THE UNIVERSITY OF LETHBRIDGE
CHEMISTRY 2810
DEPARTMENT OF CHEMISTRY AND BIOCHEMISTRY
April 25th, 2002
FINAL EXAMINATION
Instructor: Prof. R. Boeré
Time: 2:00 - 5:00 pm (3 Hours)
No. of Pages = 4 + 3
STUDENTS MUST COUNT THE NUMBER OF PAGES IN THIS EXAMINATION PAPER BEFORE BEGINNING TO WRITE, AND
REPORT ANY DISCREPANCY IMMEDIATELY TO THE INVIGILATOR. Answer all questions in the examination booklets, starting
each new question at the top of a fresh page. Write neatly and clearly. Cross out with a single line any material you do not wish to
have marked. If this is not done, the first answer to any question encountered in your booklet will be marked and subsequent material
will be ignored. Put your name and registration number on all booklets used, and hand in all materials including this question sheet
before leaving the examination hall.
Data follows the main body of the exam. Calculators, slide rules, rulers and model kits are permitted.
All alphanumeric memories MUST be cleared before the exam commences.
Make careful use of your time. The value assigned to each question is given in the margin
Maximum score = 146 points
Part 1
1.
The following diagram displays the wavefunction of one of the hydrogenic orbitals.
r2
r
r
[6]
a)
b)
c)
2.
Identify the orbital. Justify your assignment in detail.
Sketch accurately the corresponding plots of the radial probability density function of this same orbital.
Could this wavefunction be applied to an orbital with a value of the principal quantum number that is one higher? Explain.
Using suitable, labeled, right-hand coordinate systems provide sketches of the shapes of the following orbitals as 2-D slices
through the orbital at the mid-point. Try to be accurate in rendering the shape, and indicate the phase of the orbital using shading.
Indicate how many, and what kind of, nodes each orbital has, and where these are located in the diagrams.
[6]
a) 3d z2
3.
b) 3d x 2–y 2
Draw the Lewis structure(s) of the molecule S2N2, which has the connectivity indicated below, and for which there is more than
one resonance isomer. Show formal charges, and indicate if any resonance forms are more important contributors than others to
the true electronic structure.
S N
N
[6]
4.
a)
S
For the following molecules and ions, provide the Lewis structure (including resonance and formal charge, if relevant) and the
VSEPR structure.
[16]
i) SeF4
April 25th, 2002
ii) GaF3
iii) IOF3
iv) SO3Cl–
Page 1
Chemistry 2810
Final Examination
Part 2
Vanadium is an element with rich acid-base, redox, coordination and biological chemistry. Several of the questions on this
exam will deal with vanadium. The following information is essential background that you will need to read in order to be able
to answer these questions. Please refer to the diagrams provided on the data sheet while reading this material. Then use the
following introductory information in combination with the graphics to answer the following questions.
Vanadium has several solid forms that appear in a central diagonal zone of the Pourbaix diagram. These are VO, V2O3, VO2 and
V2O5. Interconversion of these vanadium oxides is extremely easy, and all tend to oxidize towards V(+5). VO has the rock-salt
structure (NaCl lattice). VO has a rock-salt structure. Solid vanadium pentoxide, V2O5, does not belong to one of the simple ionic
crystal lattices. For this solid, two pictures are provided, one of a single complete unit cell, the other of several unit cells where the
local geometry of a single V ion is indicated. These are below the Pourbaix diagram on the graphics page.
Another fascinating characteristic of vanadium that reflects its strong affinity for oxygen is the presence of many unusual
polymeric forms of its oxo -anions. This is a peculiar property of V(+5). First, instead of a true aqua ion, it exists in solution as
aquated VO2+ , i.e. [VO 2(OH2)4]+ . At higher pH it forms an oxide. Then, the oxide resdissolves with excess hydroxide. Here is where
the fun really begins. There are at least five intermediate polyvanadate ions, such as H2V10O284–, HV10O285–, V10O286–, V4O124–, V2O74–,
on the way to “vanadate”, VO 43–. However, these are all anionic forms of vanadium(5+), differing only in degrees of aggregation.
In practice, all these forms are commonly referred to as “vanadate”. In answering the questions on this test, it may be easier to
pretend that any species right of V2O5 is actually VO 43–.
