CHEMISTRY 20B SAMPLE FINAL EXAM

CHEMISTRY 20B
SAMPLE FINAL EXAM
NAME
________________________________________
STUDENT ID #
_______________________
INSTRUCTIONS:
This exam consists of 7 questions on 15 single-sided pages.
This is a closed-book exam; the front and back of one 8.5”x11” note sheet is allowed.
You may use a calculator that is not pre-programmed.
All cell phones and wireless communications of any form must be turned off or disabled.
Show all of your work; no credit will be given for an answer alone.
Give units for all numerical answers and employ significant figures.
SOME HELPFUL CONSTANTS AND CONVERSIONS:
Gas Constant :
R = 8.314 J K-1 mol-1 = 0.08206 L atm K-1 mol-1
Avogadro’s Number :
N0 = 6.0221 x 1023 mol-1
Boltzmann’s Constant:
kB = 1.3807 x 10-23 J K-1 = 1.3807 x 10-16 erg K-1
Planck’s Constant:
h = 6.626 x 10-34 J s = 6.626 x 10-27 erg s
Gravitational Acceleration g = 980 cm s-2 = 9.80 m s-2
5
1 atm = 1.013 x 10 Pa = 760 torr
Kw(25 °C) = 10-14
Question
1
2
3
4
5
6
7
Value
30
30
20
30
30
30
30
Total
200
Score
Letter Grade for 20B Class: _______
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Question 1
(30 points)
Acrylic acid (H2C=CHCOOH) is used frequently to produce many kinds of plastics.
Acrylic acid has an ionization constant Ka of 5.6 x 10-5 at 25 °C. For all of the questions
below, you may assume that the temperature is fixed at 25 °C.
1. (a) Suppose 0.035 moles of acrylic acid are added to 500.0 mL of water. What is the
pH of the aqueous solution of acrylic acid at equilibrium?
1. (b) What is the conjugate base of acrylic acid? At equilibrium, what percentage of
acrylic acid has dissociated into its conjugate base in the solution of part (a)?
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1. (c) Suppose we add 500.0 mL of a solution of 0.010 M hydrochloric acid to the acrylic
acid solution in part (a). After equilibrium is re-established, what is the
concentration of acrylic acid? (You may assume that the hydrochloric acid remains
fully dissociated.)
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1. (d) Using what you know about acrylic acid, what is the pH after 0.0500 moles of the
salt sodium acrylate (NaH2C=CHCOO) is added to 1.00 L of water?
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Question 2
(30 points)
Consider the following simple combination reaction: 2A " A2 .
2. (a) Suppose the reaction is first order in [A]. If the rate constant is k = 1.0 x 106 s-1,
what is the time required for the concentration of [A] to decrease from 1.0 M
!
initially down to 0.10 M? (Note: the reaction stated in this part is not elementary.)
2. (b) Now, suppose the reaction is second order in [A]. If the rate constant is k =
1.0 x 106 L mol-1 s-1, what is the time required for the concentration of [A] to
decrease from 1.0 M initially down to 0.10 M?
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2. (c) Based on your results in parts (a) and (b), which order of reaction leads to a faster
decrease to one tenth of the initial concentration? On the same graph, sketch a plot
of [A(t)] versus t, where t is time, for both first order (solid line) and second order
(dashed line) reactions of parts (a) and (b).
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Question 3
(20 points)
The following questions pertain to aqueous solutions. The normal boiling point of water
is 100.0 °C, and the normal freezing point of water is 0.0 °C. The freezing point
depression constant for water is kf = 1.86 K kg mol-1, and the boiling point elevation
constant for water is kb = 0.512 K kg mol-1. The mass density of water is 1.00 g mL-1.
3. (a) Suppose that 0.10 moles of sodium chloride (NaCl) salt are added to 1.0 L of pure
liquid water. What is the new normal freezing point in °C of the salt solution?
3. (b) Suppose that 100.0 mL of a homogeneous aqueous solution contains 3.0 g of an
unknown material that dissolves but does not dissociate. The normal boiling point
of the solution is measured to be 101.0 °C. What is the molar mass (i.e. “molecular
weight”) of the unknown material?
-7-
Question 4
(30 points)
3+
The vanadic ion V forms green salts and is a good reducing agent. In a neutral aqueous
solution, it is transformed into the colorless vanadic hydroxide ion, V(OH)4+. The salt,
vanadic sulfate V2(SO4)3 , can be oxidized in aqueous solution according to the following
incomplete and unbalanced equation fragment:
V2 (SO 4 ) 3 (aq) + ... " V(OH) 4 + (aq) + SO 4 2# (aq) + ...
4. (a) What is the oxidation number of vanadium on the left hand side of the equation
fragment? What is the oxidation number of vanadium on the right hand side?
!
4. (b) Using the equation fragment as a guide, complete and balance the reaction for the
oxidation of vanadium sulfate using common species that commonly participate in
aqueous redox reactions of electrolytes (e.g. hydronium ions, hydroxide ions,
water molecules, electrons). Add only species that are absolutely necessary.
