Columbia University in the City of New York
New York, N.Y. 10027
Chemistry C2407x
Final Exam
December 18, 2001
2001
George Flynn
Total Points: 300
3 Hours
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for you. Good luck!
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Columbia University in the City of New York
New York, N.Y. 10027
Chemistry C2407x
Final Exam
December 18, 2001
2001
George Flynn
Total Points: 300
3 Hours
All questions are not weighted equally. I have attempted to order the questions from the least difficult to the
most difficult, but "beauty is in the eye of the beholder", so skip around to find the problems that are easiest
for you. Good luck!
Please print your name in the boxes provided.
Print your last name:
Print your first name:
Do not write anything else on this page. Answer the questions in the spaces provided on the
following pages.
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1b
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1c
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5c
6c
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1d
2d
3d
6d
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3e
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6f
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1e
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Problem 1 (40 points) The enthalpy of fusion of ethanol is 5.031 kJ/mole at its normal melting
point of 159 °K. Assume that the volume of 1 mole of liquid ethanol is 0.050 liter and the
volume of one mole of solid ethanol is 0.045 liter at this melting temperature.
a) (5 points) Determine q, the heat absorbed by the system for the reversible conversion of one
mole of solid ethanol to one mole of liquid ethanol at one atmosphere pressure and T=159 °K.
Show reasoning clearly.
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b) (10 points) Determine w, the work done on the system for the reversible conversion of one
mole of solid ethanol to one mole of liquid ethanol at a constant pressure of one atmosphere and
T=159 °K. Show reasoning clearly.
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c) (10 points) Determine ∆S, the entropy change for the system, in the reversible conversion of
one mole of solid ethanol to one mole of liquid ethanol at one atmosphere pressure and T=159
°K. Show reasoning clearly.
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d) (5 points) Determine ∆E, the energy change for the system, in the reversible conversion of
one mole of solid ethanol to one mole of liquid ethanol at one atmosphere pressure and T=159
°K. Show reasoning clearly.
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e) (10 points) Using the data from parts a-d, determine ∆G, the free energy change for the
system, in the reversible conversion of one mole of solid ethanol to one mole of liquid ethanol at
one atmosphere pressure and T=159 °K. Does the result surprise you? Show reasoning clearly.
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Problem 2 (50 points) Propionic Acid is a weak acid:
CH3CH2COOH + H2O = CH3CH2COO- + H3O+
Ka = 1.34×10-5
Phenolphthalein is an indicator with a pKa of 8.0:
PhenH(colorless) + H2O = Phen-(red) + H3O+
A solution is prepared by dissolving 0.50 moles of sodium propionate Na(CH3CH2COO) in one
liter of water. This salt completely dissociates in solution to Na+ and CH3CH2COO-. A drop of
phenolphthalein is added to follow the solution pH. The phenolphthalein does not affect the
concentration of H3O+ because there is such a small amount of it. However, the color of
phenolphthalein is, of course, affected by the concentration of H3O+.
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a) (15 points) What is the pH of this solution? Show reasoning clearly.
b) (10 points) What is the color of the solution? Show all reasoning clearly.
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c) (10 points) What is the pH for this mixture if 0.3 moles of HCl ( a strong acid) is added to the
solution without changing the volume? Show reasoning clearly.
d) (15 points) What is the pH for this mixture if another 0.2 moles of HCl (a strong acid) is
added to the solution of part c without changing the volume? Show reasoning clearly.
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Problem 3: (40 points) Consider the very important chemical transformation (one at the heart of
the alternate fuels industry):
H2O(g) + CO(g) = CO2(g) + H2(g)
and the data:
CO(g)
CO2(g)
H2O(g)
H2(g)
∆H°f(25°C)
(kJ/mole)
-110.5
-393.5
-241.8
S° (25°C)
(J/K°mole)
197.6
213.6
130.6
∆G°f (25°C)
(kJ/mole)
-137.2
-394.4
-228.6
Cp(25°C)
(J/K°mole
29.14
37.11
35.58
28.82
a)(5 points) Calculate ∆H°298 for this reaction. Show all reasoning clearly.
b)(5 points) Calculate ∆G°298 for this reaction. Show all reasoning clearly.