Finally, a warning: please read the formulae of the vanadium species very carefully. It is easy to misread VO 2+ for VO 2+, as one
example, and there are many similar instances. If in doubt, ask for clarification.
5.
a)
What are the oxidation states of V in its solid forms, as listed here?
(i) VO
(ii) V2O3 (iii) VO2
(iv) V2O5
[20]
b) Calculate the pK a values for each of the prototypical hexaqua ions, [V(OH2)6]n+ , and use the results to rank the acidity of each
aqua ion of vanadium in its positive oxidation states.
c)
Starting with [V(OH2)6]3+, write two balanced overall reactions for the sequential hydrolysis process that convert this ion in
the same oxidation state to the basic forms shown on the Pourbaix diagram. Thus you should have equations of type: A ? B,
then B ? C.
d) In what “group” of the Qualitative Analysis scheme does V3+ fall? Write a balanced equation for the reaction you would
perform in the appropriate qual test reaction for this ion. How is this laboratory procedure different from that shown on the
Pourbaix diagram?
e)
6.
Use the results of (b) and (c) to discuss which Brønsted acid-base forms predominate for the positive oxidation states of
vanadium. Note the exceptional behaviour of V(+4) and V(+5) in this regard. **
Consider the diagrams for the crystal structure of V2O5. It is an orthorhombic unit cell (all angles 90?, all edge lengths different).
You will need the following information to visualize this complex unit cell diagram. All oxide ions are either on the face or edge of
the unit cell. The ones you can see easily are shown in grey (large spheres). The large white spheres labeled “R” are on the rear
face, “F” are on the front face. Similarly, the vanadium ions on the front and rear faces are small white spheres with “F” and “R”
labels. The remaining vanadium ions are inside the unit cell.
[10]
a)
Confirm the stoichiometry of the compound from the unit cell. Give clear explanations for your conclusions.
The second diagram shows the full local coordination environment of one representative V ion. The V–O distances in this local
structure are shown next to the attached oxide ion, and range from 1.57 to 2.02 Å.
b)
Can you find any explanation in the chemical behaviour of vanadium(+5) for the preference this ion shows for such an
unusually irregular coordination environment in the solid-state lattice? **
April 25th, 2002
Page 2
Chemistry 2810
7.
Final Examination
Vanadium monoxide, VO, is a black solid that crystallizes in the rock-salt (NaCl) lattice. This compound is famous for forming nonstoichiometric crystals, containing either an excess or a deficiency of oxygen. There is strong evidence that the oxygen in such
crystals is always in the standard O(2–) oxidation state. Despite significant changes in composition, the unit cell edge lengths are
almost invariant, and you can safely use the “normal” value of 4.09 Å for the following problem.
[20]
(a) Sketch the unit cell of VO (in the ideal form, with no “missing” ions). Label the atoms in some fashion.
(b) You are given a large single-crystal (uniform composition) of “VO” and measure its density to be 6.34 g/cm3. Calculate the
actual composition of this sample as a formula of type VO x, where x may be a little smaller or a little larger than 1.
(c) Assuming the oxidation state of oxide to be 2–, speculate on the oxidation state(s) of the vanadium ions in your crystal in (b)
HINT: It is easier to convert your fractional formula to whole numbers, e.g. Fe0.667O1..5 ? 2 = Fe2O3, and then determine
oxidation states in the usual fashion. Avoid fractional oxidation states if at all possible!
8.
The standard reduction potentials for vanadium in both acid and base solution are provided in the form of Latimer diagrams on the
data sheets.
[30]
a)
Calculate values of nE for each oxidation state of vanadium in both solutions, and construct a comparative Frost diagram on
the graph paper provided. Ensure the diagram is legible, including a sensible choice of scale, and that all points on the
diagram are clearly labeled.
b) Contrast the redox chemistry of vanadium in strong acid solution to that in strong base solution.
c)
Identify the vanadium species and condition that is the strongest oxidizing agent. Justify your answer.
d) Identify the vanadium species and condition that is the strongest reducing agent. Justify your answer.
e)
Is VO 2+ stable in acid solution? Justify your answer.
f)
Is HV2O5– (i.e. the dinuclear hydroxo anion [O2VOVO(OH)]– of V in the +4 oxidation state) stable in basic solution? Justify
your answer.
g) What product(s) would form if solutions containing equal moles of V2+(aq) and VO 2+(aq) were mixed together? Justify your
answer, and write a balanced equation.
h) Calculate a redox potential for the reaction in (g).
