Chemical engineering exam

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SUPPLEMENTAL QUESTIONS FOR CHEM 1A – EXAM #5

The following questions are provided to supplement your studying efforts for the first
exam. I suggest you use these problems as “practice exams,” so try them WITHOUT
your notes or text available, do them in a quiet place with all distractions silenced, and
give yourself some type of time limit in which to finish a set number of them. This will
best simulate the exam environment. Based on class progress, the set of questions
below may not be an exhaustive list – I will make you aware of any changes to this
question set if any needs to be made. When performing numerical calculations, pay
attention to your significant figures!!! Questions in bold type are questions I consider
to be more challenging.

1. Three 200.0 L tanks, each at 24 °C, are to be filled separately with the gases
helium, chlorine, and argon. What mass of each gas, in g, must be placed inside each
respective tank in order to create a pressure of 13.6 atm?

2. A sample of a noble gas has a density of 0.003749 g mL−1 at STP. What is the
most likely identity of this noble gas?

3. A chemist traps a sample of gas in a balloon at an initial temperature of 42.2 °C.
At a pressure of 1.000 atm, the gas collection balloon inflates to a volume of 22.6 mL.
The entire experiment is placed into a chamber with a pressure of 2.000 atm and
temperature of 55.9 °C. Find the new volume of the balloon, in mL.

4. A helium balloon is observed to shrink to 68% of its original volume when
placed into a dry ice/acetone bath. If the balloon was originally at 22 °C, what is
the temperature, in °C, in the bath?

5. The box below contains a visualized mixture of gas A (represented by the black
circles) and gas B (represented by the white circles). If the partial pressure of gas A is
422 Torr, determine PT in the box, in Torr.

6. Two equal volume glass bulbs, one containing 6.26 g of nitrogen and one
containing 7.11 g of argon are connected via a valve. Both bulbs are being held at
298 K. Once the bulbs are connected, the total pressure in the system is 2.45 atm.
Determine the partial pressure, in atm, of each gas after the valve is opened, and the
volume, in L, of each glass bulb. You should assume there is no temperature change
upon valve opening.

7. A 9.0 L tank of He with a pressure of 89.3 psi, a 5.7 L tank of Ar with a pressure
of 92.5 psi, and a 3.7 L tank of Kr with a pressure of 88.2 psi (all held at 45.9 °C) are
connected via a three-way valve. Determine the total pressure, in psi, in all three tanks
and the molarity of each gas present when they are connected and cooled to 13.8 °C.
You may omit the volume of any tubing and valves connecting the tanks.

8. A spherical glass container contains helium gas at 25 °C and 1.960 atm.
When a portion of the helium is withdrawn and adjusted to 1.00 atm and 25 °C in a
flexible container, it is found to have a volume of 1.75 cm3. When this portion of
helium is removed, the gas remaining in the first container shows a pressure of
1.710 atm. Calculate the volume, in L, of the spherical glass container.

9. The Haber process is the reaction of hydrogen and nitrogen gases to produce
ammonia gas. This reaction will be taking place inside a 24.00 L glass reaction vessel
being held at 355 K.

a. What is the balanced reaction?

b. 6.99 g of hydrogen and 8.33 g of nitrogen are placed into this vessel. What are
the partial pressures of each gas, in atm, prior to the reaction?

c. If the reaction proceeds with 100 % yield, calculate the partial pressures of each
gas and the total pressure at the end of the reaction.

d. Using the same conditions as in part a, determine the molarities of each gas
before and after the reaction is complete.

e. If the partial pressure of NH3 at the end of the reaction is 0.211 atm, what is the
percent yield? Assume the same starting conditions as given in part b.

f. If the reaction has the percent yield as determined in part d, what are the partial
pressures and molarities of the nitrogen and hydrogen gases and the total pressure at
the end of the reaction? Assume again the same initial conditions as in part b.

g. Take your expected PT value from part c, multiply it by the percent yield
from part d, and compare this value to the calculated PT in part e. You should see
the two are different, meaning you are not able to multiply a theoretical PT by a
percent yield to obtain an actual PT. Why do you think that is true for this
particular reaction?

