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Grade:
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+2 points
Final Exam
CHEM 181: Introduction to Chemical Principles
December 19, 2014
Directions:
Do all seven problems.
Show all of your work neatly and clearly. Do not skip steps. Partial credit will be
awarded for all problems. Correct answers will not receive credit if your work is not
shown.
If you are not sure exactly what a question means, ask!
Not all problems are of equal difficulty, but all are worth the same fraction of the
overall grade.
1
1. The major resonance structure of 1,4-diazepine is shown below:
H
H
H
N
H
N
C
C
or
H
C
C
C
H
N
N
H
Show all reasonable resonance structures; label them as major (if equivalent to
the one above), minor, or very minor. Label all non-zero formal charges. (If
you prefer, you can skip writing the carbons and their attached hydrogens, as
shown above on the right.)
2
2. Consider the following resonance structures of cytosine:
H
H
H
H
N
H
N
C
H
C
C
N
C
N
C
C
C
C
H
N
O
H
N
H
H
H
H
H
H
N
N
H
O
H
C
C
C
N
C
N
C
C
C
C
H
N
H
O
N
O
H
H
There are other (more minor) resonance structures that are not important for
this problem.
(next page)
3
When an acid protonates cytosine, the H+ is added only at one particular
nitrogen. Draw the Lewis structure for protonated cytosine, including resonance
structures and formal charges. Explain the reason that this site is protonated
while the others are not.
4
3. Citric acid (C6 H8 O7 ) is a triprotic acid. Abbreviating citrate as Cit = C6 H5 O3−
7 ,
the Ka values are
H3 Cit(aq) H2 Cit− (aq) + H+ (aq)
H2 Cit− (aq) HCit2− (aq) + H+ (aq)
HCit2− (aq) Cit3− (aq) + H+ (aq)
Ka1 = 8.4 × 10−4
Ka2 = 1.8 × 10−5
Ka3 = 4.0 × 10−6
Given orange juice with a pH of 3.5, what are the relative concentrations (expressed as percentages) of H3 Cit, H2 Cit− , HCit2− , and Cit3− ?
5
4. Use the following reactions and equilibrium constants:
Ag3 AsO4 (s) 3Ag+ (aq) + AsO3−
4 (aq)
AgBr(s) Ag+ (aq) + Br− (aq)
Ksp = 1.03 × 10−22
Ksp = 5.35 × 10−13
What are the equilibrium concentrations of Ag+ (aq), Br− (aq) and AsO3−
4 (aq)
in a solution where there is an excess of both solids?
(An approximate answer within 10% of the correct value will receive full credit
if you also state whether your approximation is above or below the exact value.)
6
5. Definitions and constants:
(a) The enthalpy of formation for a compound is the heat that goes into the
system when pure elements in their most stable forms react to make the
compound. The most stable forms for carbon, hydrogen, and oxygen are
C(s), H2 (g), and O2 (g).
(b) The enthalpy of formation of H2 CO is −116 kJ/mol.
(c) The enthalpy of sublimation for carbon is the enthalpy change for the
reaction:
C(s) −→ C(g)
and is equal to 715 kJ/mol.
(d) The bond dissociation enthalpies for H2 and O2 are the heats that must go
into the system to break the H–H or O–O bonds, forming gaseous atomic
products. The exact values are
∆Hbond (H2 ) = 436 kJ/mol
and
∆Hbond (O2 ) = 498 kJ/mol
(e) The enthalpy of atomization is the heat that goes into a molecule to break
every bond, forming only atomic gas-phase products.
Calculate the enthalpy of atomization of H2 CO.
7
6. Calcium hydroxide, Ca(OH)2 , is somewhat soluble in water, but dissociates
completely when it does dissolve:
H O
2
Ca(OH)2 (s) −→
Ca2+ (aq) + 2OH− (aq)
A saturated solution (with excess solid) of Ca(OH)2 at 25 ◦ C is measured to
have a pOH of 1.46. The same solution heated to 50 ◦ C has a pOH of 1.54.
What is the enthalpy of solution of Ca(OH)2 ?
