Worksheet 1 – Properties of Gasses
Group Members: ____________________________
Team: _______________
Properties of Gasses
Introduction
The kinetic theory underlying the gas laws is one of the great successes of the development of
our molecular view of the world, with a myriad of practical applications in everyday life. For
example, a scuba diver can spend thirty minutes or more underwater due to the compressed gas
in their tanks, and internal combustion engines can do work (i.e. move your car) due to the work
that is done when a compressed gas expands. The gas laws you will learn about in this chapter
explain why gasses behave the way they do.
Learning Objectives
● Use the kinetic molecular theory to explain the properties of gasses
● Use the individual, combined, and ideal gas laws to relate changes in the volume,
temperature, pressure, and number of moles of a gas.
● Use balanced chemical equations to relate the volumes of gas-phase reactants and
products using the reaction stoichiometry
● Relate mole fraction, partial pressure, and quantity of a gas in a mixture
Resources
Gilbert, Section 9.1 - 9.9
ChemTours
All Chemtours
Videos (Khan Academy)
Ideal Gas Law
Kinetic Molecular Theory
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Prerequisites
Stoichiometry, moles
Vocabulary
Effusion, diffusion, kinetic molecular theory, root-mean square, Dalton’s Law, Boyle's Law,
Amontons’s Law, Charles’s Law, Avogadro's Law, ideal gas law, standard temperature and
pressure (STP)
Focus Information
The Kinetic Molecular Theory of Gasses and Graham’s Law
-
The particles occupy negligible volume (point masses).
Gases consist of atoms/molecules in continuous random motion.
The average kinetic energy of these atoms/molecules is proportional to T. At any T, all
gases have the same average kinetic energy.
Gas molecules undergo elastic collisions with each other and the walls of the container
(no kinetic energy is converted into potential energy or transferred to the walls).
No intermolecular forces (attractions or repulsions).
Molecular Speeds and Kinetic Energy
Average kinetic energy of a gas is proportional to its mass (m) and the square of its speed (u)
(eq 1) and to its temperature (T) (eq 2)
K E avg = 12 mu2rms
eq 1
K E avg = 32 kB T
eq 2
The gas laws and how the kinetic molecular theory explains them.
Dalton’s Law: P ∝ n (constant V & T)
More molecules ➝ more collisions with the sides of the container (➝ more force)
➝ higher P
Boyle’s Law: P ∝ 1/V (constant n & T)
Larger volume ➝ fewer collisions with container (➝ less force) ➝ lower P
PV = constant ➝ P1V1 = P2V2
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Amontons’s Law: P ∝ T (constant V & n)
Higher T ➝ faster motion ➝ more energetic collisions (➝ more force) ➝ higher P
P1/T1 = P2/T2
Charles’s Law: V ∝ T (constant P & n)
Higher temperature ➝ Faster motion ➝ More collisions (P increases) if V is constant ➝
V must increase to reduce collisions and keep P from increasing.
V/T = constant ➝ V1/T1 = V2/T2
Avogadro's Law: V ∝ n at constant P & T
Summary of the Gas Laws
The combined gas law -
P 1V 1
P 2V 2
=
any units are ok for P,V, but T must be in K
T1
T2
The Ideal Gas Law
PV = nRT
where R = Universal Gas Constant = 0.08206 L·atm/mol·K
For the ideal gas law, you MUST use T in Kelvin (K), P in atm, and V in L. Look at the units of
the gas constant (R) to remind yourself what units are needed.
STP - Standard temperature and pressure = 0°C & 1 bar (sometimes, 1 atm is used)
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Density of a gas
Derived from PV = nRT
where “molar density” would be given by n = P (recall density = m/V, so molar density
V
RT
would be n/V)
The number of moles of gas, n, is related to its mass m by n =
m
ℳ
(ℳ is molar mass, g/mol)
Substituting n = m/ℳ into the molar density equation and rearranging so d = m/V:
m
P
V ℳ = RT
➝
Pℳ
Pℳ
m
= RT ➝ d = RT
V
where ℳ s the molar mass, P is the pressure, R is the universal gas constant and T is the
temperature in K
Density is proportional to P and ℳ and inversely proportional to T.
Dalton’s Law and Mixtures of Gases
P total = P 1 + P 2 + P 3 + ....
ni
Mole fraction - χi = n
total
Partial pressure of a gas = P i = χi P total where Pi is the partial pressure of gas i.
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Worksheet 1 – Properties of Gasses
Questions to be graded - 2, 4a, 9
Homework related to 12, 20, 22
Key Questions
1. The figure below shows the distribution of molecular speeds of CO2 and SO2 molecules at
25oC.
a. Which one is the profile for SO2?
b. Which of these profiles should match that of propane (C3H8) a common fuel in portable
grills?
