Name:
Unit 8 - Properties of Gases
Pressure
Date:
Accelerated Chemistry 1
1. What is meant when we say that a collision is perfectly elastic?
2. a. How does the pressure of a gas in a closed container change if its molecules strike the walls with greater
force?
b. How does the pressure change if the molecules strike with the same force, but more frequently?
3. How will the pressure of a gas in a closed container change if the volume of the container is reduced by half?
Explain why.
4. The pressure on top of Mt. Everest averages about 235 mm Hg. Convert this pressure to
a. torr
c. in Hg
b. psi
d. atm
5. The North American record for highest recorded barometric pressure is 31.85 inches of Hg (in Hg), set in
1989 in Northway, Alaska. Convert this pressure to
a. mmHg
b. atm
6. An open-end manometer is an instrument used to determine the pressure of a given system. The manometer
illustrated below consists of a U-bend tube that contains mercury. One end of the manometer is open to the
atmosphere. Examine the heights of the mercury columns and answer the questions that follow.
a. Which vessel contains a gas with a pressure greater then atmospheric pressure? Explain.
b. Which vessel contains a gas with a pressure less than atmospheric pressure? Explain.
c. If atmospheric pressure is 1.00 atm, what is the pressure of gas B?
d. What would happen to the level of mercury in the tubes of B, if the entire apparatus were brought to the
top of a high mountain? Explain.
Unit 8 Student Handout
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Measuring Gas Pressures with a Closed Manometer
EXAMPLE: Suppose the difference in height of two mercury levels in a closed
manometer is 42 mm, as shown. What is the pressure in atm Hg of the gas in the
container?
Solving process: Because the column of mercury is 42 mm high and 760 mm of
mercury equals 1.00 atm, the pressure is
42.mm 1.00 atm
= 0.055 atm
760 mm
vacuum
gas
sample
mercury
Measuring Gas Pressures with an Open Manometer
EXAMPLE: An open manometer is filled with mercury. The difference
between mercury levels in the two arms is 63.0 mm, as shown. What is the
total pressure, in atm, of the gas in the container? The air pressure is
0.980atm.
Solving process: The mercury is lower in the arm connected to the outside
air. Thus, the pressure exerted by the gas sample must be less than the air
pressure. As a result, we must subtract the pressure of the mercury from the
air pressure to get the gas pressure. Before subtracting, however, we must
convert the 63.0 mm difference in height to atmospheres.
0.980 atm
63.0 mm
63.0 mm 1.00 atm
= 0.0829 atm
760 mm
Now we can subtract the mercury pressure: 0.980 - 0.083 = 0.897 atm
7. An open manometer, such as the one pictured above, is filled with mercury and connected to a container of
hydrogen. The mercury level is 30.0 mm higher in the arm of the tube connected to the air. Air pressure is
1.05 atm. What is the pressure of the hydrogen gas in atmospheres? Answ: 1.09 atm
8. A closed manometer is filled with mercury and connected to a container of NO2. The difference in the height
of mercury in the two arms is 345 mm. What is the pressure, in atm, of the NO2 gas? Answ: 0.454 atm
9. Draw an open-end manometer to show the heights of mercury if a trapped gas has a pressure of 400 mm Hg
and the atmospheric pressure is 1.15 atm.
10. In an open manometer, if the atmospheric pressure decreases, in which direction would the mercury in the
open arm move?
Unit 8 Student Handout
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Motion and Physical States
11. You have one container of Cl2 gas and an identical container of CH4, (methane) gas. Both are at 18C. What
is the difference in the average kinetic energy of the molecules? What is the difference in the average
velocity of the molecules?
12. In terms of the kinetic energy of molecules, explain why your coat is warm when you take it off.
13. A gas sample occupying 300 cm3 is moved to a container with a volume of 200 cm3. Describe any changes
in each of the following values.
a. average kinetic energy of the gas molecules
b. the pressure of the gas
c. the average speed of the gas molecules
d. the number of collisions of a gas molecule with other gas molecules
14. What is wrong with saying, "This container is half full of hydrogen chloride gas"? Is there anything wrong
with saying, "Here is a bottle full of argon gas"?
16. The following graph shows the distribution of molecular speeds for two
different molecules (A and B) at the same temperature.
a. Which molecule has the higher molar mass? Explain the shape of the
curve.