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c)(5 points) Calculate ∆S°298 for this reaction. Show all reasoning clearly.
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d)(10 points) Assuming all the gases involved in this reaction are ideal gases, calculate ∆E°298
for this reaction. Show all reasoning clearly.
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e)(15 points) Compute the absolute entropy [S°298] for H2O(g) at 298 K. Show all reasoning
clearly.
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Problem 4: (30 Points) In class we investigated bonding in homonuclear diatomic molecules
(molecules in which the two atoms are identical). The molecular orbital bonding picture
developed there can also be applied to heteronuclear diatomics in the second row, provided the
two atoms are relatively close to each other in the periodic chart. Three examples of these kinds
of diatomics are CO, NO and CN. The molecular orbital filling order for these heteronuclear
species is that of the homonuclear diatomics with z≤7. In what follows, you are reminded that
the atomic configurations of the relevant atoms are: C (1s22s22p2); N (1s22s22p3); O(1s22s22p4).
a)(10 points) Describe fully the molecular orbital configuration for CO
and tell the bond order and the number of unpaired electrons in the molecule. Show all reasoning
clearly. (An energy level, orbital correlation diagram is strongly recommended).
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b)(10 points) Describe fully the molecular orbital configuration for NO
and tell the bond order and the number of unpaired electrons in the molecule. Show all reasoning
clearly. (An energy level, orbital correlation diagram is strongly recommended).
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c)(10 points) Describe fully the molecular orbital configuration for CN and tell the bond order
and the number of unpaired electrons in the molecule. Show all reasoning clearly. (An energy
level, orbital correlation diagram is strongly recommended).
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Problem 5: (35 Points) The molecule ketene H2CCO is an interesting species that
illustrates many features of bonding in organic molecules. The three atoms CCO are
found to be in a straight line. The end carbon has two H atoms attached with an HCH
angle of 120 degrees. The CO bond length and bond strength are found to be very similar
to that of the double bonds in O=C=O. The CC bond length and bond strength are similar
to that for the ethylene molecule (C2H4) that we discussed in class.
a) (10 points) Describe the hybridization for the end carbon atom. Tell which H orbital is
used to form the CH bonds and be sure to indicate if there are any “leftover” atomic
valence orbitals on the end C atom that are not used in forming the CH2 fragment bonds.
A diagram is strongly recommended! Show all reasoning clearly.
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b) (10 points) Describe the hybridization for the central carbon atom. Tell which
orbitals, hybrid and/or atomic, are used to form the CC bond to the end carbon. Identify
all π and σ bonds for this CC pair. A diagram is strongly recommended! Show all
reasoning clearly.
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c)(15 points) Describe the bonding between the C and O atoms in ketene. Be sure to
indicate the nature and location of all hybrid and atomic orbitals for both atoms and the
orbital location for all valence electrons on the O atom. A diagram is strongly
recommended. Show all reasoning clearly.
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Problem 6: (50 Points) A 1.0 liter bulb is evacuated until the pressure of gas inside the bulb is
negligible. Unfortunately, there is a hole in the bulb that allows air to leak into the bulb and the
pressure to rise to 1.00×10-6 Atm after 1.00 hour. In what follows, use exact kinetic theory
formulas from the free formula sheet. You may assume that the surrounding atmosphere of gas is
pure N2 (MW=28 gm/mole) at one atmosphere pressure and that the temperature is constant at
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275 °K. The pressure of the gas surrounding the bulb never changes because the volume of the
surroundings is infinite compared to the volume of the bulb.
a) (5 points) Determine the average speed of N2 molecules in this problem. Show all reasoning
clearly!
b) (10 points) What is the number density ρs (number of molecules/cm3), of N2 molecules in the
surrounding atmosphere? Show all reasoning clearly.