9.
i)
Is this reaction an inner-sphere or an outer-sphere redox reaction? Justify your answer.
j)
There is strong evidence that the preliminary product of the reaction described in (g) is actually [VOV] 4+. Write an acid-base
hydrolysis reaction that converts [VOV] 4+ to the final product of (g). This is not a redox change, of course. **
Consider the Pourbaix diagram for vanadium and the stability field for water diagrams, and answer the following questions.
a)
Staying at pH = 1, describe the sequential processes that should occur when elemental vanadium is dissolved in an acid
solution. Unless precautions are taken, it is experimentally observed that the final product will be the V(+5) species. Write a
balanced redox half-reaction for each step.
[16]
b) What reaction(s) are expected to take place when a solution containing the V2+ aqua ion is made progressively more basic
while at the same time being saturated with oxygen? Write a balanced redox half-reaction for each conversion that takes place.
Ignore vanadium polyoxoanions (i.e. use VO 43– only for basic forms of V(+5)).
c)
What form is vanadium likely to take in normal ocean water (i.e. with exposure to open air)?
d) Sea squirts are simple creatures with a very high tendency to concentrate vanadium within their cells. They literally extract
vanadium from the ocean. In what oxidation state do sea squirts find vanadium?
( Question #9 continued on next page.)
April 25th, 2002
Page 3
Chemistry 2810
e)
Final Examination
The vanadium inside sea squirts is found predominantly in the oxidation states +3 and +4. Sea squirts employ a ligand very
similar to enterobactin to stabilize the vanadium ions they absorb. What potential problems might be overcome by the
employment of this ligand? (Physiological pH ~7.5, and inside cells is an oxygen-depleted environment.)
10. In the previous question, you learned that sea squirts concentrate vanadium to an enormous extent. The vanadium is present
primarily in oxidation state +3. The vanadium is present as a coordination complex similar to that formed by enterobactin. The
picture below shows a crystal structure for an enterobactin complex of vanadium, and next to it is the structure of free enterobactin.
The overall charge on the enterobactin–vanadium complex may be taken to be –3. (The cell has natural charge compensation
processes, rather than conventional counter ions. But think of it as [VL] 3–, where “L” = enterobactin, to answer the questions
below.
H
O
H
NHCO
O
HO
OH
O
NHCO
O
O
HO
OH
O
HO
OH
H
NHCO
Enterobactin
[16]
a)
Discuss the formation of enterobactin (and the sea-squirt analogue) complexes of V using the principles of coordination
chemistry. What changes must occur to the ligand in order to form the complex? What are the donor atoms? Classify the
ligand donor atoms and the metal using HSAB theory.
b) What biochemical role does enterobactin play? How is it suited for its task?
c)
Determine the d-electron configurations for both the V2+ and V3+ aqua ions in solution. Assume that these are hexaqua ions,
[V(OH2)6]n–, and use this information to write the appropriate ligand field splitting diagrams for these two ions. Are high spin
and low spin configurations possible?
d) Below are electronic absorption spectra that are typically found for the V2+ and V3+ aqua ions. Use your diagrams in part (c) to
qualitatively explain the origin of these spectra. Can you rationalize why the V2+ aqua ion is violet, while the V3+ aqua ion is
green in aqueous solution (see labels on the Pourbaix diagram)? (CAUTION: the two spectra have scales of opposite
direction.)
e)
Suggest a way to prove that a vanadium enterobactin complex obtained from a biological source is indeed in the +3 state. **
April 25th, 2002
Page 4
Chemistry 2810
Final Examination
USEFUL DATA
Formulae
pKa = 15.14 – 0.8816 Z2/r
pKa = 15.14 – 0.8816 [Z2/r + 9.60(? – 1.50)]
pKb1 = 10.0 + 5.7x – 10.2y for EO x y– pKa ? 8 – 5p for OpE(OH)q
G
H
T S
G
Madelung Constants
Lattice type
Zinc blende
Wurtzite
NaCl
CsCl
?-quartz
Rutile
Fluorite
nFE
A
1.63805
1.64132
1.74756
1.76267
2.201
2.4080
2.51939
V AB
H hydration
609 Z 2
(r 0.50)
d = m/V
1389 Z A Z B
1
1
rAB
n
A
4
3
Vsphere
Born Exponents
r+/r.