10. Methanol vapor (CH3OH) can be produced by the reaction of carbon monoxide
gas with hydrogen gas. A reaction balloon is initially charged with equal mols of the
reactants against a constant temperature and pressure and inflates to 3.50 L. What is
the volume of the balloon at the end of a complete reaction? What about the volume at
the end if the reaction has a 65.0 % yield?

11. Rock climbing or weightlifting “chalk” is typically finely ground magnesium
carbonate that may have silica or magnesium sulfate added as a drying agent. You
have heated a 0.1400 g sample of chalk and collected 36.11 mL of gas using a leveled
eudiometer (as we did in Expt 22). The temperature of the eudiometer is 24.1 °C and
the laboratory barometer reads 755.1 mm Hg. Given that Pvap for H2O at 24.1 °C is
22.6 Torr, determine the percent magnesium carbonate in the chalk sample.

12. Let’s assume you now have a sample of chalk claiming to be 100% pure
magnesium carbonate. Assuming the chalk is actually pure and you will be using the
same experimental conditions as in #11 (including the 0.1400 g sample of chalk), what
volume of gas, in mL, should you capture?

13. If your gas collection experiment from #11 was performed under a higher
lab pressure, would your percent magnesium carbonate be higher, lower, or
unchanged? Be able to justify your choice.

14. If your gas collection experiment from #12 was performed with a lower
temperature in the eudiometer, would your percent magnesium carbonate be
higher, lower, or unchanged? Be able to justify your choice.

15. Answer the following questions regarding the Maxwell-Boltzmann distributions
plotted below.

a) Assume we are dealing with two samples of argon gas. Which curve (dotted or
dashed) represents the sample of Ar at the higher temperature? Briefly explain your
choice.

b) Assume we are dealing with a sample of fluorine and a sample of neon, each at
the same temperature. Which curve (dotted or dashed) represents the sample of
fluorine? Briefly explain your choice.

16. A glass bulb being held at 700.0 K contains chlorine gas, and a second glass
bulb held at 250.0 K contains fluorine gas. Which bulb contains the faster species?

17. A mixture of argon and neon being held in a glass bulb has a temperature of
21 °C. KMT predicts these gases both have the same average kinetic energy, and you
will prove this by answering the following questions about this gas mixture.

a) What is urms for of each gas, in m s−1? Complete each calculation to 5 significant
digits.

#

speed

#
speed

b) Determine the average kinetic energy per particle (KEpart) for the mixture of argon
and neon as given above by using the equation which relates the mass per particle and
the average of the squares of the speeds. Assume urms is acceptable to use in the place
of u bar squared in this equation. Perform these calculations to 4 sig figs.

c) You should have gotten the same answer for each gas in part b above, which
verifies the equations derived from KMT are consistent. Let’s take this one step further:
calculate the average kinetic energy per mol (KEmol) by multiplying one of the answers
from part b by NA. Convert this to kJ/mol. Keep 4 sig figs in the calculation.

d) Finally, determine the average kinetic energy per mol for the atoms in the glass
bulb by using the equation that directly relates average kinetic energy to temperature.
Convert this to kJ/mol, again keeping 4 sig figs. You should be “pleasantly surprised” by
this answer in comparison to your answer from part c.

18. Use the principles of KMT to explain why the following can be observed for
samples of trapped gas.

a) You are unpacking from a recent trip to Hawaii, and upon opening your toiletries
bag you discover the very expensive special herbal extract shampoo you bought there
has leaked all over the inside of your bag during the flight back. Assume constant T and
n for air trapped inside the shampoo bottle.

b) Let’s assume you love cereal and “The Daily Show.” Let’s say its one of your
daily routines – you sit down on the couch with your supplies, pour the first bowl and
recap the milk and cereal containers. After the first bowl, you want more! When you
uncap the milk, you hear a slight “pffft” out of the container. Assume constant V and n
for the milk container while it is capped. (Note: if you are more of the conservative
persuasion, feel free to replace “The Daily Show” in this problem with “Fox and Friends”
or whatever you feel comfortable with).

