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Chemistry 33000
Physical Chemistry I: Thermodynamics
Fall, 2022
CUNYFirst Class 23729
WITH ANSWERS
Section L-25-LEC Regular
Exam III: Thermodynmics (T.D.) of Phase Equilibria and Liquid-Liquid Solutions
The attached exam consists of five
questions, most of which include several independent
parts that require verbal explanations and/or numerical calculations. The parts within a problem can
often be answered most readily in the sequence they are asked, but if you miss one section it is
usually possible to complete the next
.
Try to budget your time according to the number of points
allotted to each question
; expect a class average of ~60 and a curve to estimate the corresponding
letter grades.
Please write legibly
ON THE EXAM SHEET
and with sufficient coherence that I may infer
your reasoning in those instances where your numerical result is incorrect. Note any assumptions or
approximations that you make.
If you need to clarify how to interpret a question, ask me!
Before you begin to sweat and scribble, write your name
on the exam booklet.
Hand in the
exam questions with your responses and your formula sheet
when you have completed your work.
Here are some physical constants and relationships that you may find useful.
Good luck!
R = 8.31 J-mol
-1
-K
-1
= 0.082 L-atm-mol
-1
-K
-1
= 0.083 L-bar-mol
-1
-K
-1
= 1.99 cal-mol
-1
-K
-1
J = (Pa - m
3
) / (mol - K)
J = (kg-m
2
)/s
2
1 J = 1 N-m
g = 9.8 m/s
2
Standard Temperature & Pressure (STP) = 273 K, 1 atm for gases
STP (º) = 298 K, 1 bar for chemical formation reactions and phase changes
1 atm = 760 torr = 1 x 10
5
Pa
1 bar
100 cm = 10 dm = 1 m
T (K) = t (
0
C) + 273
1 calorie = 4.18 J
U = q + w
dU = TdS - pdV
dG = -SdT +Vdp
∮
dX = 0 for any state function X
C
p
- C
v
= nR for ideal gases
K
f
for water = 1.86 K-kg-mol
-1
dq
P
= nC
P
dT
dq
V
= n C
V
dT
K
f
for naphthalene = 6.94 K-kg-mol
-1
Atomic masses: H=1; C=12; O=16; Na=23; Cl=35; Ca=40
2022-EIII-ans
11/27/2022
2022-EIII-ans
12/12/2023
2
This page has been intentionally left blank.
Be encouraged to tear off the cover page and refer to it as you work the problems.
Also be encouraged to use this page as scratch paper.
1.
2022-EIII-ans
12/12/2023
3
Pure Substances:
Phase Diagrams for Compact T.D. Information
(29 points, 4 parts)
Plots of pressure vs. temperature, pressure vs. composition, and temperature vs. composition
provide a compact but information-rich picture of the phases and chemical mixtures that are
present under laboratory conditions of interest. Consider the following data for oxygen (O
2
),
which is familiar to us as a life-supporting gas but can also be present in liquid or solid phases
under appropriate circumstances. Consider the following properties:
a: triple point: 54.3 K, 1.14 torr
b: critical point: 154.6 K and 37,828 torr
c: normal melting point: 54.8 K, 760 torr
d: normal boiling point: 90.3 K, 760 torr
a: triple point: 54.3 K, ln p = ln (1.14 torr) = 0.13 torr
b: critical point: 154.6 K, ln p = ln (37,828 torr) = 10.5 torr
c: normal melting point: 54.8 K, ln p = ln (760) = 6.6 torr
d: normal boiling point: 90.3 K, ln p = ln (760) = 6.6 torr
(or mark directly on the diagram)
(3 pts) 1b.
If ln p = 7.6 torr and T = 60 K, which phase(s) are present
? Explain and mark the
phase diagram.
e: liquid only in this region
(9 pts) 1c.
Consider how pressure depends on temperature
for liquid and gas phases
of O
2
that
are in equilibrium with one another. First, answer this question qualitatively
by quoting a
relationship
that describes this dependence and explaining why it has a positive or negative
value. Then, make a quantitative estimate
by using the given data for points a-d on the O
2
phase
diagram. Do a numerical calculation
and explain briefly
.
Qualitatively
, dp/dT is positive since
∆
S and
∆
V are each positive.
∆
S is positive
since the liquid-gas conversion goes toward a state of greater disorder.
∆
V is positive
since gases spread out to occupy a larger molar volume than liquids (or solids).
Quantitatively
, use the data to calculate dp/dT:
p
(
d
)
−
p
(
a
)
T
(
d
)
−
T
(
a
)
=
(
760
−
1.14
)
(
90.3
−
54.3
)
=
758.86
36
= + 21.08
Alternatively, use the data to calculate
p
(
b
)
−
p
(
d
)
T
(
b
)
−
T
(
d
)
or
p
(
b
)
−
p
(
a
)
T
(
b
)
−
T
(
a
)
, also >
0
2022-EIII-ans
12/12/2023
(12 pts) 1a.
These data are sufficient to construct the
phase diagram shown on the right. (Note:
the y-axis
shows ln p
in order to accommodate the large range of
values that are relevant for the three phases of diatomic
oxygen.) Use the data to put a, b, c, and d labels on the
marked locations of the diagram, including the numerical values that support your choices.
4
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Complete and balance each of the following equations. If no
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tab
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H
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D
$
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C
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FA
== | ΑΣΦ
R
Submit
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F
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Nal(aq) + Hg, (C₂H₂O₂)2(aq) →
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McQuarrie • Rock • Gallogly
University Science Books
presented by Macmillan Learning
A critical reaction in the production of energy to do work or drive chemical reactions in biological systems is the hydrolysis of
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АТР(аq) + H,О() — ADP(aq) + HРО (аq)
ADP(aq) + HPO, (aq)
for which AG;ixn
= -30.5 kJ/mol at 37.0 °C and pH 7.0. Calculate the value of AGrxn in a biological cell in which
[ATP] = 5.0 mM, [ADP] = 0.10 mM, and [HPO;-] = 5.0 mM.
kJ/mol
rxn
Is the hydrolysis of ATP spontaneous under these conditions?
О yes
no
Question Source: McQuarrie, Rock, And Gallogly 4e - General Chemsitry | Publisher: University Science Books
?
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.A solution is
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bar
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3
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8.
9.
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pressure) and HCI (0.600 bar partial
pressure) is heated at 500.0 K. The
equilibrium constant K for the gas-
phase thermal decomposition of tert-
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500.0 K.
bar
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3
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partial pressures to be:
4
C
tert-butyl chloride,CH3);CCI = (x)
hydrochloric acid, HCI = (0.600 - x)
isobutylene, (CH3)2CCH2 = (0.400 - x)
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9.
+/-
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The standard heat capacity of various components is given by,
C = a + bT + cT² + dT³, where C§ is in cal/mol-K and T is in K
|Component
CH;OH
CO
b x10
с х105
-0.291
0.1283
a
d ×10"
4.55
6.726
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