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c) (5 points) What is the number density ρb (number of molecules/cm3), of N2 molecules in the
bulb at the end of one hour? Show all reasoning clearly.
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d) (10 points) To be exact, N2 molecules effuse into the bulb and once
inside can effuse out again. By considering the ratio of (the constant rate of effusion in) to (the
maximum rate of effusion out) during the one hour leak time, show that effusion out of the bulb
can be safely neglected. Show all reasoning clearly.
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e)(10 points) Determine the rate (molecules/sec) at which molecules leak into the bulb over the
1 hour period from the data given. Show all reasoning clearly.
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f) (10 points) What is the area of the hole in the bulb through which the gas leaks? Show
reasoning clearly.
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Problem 7 (55 points) The excitation of a molecule M by light to produce an excited molecule
M* can be treated by the techniques of chemical kinetics even though there need not be any
chemical change taking place in these photo-initiated events. The entire process can be described
by three elementary kinetic steps:
M+hνa → M* Rate = Iabs
M* → hνf + M
Rate constant = kf
M* + Q → M + Q
Rate constant = kq
(Absorption)
(Fluorescence)
(Quenching)
νa is the frequency of light absorbed by the molecule and νf is the frequency of light emitted by
the molecule in a process called fluorescence. Generally, νa and νf are different from each other
and the light emitted by the excited M* molecules at frequency νf can be used in the laboratory
to detect the presence of M* and measure its concentration. Iabs is the rate (not the rate constant)
of absorption of light by the molecule M (in units of moles of photons per second per liter). It is
also equal to the rate of production of M* in just the first step above. kf is the rate constant (not
the rate) for the fluorescence step and kq is the rate constant (not the rate) for the quenching step.
Q is a quencher molecule that converts M* back to M via a collision, thereby preventing reemission of light as fluorescence.
a) (5 points) Using this elementary kinetic scheme, express the rate for each of the elementary
steps and d[M*]/dt, the rate of change of [M*], the concentration of excited M. Show all
reasoning clearly.
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b) (10 points) In many experiments a light of constant intensity is shined on the sample so that
the rate of absorption of photons Iabs, is a contant. Under these conditions, make an appropriate
approximation and find [M*] as a function of Iabs, [Q], and the kinetic rate constants. Show
reasoning clearly.
c) (5 points) The rate of emission of photons in step 2 is symbolized by If (in units of moles of
photons per second per liter). Express If as a function of Iabs, [Q], and the kinetic rate constants.
Show all reasoning clearly.
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d) (10 points) Unfortunately, it is very difficult to measure the absolute number of photons
emitted. It is however, relatively easy to measure the relative number of photons emitted (If0)/If)
where If0 is the photon emission rate in the absence of quencher, Q. Describe a plot of If0/If vs
[Q] and tell what information about the kinetic scheme above can be obtained from such a plot
(called a Stern-Volmer plot after the scientists who first used this approach). Show all reasoning
clearly.
e) (15 points) Suppose now that the light shining on the sample consists of a single short pulse
(e.g. from a laser) that instantaneously produces a concentration of [M*] = [M*]0 and then shuts
itself off so there is no further excitation of M by the light in the first step above. You may
assume that no fluorescence or quenching takes place while the light pulse is on (because it is so
short) and that [M*] = [M*]0 at time t =0, the moment that the light pulse shuts off. Using your
vast knowledge of chemical kinetics, derive an expression that gives [M*] as a function of time.
(Begin with a kinetic scheme like that above, develop a differential equation for [M*], and
integrate this equation to find [M*] vs t.) Show all reasoning clearly.
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f) (10 points) Assuming that you could measure [M*] as a function of time, what kind of plots
would you make to obtain both kf and kq? Show all reasoning clearly.
The End!
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