19. An unknown diatomic “R2“ is diffusing 1.479 times faster than Cl2 in a 5.00
L glass bulb being held at 388 K. The total mass of the gas mixture is 4.48 g, and
the mixture is 34.6% by mass Cl2. Determine the pressure, in atm, in the 5.00 L
glass bulb.

20. Two samples of argon gas are prepared, described as follows:

Sample A: n = 2 mols, V = 0.400 L, T = 150 K
Sample B: n = 1 mol, V = 10.0 L, T = 800 K

a) Qualitatively, which do you predict to be more nearly ideal, meaning which of the
two samples do you predict will more closely follow ideal behavior?

b) Using the data given, determine the percent error made by the ideal gas equation
for each sample (performing similar calculations as to those in the class notes). Are the
results of your calculations consistent with your prediction? For argon, a = 1.35 atm L2
mol−2 and b = 0.0322 L mol−1.

21. On a backpacking trip, you accidentally fall into a very cold river and you are
trapped in the water for ten minutes. Back at camp with no way to make a fire, you and
your backpacking partner strip down and climb into a sleeping bag to warm you to
regular body temperature. Draw energy diagrams from the point of view of you, your
backpacking partner, and the sleeping bag. Assume the sleeping bag does not allow
heat to enter or escape and that any heat lost/gained by people inside the sleeping bag
comes from/goes to the other person present (i.e. body heat generated by metabolism is
ignored here).

22. 19.0 g of water at an original temperature of 80.0 °C is mixed with 57.0 g of
water at an original temperature of 15.0 °C and the mixture is stirred. What is the
temperature of the mixed water samples, in °C? Assume here the mixture will not
lose any heat to its container.

23. An unknown chemical Y has the following heating curve:

You have a 0.32 mol sample of Y (MM = 34.0 g/mol) in a small heating apparatus. How
much energy, in kJ, must you give this sample in order to heat it from 20.0 °C to
140.0 °C? Use the data shown and report your answer to two significant figures.

24. The diagrams below show the relative enthalpy values measured at various
points while an aqueous solution is being formed. The solid arrow represents the heat
required to prepare the solute and solvent for solution formation and the dotted arrow
represents the heat released as the solute becomes hydrated. Answer the questions
below regarding these diagrams.

T of experiment (°C)

120

45

T
o

f s
ub

st
an

ce
(

°C
)

ssolid Y 0.224 J/(g °C)
sliquid Y 1.098 J/(g °C)
svapor Y 2.983 J/(g °C)
ΔHfus Y 2102 J/mol
ΔHvap Y 31 kJ/mol

Heat added

a. Is the formation of solution #1 exothermic or endothermic? Why?
b. Is the formation of solution #2 exothermic or endothermic? Why?
c. Let’s assume in each solution, 0.445 mols of solute was dissolved in water.
Determine ΔHhyd and ΔHsoln, in kJ/mol for both solutions. Do your ΔHsoln values match
your answers to a and b above?
d. Let’s say both of these solutions involved a polar solute. Using entropy, explain
why the endothermic solution still forms readily (despite requiring energy).
e. Finally, let’s assume in both cases there was 579.0 g of water present initially at
21.5 °C. Determine the final temperature for both solutions once all the solute dissolved.

25. Assuming a similar heat of hydration for the resulting ions, do you expect ΔHsoln
for MgO to be more endothermic or more exothermic than that of FrI?

26. ΔHsoln for CsClO4 is 17.78 kJ/mol. If 1.887 g of CsClO4 are placed into 20.0 g of
water originally at 29.9 °C, what will the final temperature of the water be, in °C?