Number of molecules
15. Water has a molecular mass of about 18 amu and is a liquid at room temperature and standard pressure.
Carbon dioxide has a molecular mass of about 44 amu but is a gas at the same conditions of temperature and
pressure. Compare the two in terms of average kinetic energy, and average molecular velocity. How do you
account for the fact that CO2 is a gas even though its molecules have more than twice the mass of H2O
molecules?
A
B
Molecular speed (m/s)
Unit 8 Student Handout
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Number of molecules
17. The following graph shows the distribution of molecular speeds for the same molecule at two different
temperatures (T1 and T2). Which temperature is greater? Explain.
T1
T2
Molecular speed (m/s)
Gas Laws - Boyle’s Law
18. A sample of gas has an initial volume of 2.8 L at a pressure of 755 mm Hg. If the volume of the gas is
increased to 3.7 L, what will the pressure be? Answ: 570 mm Hg
19. A snorkeler with a lung capacity of 6.3 L inhales a lungful of air at the surface, where the pressure is 1.0
atm. The snorkeler then descends to a depth of 25 m, where the pressure increases to 3.5 atm. What is the
volume of the snorkeler’s lungs at this depth? Answ: 1.8 L
20. You are now wearing scuba gear and swimming under water at a depth of 66.0 ft. You are breathing air at
3.00 atm and your lung volume is 10.0 L. Your scuba gauge indicates that your air supply is low so, to
conserve air, you make a terrible and fatal mistake: you hold your breath while you surface. What happens to
your lungs? Why? What is the volume of your lungs at the surface assuming standard pressure at the
surface. Answ: 30.0 L
21. Use Boyle’s law to complete the following table (assume temperature and number of moles of gas to be
constant):
P1
a.
V1
P2
V2
1.90 L
4.19 atm
1.09 L
709 mmHg
b.
755 mmHg
118 mL
c.
2.75 atm
6.75 mL
d.
343 psi
Unit 8 Student Handout
49.8 mL
683 psi
8.79 L
4
Charles’ Law
22. Use Charles’s law to complete the following table (assume pressure and number of moles of gas to be
constant):
a.
V1
T1
V2
1.08 L
25.4°C
1.33 L
77 K
228 mL
298 K
119 cm3
22.4°C
b.
c.
115 cm3
d.
232 L
18.4°C
T2
96.2°C
23. A 48.3 mL sample of gas in a cylinder is warmed from 22°C to 87°C. What is its volume at the final
temperature? Answ: 58.9 mL
24. If 15.0 liters of neon at 25.0 °C is allowed to expand to 45.0 liters, what must the new temperature be (in °C)
to maintain constant pressure? Answ: 621 °C
Combined Gas Law
25. A sample of gas has an initial volume of 158 mL at a pressure of 735 mm Hg and a temperature of 34C. If
the gas is compressed to a volume of 108 mL and heated to a temperature of 85C, what is the final pressure
in mm of Hg? Answ: 1250 mm Hg
26. A balloon has a volume of 3.7 L at a pressure of 1.1 atm and a temperature of 30C. If the balloon is
submerged in water to a depth where the pressure is 4.7 atm and the temperature is 15C, what will its
volume be (assume that any changes in pressure caused by the skin of the balloon are negligible.) Answ:
0.82 L
27. A bag of potato chips contains 585 mL of air at 25C and a pressure of 765 mm Hg. Assuming the bag does
not break, what will be its volume at the top of the mountain where the pressure is 442 mm Hg and the
temperature is 5.0C? Answ: 945 mL
Unit 8 Student Handout
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Ideal Gas Law
28. Calculate the volume occupied by 23.67 g of nitrogen gas at a pressure of 1.37 atm and a temperature of
42C. Answ: 15.9 L
29. Calculate the number of molecules of gas in a basketball inflated to a total pressure of 24.2 psi with a
volume of 3.2 L at 25C. Answ: 1.3x1023 molecules
30. A bicycle tire has an internal volume of 1.52 L and contains 0.406 mol of air. The tire will burst if its
internal pressure reaches 7.25 atm. To what temperature, in degrees C, does the air in the tire have to be
heated to cause a blowout? Answ: 58 °C
31. The temperature of the atmosphere on Mars can be as high as 27C at the equator at noon, and the