8
7. The MO diagram for HCl is formed from the 1s atomic orbital of H and the 3s
and 3p atomic orbitals of the Cl, and is shown below (vertical energy scale is
not exact):
H
Cl
⇤
z
⇡y
⇡x
(or
)
z
s
On the same energy scale as the molecular orbitals, draw in (horizontal lines)
and label the 3s, 3p, 3d, 4s, and 4p energy levels for atomic chlorine and the 1s
energy level for atomic hydrogen.
(next page)
9
The table below gives the wavelengths for the lowest-energy absorption features
of Cl and HCl. Because some of the molecular orbitals of HCl look very much
like some of the Cl atomic orbitals, some of the electronic transitions are very
similar between HCl and Cl.
Each transition corresponds to exciting a single electron from an initial to a
final state.
Example of how to describe transitions: the 3p → 5p transition in chlorine
causes an absorption at 105 nm, while the σz → Cl(5s) transition is at 100 nm.
(These values will probably not be used.)
λ (nm)
λ (nm)
Cl transition
HCl transition
200
134
136
125
120
120
116
Fill in the above blanks with the starting and ending states for each
transition.
10
Units Prefixes:
atto
femto
pico
nano
micro
milli
kilo
mega
n 1 × 10−18
n 1 × 10−15
n 1 × 10−12
n 1 × 10−9
µ 1 × 10−6
m 1 × 10−3
k 1 × 103
M 1 × 106
Constants:
Avogadro’s number:
NA
Speed of light:
c
Planck’s constant:
h
Rydberg constant
R
Kelvin/Celsius:
0 ◦C
Gas constant:
R
=
=
=
=
=
=
=
6.022 × 1023 mol−1
2.9979 × 108 m/s
6.6261 × 10−34 J s
1.09737 × 107 m−1
273.15 K
0.08206 L atm mol−1 K−1
8.314 J mol−1 K−1
Equations:
c
λ
E = hν
Rhc
En = − 2
n
ν =
−18
∆E = −2.18 × 10
J
1
1
1
= −R
−
λ
n21 n22
1 2
K.E. =
mv
2
11
1
1
− 2
2
n1 n2
More Equations:
∆E = q + w
q = C∆T
[mCs ∆T]cold
= − [mCs ∆T
]hot ∆Hvap
P2
1
= − R
− T11
ln P1
T2
K2
∆H ◦
1
1
ln K1
= − R T2 − T1
∆H = ∆E + P ∆V
∆Ssys = qrev
T
∆G = ∆H − T ∆S
∆G = ∆G◦ + RT ln Q
∆G◦ = −RT ln K
Q
∆G = RT ln K
Electronegativity:
Atom
F
O
Cl
N
Br
I
S
C
H
χ
3.98
3.44
3.16
3.04
2.96
2.66
2.58
2.55
2.20
12
C = mCs = nCp
at constant P
For a chemical reaction
aA + bB cC + dD
the equilibrium constant expressions are
K=
[C]c [D]d
KP =
and
[A]a [B]b
PCc PDd
PAa PBb
K is also written as KC .