27. The reactions of magnesium, aluminum and manganese metals with aqueous
chloric acid have ΔHrxn = −555 kJ/mol, ΔHrxn = −531 kJ/mol, and ΔHrxn = −411 kJ/mol
respectively (Mn will become Mn4+ when reacting with the acid). A 0.100 g pellet of each
metal will be placed into separate constant pressure calorimeters, each containing
excess acid at 23.5 °C. Assuming 60.0 g of total solution in the calorimeter and a 100%
yield for the reaction, predict the final temperature of each calorimeter after the
metal/acid reactions.

28. You find a sample of metal labeled “magnesium/silver alloy” and want to
determine the mass percent magnesium, so you drop this sample into one of the same
calorimeters as used in #27 (assume same mass of solution and original temperature).
The final temperature of the calorimeter solution reaches 35.5 °C. If the sample of alloy
had a mass of 0.1775 g, what is the alloy’s mass percent magnesium? Assume a 100%
yield for this reaction.

29. Assume the precipitation of Fe(OH)3 from originally soluble ions has
ΔHrxn = −32 kJ/mol. 200.0 mL of 0.322 M Fe(NO3)3 are mixed with 100.0 mL of 1.000 M
NaOH in a constant pressure calorimeter. Answer the following questions regarding this
reaction.

a) What is the net ionic reaction?
b) What is q for the reaction?
c) What is q for the calorimeter?
d) Assuming the mixed solutions has a density of 1.00 g/mL and the same specific
heat capacity of water, determine the temperature change which should be observed.

30. The general reaction A(aq) + 2 E(aq) → 5 G(aq) has ΔHrxn = −954 kJ/mol.
400.0 mL of 2.55 M A are mixed with 188.0 mL of 4.0 M E in a calorimeter to
produce a solution with a density of 1.44 g/mL and s = 4.992 J g−1 °C−1. During the
course of the reaction the temperature of the mixed solutions increases 11.0 °C.
Use this information to determine the % yield of the reaction. You may assume
the volumes of the two solutions being mixed are additive.

31. Use the table provided below to answer the questions that follow. Report any
ΔHrxnº values in kJ/mol.

Stuff ΔHfº (kJ/mol
CaCl2(s) −798.8
CaCO3(s) −1206.92

HCl(g) −92.307
H2O(l) −285.830
H2O(g) −241.818
CO(g) −110.525
CO2(g) −393.509

a) Write the proper formation reaction for calcium carbonate.
b) What is ΔHrxnº for the reaction you wrote in part a?
c) What is ΔHrxnº for: CO(g) → C(s) + ½ O2(g)
d) What is ΔHrxnº for the formation of calcium chloride solid, carbon dioxide gas and

water vapor from the reaction of hydrogen chloride gas and solid calcium
carbonate?

e) The combustion of acetaldehyde gas (formula = CH3CHO) in the presence of O2
to produce carbon dioxide gas and water vapor has ΔHrxnº = −2199.9 kJ/mol.
What is ΔHfº for acetaldehyde?

f) 38.0 g of carbon and 3.93 g of oxygen are placed into a constant-volume
calorimeter with C = 1.37 kJ/°C. As they react to produce CO gas, the
temperature of the calorimeter rises by 11.5 °C. What is the apparent
percent yield of the reaction?

32. Given the following data:

Fe2O3(s) + 3 CO(g) → 2 Fe(s) + 3 CO2(g) ΔHrxnº = −23 kJ/mol
3 Fe2O3(s) + CO(g) → 2 Fe3O4(s) + CO2(g) ΔHrxnº = −39 kJ/mol
Fe3O4(s) + CO(g) → 3 FeO(s) + CO2(g) ΔHrxnº = 18 kJ/mol

Determine ΔHrxnº for: FeO(s) + CO(g) → Fe(s) + CO2(g)

33. Use the bond enthalpy data provided in your textbook to estimate ΔHrxn for the
reaction of carbon monoxide gas with oxygen gas to produce carbon dioxide gas. Use
whole numbers when balancing this equation. Compare this value to a calculated value
from ΔHfº data in your textbook and comment on any difference.