atmospheric pressure is about 8 mm Hg. If a spacecraft could collect 10. m3 of this atmosphere, compress it
to a small volume, and send it back to Earth, how many moles would the sample contain? Answ: 4 moles
Partial Pressure
32. A gas mixture contains each of the following gases at the indicated partial pressure. What is the total
pressure of the mixture in atm? Answ: 0.937 atm
N2 = 355 torr; O2 = 128 torr; He = 229 torr
Vapor Pressure of Water
33. A mixture of helium, nitrogen, and oxygen has a total pressure
of 752 mm Hg. The partial pressures of helium and nitrogen are
234 mm Hg and 197 mm Hg, respectively. What is the partial
pressure of oxygen in the mixture? Answ: 321 mm Hg
34. The oxygen gas emitted from an aquatic plant during
Temperature, °C
10°C
20°C
25°C
30°C
40°C
50°C
60°C
70°C
80°C
Pressure (mm Hg)
9.2
17.5
23.8
31.8
55.3
92.5
149.4
233.7
355.1
photosynthesis is collected over water at a temperature of 25°C
and a total pressure of 753 torr. What is the partial pressure of the oxygen gas? Answ: 729 mm Hg
Unit 8 Student Handout
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35. A gas mixture contains 78% nitrogen and 22% oxygen. If the total pressure is 1.12 atm, what are the partial
pressures of each component? Answ: PN2 = 0.87 atm, PO2 = 0.25 atm
36. An air sample contains 0.038% CO2. If the total pressure is 758 mm Hg, what is the partial pressure of
CO2? Answ: 0.29 mm Hg
37. A heliox deep-sea diving mixture contains 4.0% oxygen and 96% helium. What is the partial pressure of
oxygen when this mixture is delivered at a total pressure of 8.5 atm? Answ: 0.34 atm
38. A scuba diver breathing normal air descends to 100 m of depth, where the total pressure is 11 atm. What is
the partial pressure of oxygen that the diver experiences at this depth? Is the diver in danger of experiencing
oxygen toxicity? (Oxygen toxicity is experienced when the partial pressure of O2(g) in blood is 1.4 atm.)
Answ: 2.3 atm, yes since the threshold is 1.4 atm
39. What is the total pressure, in atmospheres, of a gas mixture that contains 1.0 g of H2 and 8.0 g of Ar in a 3.0
L container at 37°C? What are the partial pressures of the two gases? Answ: PT = 5.9 atm, PAr = 1.7 atm,
PH2 = 4.2 atm
40. A halothane-oxygen mixture (C2HBrClF3 + O2) can be used as an anesthetic. A tank containing such a
mixture has the following partial pressures: P (C2HBrClF3) = 170 mm Hg and P(O2) = 570 mm Hg.
A) What is the ratio of the number of moles of halothane to the number of moles of oxygen? Answ: 0.30
halo:1 O2
B) If the tank contains 160 g of oxygen, what mass of halothane is present? Answ: 77% O2: 23% Halo
Unit 8 Student Handout
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Graham’s Law of Effusion
41. Which gas effuses faster: hydrogen or chlorine? How many times faster? Answ:H2, 6x’s faster
42. Suppose you have two vials - one containing ammonia, and the other containing chlorine. When they are
opened across the room, which would you expect to smell first? Why?
43. Which gas effuses faster at the same temperature: oxygen or argon? How many times faster? Answ:O2,
1.12x’s faster
44. What is the ratio of effusion rates for the lightest gas, H2, and the heaviest known gas, UF6? Answ: 13
45. Calculate the ratio of the velocity of helium gas to the velocity of neon gas at the same temperature. Answ:
2.24
46. What is the molar mass of an unknown gas if it diffuses 0.912 times as fast as argon gas (39.9 g/mol)?
Answ: 48.0 g/mol
47. Suppose a gas diffuses 1.41 times a fast as sulfur dioxide at the same temperature and pressure. What is the
molar mass of the unknown gas? Answ: 32.2 g/mol
48. At a given pressure and temperature, it takes 4.55 min for a 1.5-L sample of He to effuse through a
membrane. How long does it take for 1.5 L of F2 to effuse under the same conditions? Answ: 14.0 min
Unit 8 Student Handout
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49. A sample of an unknown gas effuses in 11.1 min. An equal volume of H2 in the same apparatus at the same
temperature and pressure effuses in 2.42 min. What is the molar mass of the unknown gas? Answ:42.5