Noble Gas Conf’n
Born Exponent
0.225-0.414
He
5
0.225-0.414
Ne
7
0.414-0.732
Ar
9
0.732-1.00
Kr
10
0.225-0.414
Xe
0.414-0.732
Rn
14
0.732-1.00
r3
Vcube
a3
12
Partial Ionic Radii Data
Zr
+4
0.73(4)
0.86(6)
0.98(8)
O
-2
1.21(2)
1.22(3)
1.24(4)
1.26(6)
1.28(8)
Pu
+3
+4
+5
+6
1.14(6)
1.00(6)
1.10(8)
0.88(6)
0.85(6)
Cu
+1
0.60(2)
+1
1.74(4)
1.91(6)
+2 0.76(4SQ)
0.87(6)
+3 0.68(6L)
K
1.52(6)
1.65(8)
1.73(10)
1.78(12)
V
+2
+3
+4
+5
Classification of Cation Acidity
Classification of Oxo Anion Basicity
Category
nonacidic
feebly acidic
weakly acidic
moderately acidic
strongly acidic
very strongly acidic
Category
nonbasic
feebly basic
moderately basic
very strongly basic
Fundamental Constants
Atomic mass unit
Avogadro's number
Electron charge (e)
Electron mass
April 25th, 2002
pKa1 range
14 –15
11.5 –14
6 –11.5
1 –6
(–4) –1
–4
1.6605 ? 10-24 g
6.022 ? 1023
1.6022 ? 10-19 C
9.1095 ? 10-28 g
Planck's constant
Proton mass
Neutron mass
Speed of light in vacuum
0.93(6)
0.78(6)
0.72(6)
0.86(8)
0.494(4)
0.68(6)
Sr
+3
0.885(6)
1.010(8)
pKb1 range
16.9 – 22.6
11.3 – 16.8
5.5 – 11.2
(–14.7) – 5.4
6.626 ? 10-34 J s
1.67252 ? 10-24 g
1.6749 ? 10-24 g
2.998 x 108 m s -1
Page 5
Chemistry 2810
Final Examination
1
Chem 2810 Standard Periodic Table
18
1.0079
Including Pauling-type Electronegativity
4.0026
H
(as last entry, in brackets)
He
1
(2.20)
6.941
2
13
14
15
16
17
9.0122
10.811
12.011
Li
Be
B
C
14.006
7
15.999
4
18.998
4
3
(0.98)
4
(1.57)
5
(2.04)
6
(2.55)
22.989
8
24.305
0
26.9 81
5
Na
Mg
11
(0.93)
39.098
3
12
(1.31)
40.078
K
20
(1.00)
19
(0.82)
85.467
8
Rb
3
(0.82)7
132.90
5
Ca
87.62
Sr
38
(0.95)
137.32
7
Cs
Ba
55
(0.79)
(223)
56
(0.89)
226.02
5
Fr
87
(0.70)
3
4
44.955
9
47.88
Sc
22
(1.54)
21
(1.36)
88.905
9
Y
39
(1.22)
Ti
91.224
Zr
40
(1.33)
178.49
La-Lu
Hf
72
(1.30)
(261)
Ac-Lr
Ra
Rf
104
N
O
F
9
(3.98)
35.452
7
10
28.085
5
8
(3.44)
32.066
Al
Si
P
Cl
18
13
(1.61)
69.723
14
(1.90)
72.61
15
(2.19)
74.921
6
16
(2.58)
6
7
8
9
10
11
50.941
5
51.996
1
54.938
0
55.847
58.933
2
58.693
63.546
Ni
Cu
Zn
Ga
Ge
V
Cr
Mn
Co
23
(1.63)
92.906
4
24
(1.66)
95.94
25
(1.55)
(98)
26
(1.83)
28
(1.91)
29
(1.90)
30
(1.65)
31
(1.81)
32
(2.01)
106.42
Tc
Ru
107.86
8
112.41
1
114.82
Mo
118.71
0
33
(2.18)
121.75
7
Nb
42
(2.16)
43
(1.90)