34. A tautomerization reaction is one in which an organic molecule’s structure
changes based on the positioning of a double bond. Below is an example of “keto-enol”
tautomerization, where an organic molecule with a carbon/oxygen double bond (a
“ketone”) rearranges to carbon/carbon double bond with an OH substitution (an “enol”):

Use the bond enthalpy data provided in your textbook to estimate ΔHrxn for this
tautomerization.

35. The table below gives selected data for aluminum solid and fluorine gas. Each provided
data point is in kJ/mol. Given that the lattice energy of aluminum fluoride solid is
−6218 kJ/mol, determine ΔHfº for solid aluminum fluoride. Assume all data provided is at
thermodynamic standard conditions.

Species ΔEsub I1 I2 I3 e− affinity ΔEbond
Al(s) 326
Al(g) 580. 1815 2740.
F2(g) 154
F(g) −328

36. A sample of gas will be expanded from 2.0 L to 5.0 L, with the work to expand being
supplied by a crank you will turn. Each “crank” of the lever results in 105 J of work being put
into the expansion. Determine the number of “cranks” required to perform this expansion:

a. at the beach (Pext = 1.00 atm).
b. at the bottom of the Mariana Trench (Pext = 15,750 psi)
c. on Mars (Pext = 4.5 mm Hg)

37. A system contains a gas being held against constant pressure. Determine both
ΔEsys and ΔEsurr for the following processes.

a) Volume contracts from 3.00 L to 0.224 L with an accompanying release of 21 J of

heat. Pext = 0.200 atm
b) Volume expands from 1.00 L to 5.00 L with an accompanying absorption of 155 J of

heat. Pext = 1.000 atm
c) Volume expands from 0.004 L to 903.9 L with an accompanying release of 34 J of

heat. Pext = 0.00 atm

38. What do you expect the sign of ΔV and w to be for the following reactions taking
place in a flexible container, with constant T and Pext = 1 atm? Provide a brief explanation of
your choice.

a) N2(g) + 2 O2(g) → N2O4(g)
b) P4(s) + 5 O2(g) → P4O10(s)

39. Hydrobromic acid vapor is formed from the reaction of hydrogen gas and excess
bromine liquid. The reaction takes place in a flexible reaction balloon being held at
1.000 atm pressure and 298.15 K. ΔHf° for HBr(g) = −36 kJ/mol.

a) Assuming a complete reaction, what is ΔErxn°, in kJ/mol, if 0.0455 mols of H2 are
reacted with excess Br2 liquid? Use whole numbers to balance the reaction.

b) Using the same conditions as in a above but this time assuming a 78.9% yield for the
reaction, determine ΔErxn°, in kJ/mol.

c) Assuming a complete reaction under the same conditions as a and b, what is ΔErxn°,
in kJ/mol if 1.99 mols of H2 are reacted with excess Br2 liquid? Use whole numbers to
balance the reaction.

40. 330.0 g of liquid bromine (d = 3.10 g/mL, ΔHvap = 29.96 kJ/mol) are vaporized at
the normal boiling point (332 K) in a closed flexible container. Determine ΔEsys for this
process, in kJ/mol.

41. An experiment is completed in two parts. The first is the combustion of
propane gas in a constant-volume calorimeter with C = 0.334 kJ/°C. It is observed
0.4162 g of oxygen gas being combusted in excess propane increased the
temperature of this calorimeter by 17.1 °C. In the second experiment, 22.0 g propane
gas is combusted with 22.0 g of oxygen gas in a flexible container being held at a
constant external pressure of 1.000 atm and a temperature of 298 K. Determine ΔErxn
for propane combustion, in kJ/mol. Assume the molar heat of combustion for
propane is temperature independent.