance 0.5a0 from the nucleus relative to the
probability of finding it in the small region located right at the nucleus? The 1s
orbital wave function of a H atom: (no need of calculation, just write down the
simplest equation expression of the correct answer).
ψ ( r ,θ , φ ) = (
1 1 / 2 −r / a0
) e
, a0 = 52.9 pm
3
π ⋅ a0
(6%)
2
Write the electron configuration and expect the number of unpaired electrons for the
following elements in the ground-state: (a) copper; (b) sulfur; (c) tin. (9%)
3
Consider a particle of mass m in a 1-dimensional box between two rigid walls a
distance L apart, and answer the following questions.
3.1 What’s the wave length of this particle of quantum number n = 5?
(2%)
3.2 Are any of the energy levels of this particle degenerate? If so, find one set of
quantum numbers as an example.
(2%)
3.3 If the particle can absorb green light and transition from n = 1 to n =2. After
changing the size of the box from L to L’, this particle absorbs red light for the
same transition. Is L’ > L or L’ < L?
(2%)
3.4 Is the statement: “when n = 0, the energy of this particle is 0, it is also called
the zero-point energy”, correct? Why?
(2+2%)
4
(a) X+, Y3+, and O2– are isoelectronic. What is the element Y? (2%)
(b) Write the three quantum numbers {n, l, ml} of the valence electron of a X atom in
the ground state. (3%)
(c) Which has the largest atomic radius, X, Y, or O? (2%)
(d) Which has the largest second ionization energy, X or Y? (use the element
symbols for answering (a), (c), (d)) (2%)
5
Please select the most correct answer for each following question. (2% each; 14%
total)
5.1 For a compound AB, the greater the electronegativity difference between the
two bonded atoms , the
(a) greater the bond strength
(b) greater the ionic character of the bond
(c) longer the bond length
(d) more unstable the bond
(e) less soluble in water
5.2 For a compound AB, the greater the formal charge on the two bonded atoms, the
(a) greater the bond strength
(b) greater the ionic character of the bond
(c) longer the bond length
(d) more unstable the bond
(e) less soluble in water
2 5.3 What is the correct order of the following bonds in terms of decreasing polarity?
(a) N-Cl, P-Cl, As-Cl
(b) As-Cl, P-Cl, N-Cl
(c) As-Cl, N-Cl, P-Cl
(d) P-Cl, As-Cl, N-Cl
(e) P-Cl, N-Cl, As-Cl
5.4 In the gaseous phase, which of the following diatomic molecules would have
the most covalent character?
(a) CsBr
(b) CsF
(c) NaCl
(d) NaF
(e) LiBr
5.5 Which of the following has the lowest lattice energy?
(a) CsBr
(b) CsF
(c) NaCl
(d) NaF
5.6 Which of the following is polar?
(b) PCl5
(c) ICl4(a) XeF4
(d) SF6
(e) LiBr
(e) IF5
5.7 All of the following have an angular shape except
(a) HOCl
(b) S32- 
(c) I3(d) ClO26
Consider the following molecules. (2% each; 6% total)
BF3
C3H4 (Allene, nonpolar molecule)
N2O
HXeO4
NO2
SF4
CH3O
6.1
6.2
6.3
7
Which molecules violate the octet rule?
Which molecules are radicals?
Which molecules may have resonance structures?
Please draw the most stable Lewis structure of the following molecules. All of the
lone pairs have to be drawn clearly and determine the formal charge on each atom.
If there are several resonance structures, please just write one of the most favorite
structure. (4% each; 12% total)
7.1 BrO2
7.2 SO327.3 XeO3
3 8
(3% each; 6% total)
8.1 This is a neutral molecule. E is an element on the Period 3. Please calculate
the formal charge and the number of the valence electron of the element E.
Please identify the element E
8.2
9
This is an anion with the charge of -1. E is an element of the main group on
the Period 4. Please calculate the formal charge and the number of the
valence electron of the element E. Please identify the element E (2% each; 4% total)
Do you expect the ionization energy of H2- to be
9-1 higher or lower than that of H2 ?
9-2 higher or lower than that of H ?
10 (4% each; 8% total)
10-1 What do you predict for the hybridization of the central C atom, and the
number of σ and π bonds in HCN?