44
(2.20)
Ag
Cd
Sn
Sb
183.85
186.20
7
190.2
47
(1.93)
196.96
7
48
(1.69)
200.59
49
(1.78)
50
(1.80)
207.19
51
(2.05)
208.98
0
Au
80
(2.00)
41
(1.60)
180.94
8
Ta
73
(1.50)
(262)
Db
105
W
74
(2.36)
(263)
Sg
106
Re
75
(1.90)
(262)
Bh
107
101.07
27
(1.88)
102.90
6
Rh
45
(2.28)
192.22
Pd
46
(2.20)
195.08
Os
Ir
Pt
76
(2.20)
77
(2.20)
78
(2.28)
(265)
(266)
Hs
108
79
(2.54)
65.39
Hg
20.179
7
7
(3.04)
30.973
8
5
Fe
12
2
In
204.38
3
Tl
81
(2.04)
Pb
82
(2.33)
As
Bi
83
(2.02)
S
78.96
Ne
1732.1
6(3.16)
79.904
39.948
Ar
83.80
Se
Br
Kr
34
(2.55)
35
(2.96)
36
(3.00)
127.60
126.90
5
131.29
I
54
(2.16)
Te
52
(2.10)
(210)
53
(2.66)
(210)
Po
At
84
(2.00)
85
(2.20)
Xe
(222)
Rn
86
Mt
109
88
(0.90)
April 25th, 2002
Page 6
Chemistry 2810
Final Examination
138.90
6
140.11
5
140.90
8
144.24
60
(1.14)
61
238.02
9
237.04
8
Nd
(145)
Pm
La
Ce
Pr
57
(1.10)
227.02
8
58
(1.12)
232.03
8
59
(1.13)
231.03
6
Ac
Th
Pa
U
Np
89
(1.10)
90
(1.30)
91
(1.50)
92
(1.38)
93
(1.36)
April 25th, 2002
150.36
Sm
151.96
5
157.25
Eu
Gd
158.92
5
162.50
Tb
Dy
62
(1.17)
63
64
(1.20)
65
66
(1.22)
(240)
(243)
(247)
164.93
0
167.26
Ho
68
(1.24)
67
(1.23)
(252)
Er
(257)
168.93
4
Tm
69
(1.25)
(258)
173.04
Yb
70
(247)
(251)
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
(259)
No
94
(1.28)
95
(1.30)
96
(1.30)
97
(1.30)
98
(1.30)
99
(1.30)
100
(1.30)
101
(1.30)
102
(1.30)
174.96
7
Lu
71
(1.270)
(260)
Lr
103
Page 7
Chemistry 2810
Final Examination
Focus on Vanadium: Several of the questions on this exam are based on the chemistry of the element vanadium. The following data
may be used on several questions.
Vanadium Redox Potentials (Latimer Diagram)
+5
acidic solution
+4
1.00
VO2+
basic solution
VO43-
+3
VO2+
-0.66
HV 2O 5+
VO2
0.38
-0.40
-1.38
V 2 O3
H2 V10 O284 HV1 0O2 85 -
-1.13
V 2+
V
-1.96
VO
V
O2
polyvanadate
(orange)
2+
VO
4-
vanadyl
(blue)
E(V)
-0.26
V 3+
0
V 2O 5(brown) V O 610
28
(yellow)
V
+2
V4O12
(colourless)
VO2
3+
V2O74-
(colourless)
VO4
(blue-black)
(green)
V(OH)
2+
V
HV2O5-
3-
(colourless)
(brown)
H2
V2O3
2+
(black)
(violet)
pH
VO (black)
V metal
Pourbaix Diagram for Vanadium in aqueous solution
c
z
y
x
1.57 Å
b
2.02 Å
1.88 Å
a
Unit cell of V2O5
April 25th, 2002
1.88 Å
1.79 Å
View of V2O5 showing the CN of a single V ion
Page 8