g/mol
Gas Stoichiometry
1. Calculate the volume of each of the following gas samples at STP.
a. 73.9 g nitrogen Answ: 59.1 L
c. 148 g nitrogen dioxide Answ: 72.1 L
b. 42.9 g oxygen Answ: 30.0 L
d. 245 mg carbon dioxide Answ: 0.125 L
2. Calculate the mass of each of the following gas samples at STP.
a. 178 mL carbon dioxide Answ: 0.350 g
c. 1.25 L sulfur hexafluoride Answ: 8.15 g
b. 144 mL oxygen Answ: 0.206 g
3. Consider the following chemical reaction: C(s) + H2O(g)  CO(l) + H2(g)
How many liters of hydrogen gas are formed from the complete reaction of 1.45 mol of C? Assume that the
hydrogen gas is collected at a pressure of 1.0 atm and temperature of 355 K. Answ: 42 L
4. Oxygen gas reacts with powdered aluminum to produce aluminum oxide. How many liters of O2 gas,
measured at 782 mm Hg and 25°C, are required to completely react with 2.4 mol of Al? Answ: 43 L
Unit 8 Student Handout
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5. Nitrogen reacts with powdered aluminum to produce aluminum nitride. How many liters of N2 gas, measured
at STP, are required to completely react with 18.5 g of Al? Answ: 7.68 L
6. Consider the following reaction: P4(s) + 6 H2(g)  4 PH3(g)
a. If 88.6 L of H2(g), measured at STP, is allowed to react with 158.3 g of P4, what is the limiting reactant?
Answ: H2 limits
b. If 48.3 L of PH3, measure at STP, forms, what is the percent yield? Answ: 81.7 %
Cumulative Problems
1. Cylinder A in the picture below contains 0.1 mol of a gas that behaves ideally. Choose the cylinder (B, C, or
D) that correctly represents the volume of the gas after each of the following changes. If none of the
cylinders is correct, specify “none”.
a. P is doubled at fixed n and T.
b. t is reduced from 400 K to 200 K at fixed n and P.
c. T is increased from 100°C to 200°C at fixed n and P.
d. 0.1 mol of gas is added at fixed P and T.
e. 0.1 mol of gas is added and P is doubled at fixed T.
2. Which of the following samples of gases occupies the largest volume, assuming each sample is at the same
temperature and pressure—50.0 g of neon, 50.0 g of argon, or 50.0 g of xenon?
Unit 8 Student Handout
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3. Suppose you have a sample of Gas A, with a molar mass of 75 g/mol, and another sample of Gas B, with a
molar mass of 150 g/mol. Assume each gas has a distinctive odor; you are seated 10 meters away when
these gases are released into the air, and it takes 20 seconds to smell the first gas. Which do you smell first,
and how long does it take (from t=0 sec) before you smell the second gas? Answ: approximately 30 s
4. What volume of carbon dioxide gas contains the same number of oxygen atoms as 250.0 cm3 of carbon
monoxide gas, if each gas sample is measured at the same temperature and pressure? Answ: 125.0 cm3
5. A gaseous compound containing hydrogen and carbon is decomposed and found to contain 82.66% carbon
and 17.34% hydrogen by mass. The mass of 158 mL of the gas, measured at 556 mm Hg and 25°C, is found
to be 0.275 g. What is the molecular formula of the compound? Answ: C4H10
6. A gaseous compound containing hydrogen and carbon is decomposed and found to contain 85.6% carbon and
14.37 % H by mass. The mass of 258 mL of the gas, measured at STP, is found to be 0.646 g. What is the
molecular formula of the compound? Answ: C4H8
Unit 8 Student Handout
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7. The partial pressure of carbon dioxide varies with seasons. Would you expect the partial pressure in the
Northern Hemisphere to be higher in the summer or winter? Explain.
8. A healthy adult exhales about 5.0 × 102 mL of a gaseous mixture with each breath. Calculate the number of
molecules present in this volume at 37°C and 1.1 atm. Answ: 1.3x1022 molecules
9. Containers A, B, and C are attached by closed stopcocks of negligible volume. If each particle shown
represents 106 particles,
a. how many gray and black particles are in B after the
stopcocks are opened and the pressure stops changing?
b. If the pressure in C, PC, is 750 mm Hg before the stopcocks
are opened, what is PC afterward?
A
B
C
Answ: 2x106 black and gray
500 mm Hg
Unit 8 Student Handout
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