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4. (c) Suppose you are given 0.540 g of an unknown substance X and have a 0.200 M
aqueous solution of vanadium sulfate. Suppose each molecule of X can accept one
electron. You would like to know the molecular weight of X, so you add the
vanadium sulfate solution to X in a beaker a little bit at a time and stir thoroughly
while watching. What kind of color change do you expect to see as you increase
the vanadium sulfate solution? If the solution changes color after 15.0 mL have
been added to substance X, what is the molecular weight of X?
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Question 5
Consider the following reaction:
(30 points)
"
2NO2(g) #
N2O4 (g)
At 298 K for this reaction, !H° = -58.0 kJ and !S° = -176.6 J/K.
! forward reaction at 298 K? Is the reaction spontaneous at
5. (a) What is !G° for the
298 K? Assuming the enthalpy and entropy change do not vary with temperature,
at what special temperature, T*, does !G° = 0.0 J?
5. (b) Express the equilibrium constant K for this reaction in terms of equilibrium
pressures of the reactant and product gases. What is K at 298 K?
-10-
5. (c) Suppose the initial pressures are: pNO 2 = 1.00 atm and pN 2O 4 = 1.00 atm at
298 K. Predict the direction in which the reaction will shift as equilibrium is
approached. Show your work and give a brief sentence to explain your reasoning.
!
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Question 6
(30 points)
Suppose you have bought a house and you are trying to make a decision about whether to
purchase a resistive heater or a heat pump; either device would be driven by your existing
solar electric system. The resistive heater and the heat pump cost the same, so you base
your decision on the efficiency of the system. For the purposes of this problem, you can
consider the heat pump to be based on an idealized Carnot process (i.e. refrigerator
cycle). You can also assume that the total heat input to the house by the resistive heater to
be equal to the work that an electrical motor can do to drive the heat pump. Assume the
motor is ideal and converts all electrical energy into mechanical energy.
6. (a) If the outdoor temperature is 5.0 °C and you want the interior of your house to be
at 20.0 °C, what must the coefficient of performance of the heat pump be?
6. (b) Would you choose a heat pump or a resistive heater to go with your solar system?
Why? Explain in a brief sentence using a quantitative comparison.
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6. (c) Suppose that your solar system is capable of generating 10.0 kW.hr of total energy
during a bright sunny day. Using an ideal heat pump, how much heat could you
pump into the house from the air outside per day?
6. (d) Your plan is to use passive solar heating to keep the house reasonably warm during
the day and then to run the heat pump from the energy stored by the active solar
panel system after the sun goes down. Suppose the heat capacity of the house is
1.0 x 107 J K-1. If the interior temperature only reaches 15.0 °C at the end of the
day (by passive heating), will the heat pump be able to reach the desired
temperature of 20.0 °C for an enjoyable evening? Would the resistive heater be
able to reach 20.0 °C as well? Recall: a total electrical energy of 10.0 kW.hr is
available from the active solar panels after one day.
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Question 7
(30 points)
The following parts of this question are independent of each other.
7. (a) Suppose 2 mol of ideal gas is expanded adiabatically from a volume of 30.0 L at
298 K to a volume of 50.0 L. What is the pressure of the gas after the expansion?
7. (b) Suppose you have a 1.00 M solution of acetic acid (CH3COOH) and a 1.00 M
solution of sodium acetate (NaCH3COO). The pKa for acetic acid is 4.75.
Describe a simple method for making 1.00 L of a buffer from these solutions at a
desired pH of 4.9.
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7. (c) You read a blogger’s webpage that says that the second law of thermodynamics
can be violated. The blogger provides an example of the crystallization of
microscale hard spherical particles in solution that do not have any repulsive or
attractive interactions but also can’t interpenetrate. When the volume fraction of
the spheres is quickly raised to 0.54, the spheres are initially disordered in
position, as in a liquid. However, without any further intervention, the spheres
begin to spontaneously crystallize into a regular lattice, giving an opal-like
appearance--a “colloidal crystal”. The observations on the webpage appear to be
valid and have not been tampered with digitally. The blogger says: “These
observations of spontaneous crystallization completely blow away the longstanding theory of the 2nd law of thermodynamics because the ordering is
spontaneous and the disorder is not increasing over time. The 2nd law can be
overcome by clever people.” You repeat the experiment yourself, and indeed
observe the reported ordering effect. However, using a microscope, you also
notice that the spheres cannot move very much due to the disorder initially, yet,
later, when the spheres form an ordered lattice, each sphere has more space to
diffuse before it hits its neighbors. Based on your observations, would you agree
with the blogger’s conclusion about the second law being invalid? Using your
observations and your understanding of how systems of thermally driven particles
explore available phase space, explain why the observed “spontaneous
crystallization” is still consistent with the second law of thermodynamics. You
smile as you post your message to the blogger’s webpage...
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