10-2 What do you predict for the hybridization of the central C atom, and the
number of σ and π bonds in CO2?
11. (14% total)
11-1(6%) Sketch the energy level diagram of O2 including only MO formed by the
2s and 2p atomic orbitals. Name these MO. Place the electrons of O2 in these MO.
Explain why O2 is paramagnetic?
11-2 (2%) In a photoelectron spectrum of N2, you would expect the electrons coming
off with the highest kinetic energy to be associated with which molecular orbital? (a)
1s N, (b) σ2s, (c) π2p, (d) σ2pz, (e) π*2p
11-3 (2%) If you remove one electron from N2 what will happen to its bond length?
(a) increase, (b) decrease, (c) remain the same
11-4 (4%) What do you predict for the bond orders of N 2 , O2 , O-2 , and O+2
12.(1% each; 4% total)
What do VSEPR, LCAO, LUMO, and HOMO stand for? Please write them in
English.
4 Solution
1
[modified example 1.9, exercises 1.39]
probability density:
ψ 2 (r , θ , φ ) = (
1
)e −2 r / a0
3
π ⋅ a0
(2%)
here, the ration of the probability = the ration of the probability density
1
)e −a0 / a0
3
ψ (0.5a0 ) π ⋅ a0
=
= e −1 = 0.37
2
1
ψ (0)
(
)e 0
3
π ⋅ a0
(
2
(equation 2%, result 2%, either e-1 or 0.37 is correct)
2
[modified exercises 1.74+1.82]
Cu: [Ar]3d10 4s1 , 1 unpaired electron;
S: [Ne]3s2 3p4 , 2 unpaired electrons;
Sn: [Kr]4d10 5s2 5p2 , 2 unpaired electrons
(each electron configuration 2%, each # of unpaired electrons 2%, total 12%)
3
(a) 2L/5
(2%)
(b) No
(2%)
(c) L’ > L
(2%)
(d) No. The lowest possible energy of this particle is always > 0.
(2+2%)
4
(a) Y = Al ; (b) {3, 0, 0} ; (c) Na or X ; (d) Na or X
(2+3+2+2%)
5
5-1 (b)
6
(2% each)
6.1
6.2
6.3
5-2 (d)
5-3 (b)
5-4 (e)
5-5 (a)
-
5-7 (c) (2% each)
Ans: BF3, HXeO4 , SF4, NO2, CH3O (2% each,答錯一個扣 1 分，答錯兩個
就 0 分)
Ans : NO2, CH3O
(2% each,答錯一個扣 1 分，答錯兩個就 0 分)
Ans : N2O, HXeO4 , NO2
(2% each,答錯一個扣 1 分，答錯兩個就 0 分)
5 5-6 (e)
7
(4% each, 每小題 4 分，答錯一個扣 1 分，答錯 4 個就 0 分)
7-1
8
9.
7-2
7-3
(3% each)
8.1 formal charge = 0 (1%)
number of valence electrons=6
Element E is S.
(1%)
8.2 formal charge = +2 (1%)
number of valence electrons=7
Element E is Br.
(1%)
9-1 lower
9-2 lower
10. 10-1
10-2
(1%)
(1%)
(2%)
(2%)
sp hybridization for the central C atom of HCN
2 σ and 2 π bonds for HCN
(2%)
sp hybridization for the central C atom of CO2
2 σ and 2 π bonds for CO2
(2%)
6 (2%)
(2%)
11.
11-1
Because there are two unpaired electrons on π2p*, O2 is paramagnetic. (1%)
Sketch the energy level diagram of O2 (2%,答錯一個扣 1 分，答錯兩個就 0
分)
Name these MO. (2%,答錯一個扣 1 分，答錯兩個就 0 分)
Place the electrons of O2 in these MO. (1%)
11-2
11-3
11-4
d
(2%)
a
(2%)
3, 2, 1.5, 2.5
(4%,答錯一個扣1分)
12. 英文單字必須相同才給分
VSEPR: valence shell electron pair repulsion
LCAO: linear combination of atomic orbitals
LUMO: lowest unoccupied molecular orbital
HOMO: highest occupied molecular orbital
7 (1%)
(1%)
(1%)
(1%)