Quadratic formula for
ax2 + bx + c = 0
the solution is
x=
−b ±
√
b2 − 4ac
2a
For an acid HA,
HA(aq) H+ (aq) + A− (aq)
Ka is defined as
[H+ ][A− ]
Ka =
[HA]
For a base B,
B(aq) + H2 O(`) BH+ (aq) + OH− (aq)
and
Kb =
[BH+ ][OH− ]
[B]
Henderson-Hasselbalch equation:
pH = pKa + log10
[A− ]
[HA]
Also:
pH = − log10 [H+ ]
pOH = − log10 [OH− ]
pKa = − log10 Ka
and at 25 ◦ C,
Kw = 1.011 × 10−14 M2
13
23
24
25
26
27
28
29
30
7
8
9
39
Y
38
37
57
La
87.62
56
85.4678
55
(227)
Actinium
138.9055
(261)
Rutherfordium
Rf
104
178.49
Hafnium
Hf
72
91.224
Zirconium
Zr
40
47.867
V
Cr
Mn
92
U
140.90765
91
Pa
Protactinium
140.116
90
Th
Thorium
Nd
232.0381 231.03588 238.0289
Uranium
144.24
Neodymium
Pr
Praseodymium
Ce
Cerium
60
59
58
(262)
Bohrium
Bh
107
186.207
Rhenium
Re
75
(98)
Technetium
Tc
43
54.938049
Manganese
(263)
Seaborgium
Sg
106
183.84
Tungsten
W
74
95.94
Molybdenum
Mo
42
51.9961
Chromium
(262)
Dubnium
Db
105
180.9479
Tantalum
Ta
73
92.90638
Niobium
Nb
41
50.9415
Vanadium
1995 IUPAC masses and Approved Names from http://www.chem.qmw.ac.uk/iupac/AtWt/
masses for 107-111 from C&EN, March 13, 1995, p. 35
112 from http://www.gsi.de/z112e.html
(226)
(223)
Ac
Ra
Radium
Fr
88
87
Francium
89
137.327
132.90545
Lanthanum
Ba
Barium
Cs
Cesium
88.90585
Yttrium
Sr
Strontium
Rb
Rubidium
44.955910
40.078
39.0983
Titanium
Ti
Sc
Scandium
Ca
Calcium
22
21
K
20
19
Potassium
24.3050
22.989770
(237)
Neptunium
Np
93
(145)
Promethium
Pm
61
(265)
Hassium
Hs
108
190.23
Osmium
Os
76
101.07
Ruthenium
Ru
44
55.845
Iron
Fe
(244)
Plutonium
Pu
94
150.36
Samarium
Sm
62
(266)
Meitnerium
Mt
109
192.217
Iridium
Ir
77
102.90550
Rhodium
Rh
45
58.933200
Cobalt
Co
(243)
Americium
Am
95
151.964
Europium
Eu
63
(269)
110
195.078
Platinum
Pt
78
106.42
Palladium
Pd
46
58.6934
Nickel
Ni
(247)
Curium
Cm
96
157.25
Gadolinium
Gd
64
(272)
111
196.96655
Gold
Au
79
107.8682
Silver
Ag
47
63.546
Copper
Cu
(247)
Berkelium
Bk
97
158.92534
Terbium
Tb
65
(277)
112
200.59
Mercury
Hg
80
112.411
Cadmium
Cd
48
65.39
Zinc
Zn
Al
Mg
Magnesium
Na
12
11
Sodium
13
9.012182
6.941
(251)
Californium
Cf
98
162.50
Dysprosium
Dy
66
113
204.3833
Thallium
Tl
81
114.818
Indium
In
49
69.723
Gallium
Ga
31
26.981538
Aluminum
10.811
Boron
Be
Beryllium
Li
Lithium
B
(252)
Einsteinium
Es
99
164.93032
Holmium
Ho
67
114
207.2
Lead
Pb
82
118.710
Tin
Sn
50
72.61
Germanium
Ge
32
28.0855
Silicon
Si
14
12.0107
Carbon
C
(257)
Fermium
Fm
100
167.26
Erbium
Er
68
208.98038
Bismuth
Bi
83
121.760
Antimony
Sb
51
74.92160
Arsenic
As
33
30.973761
Phosphorus
P
15
14.00674
Nitrogen
N
F
Fluorine
Neon
Ne
(258)
Mendelevium
Md
101
168.93421
Thulium
Tm
69
(209)
Polonium
Po
84
127.60
Tellurium
Te
52
78.96
Selenium
Se
34
32.066
Sulfur
S
16
(259)
Nobelium
No
102
173.04
Ytterbium
Yb
70
(210)
Astatine
At
85
126.90447
Iodine
I
53
79.904
Bromine
Br
35
35.4527
Chlorine
Cl
17
(262)
Lawrencium
Lr
103
174.967
Lutetium
Lu
71
(222)
Radon
Rn
86
131.29
Xenon
Xe
54
83.80
Krypton
Kr
36
39.948
Argon
Ar
18
15.9994 18.9984032 20.1797
Oxygen
O
10
6
3
5
4.003
1.00794
4
He
Helium
H
2
Hydrogen
1
The Periodic Table of the Elements