2. For the balloon on the left in the Figure below, which particulate view on the right (i, ii, or
iii) best represents the distribution of the helium atoms inside the balloon after each change?
a. The atmospheric pressure is increased at constant temperature.
b. The temperature is decreased at constant pressure.
3. How does kinetic molecular theory explain why pressure is directly proportional to
temperature at fixed volume?
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4. Use representations [A] through [I] in the figure to answer questions a–f. The pink balloons
contain hydrogen, the yellow balloons contain nitrogen, and the gray balloons contain
oxygen.
a. Identify three changes that could be responsible for the change in size of the pink balloon
from [A] to [C].
b. If the smaller pink balloon in [A] corresponds to the particulate view in [B], which of the
changes identified in the previous question would result in the larger pink balloon in [C]
also corresponding to the particulate
view in [B]?
c. If the smaller yellow balloon in [D]
corresponds to the particulate view in
[E], which particulate view
corresponds to the larger yellow
balloon in [F] if no additional nitrogen
has been added?
d. If the larger gray balloon in [I]
corresponds to the particulate view in
[E], which particulate view represents
the gas at a lower temperature?
e. If the gray balloons in [G] and [I] each
contain 1 mol of gas at 25°C, in which
gray balloon are the collisions between the oxygen molecules and the inside of the
balloon more frequent?
f. Which balloon contains the gas with the shortest mean free path?
5. Consider the three Torricelli barometers in the figure
below. Which one is most likely sensing atmospheric
pressure at each of the following locations?
a. San Diego, California (sea level)
b. The summit of Mount Everest (8.8 km above sea
level)
c. The bottom of the Tau Tona gold mine in South
Africa (3.9 km below sea level)
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6. Describe the difference between force and pressure.
7. Why does atmospheric pressure decrease with increasing elevation?
8. The two plots of volume versus reciprocal pressure in the
figure below correspond to the same quantity of gas at
two temperatures. Which line corresponds to the higher
temperature?
9. In the figure below, which of the two plots of volume
versus temperature at constant pressure is not consistent
with the ideal gas law?
10. The volume of a quantity of gas at 1.00 atm is
compressed from 3.25 L to 2.24 L. What is the final pressure of the gas if no change in
temperature occurs?
11. Balloons for a New Year’s Eve party in Potsdam, New York, are filled to a volume of 5.0 L at
a temperature of 20°C and then hung outside, where the temperature is –25°C. What is the
volume of the balloons after they have cooled to the outside temperature? Assume that
atmospheric pressure inside and outside the house is the same.
12. How many moles of air must be in a racing bicycle tire with a volume of 2.36 L if it has an
internal pressure of 6.8 atm at 17.0°C?
13. The fuel canister for a portable camping stove contains 190 g of pressurized butane (C4H10).
a. Find the moles of butane in the canister
b. What volume of butane does this represent at 25°C if it escapes into the air at 750
mmHg?
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14. Hyperbaric oxygen chambers are used to treat divers suffering from decompression sickness
(the “bends”) with pure oxygen at greater than atmospheric pressure. Other clinical uses
include treatment of patients with thermal burns and CO poisoning.
a. Find the moles of O2 in the chamber that contains 15.00 kg of O2
b. What is the pressure in a chamber with a volume of 4.85 × 103 L that contains O2 gas at a
temperature of 298 K?
15. In some cities, public buses are fueled by compressed natural gas (CNG; mostly methane,
CH4. How many grams of CH4 gas are in a 250 L fuel tank at a pressure of 255 bar at 20°C?
16. Students at the University of North Texas and the University of Washington built a car
propelled by compressed nitrogen gas. The gas was obtained by boiling liquid nitrogen stored
in a 182 L tank.
a. How many moles of N2 are in the tank?
b. What volume of N2 is released at 0.927 atm of pressure and 25°C from a tank full of
liquid N2 (d = 0.808 g/mL)?
17. Do all gases at the same pressure and temperature have the same density? Explain your
answer.
18. Birds and sailplanes take advantage of thermals (rising columns of warm air) to gain altitude
with less effort than usual. Why does warm air rise?
19. How does the density of a gas sample change when
a. its pressure is increased
b. its temperature is decreased?
20. The density of an unknown gas is 1.107 g/L at 300 K and 740 mmHg. What is the molar
mass of the gas?
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21. The CO2 that builds up in the air of a submerged submarine can be removed by reacting it
with an aqueous solution of 2-aminoethanol ( H OCH 2 CH 2 N H 2 (aq) ):
C O2 (g) + 2 HOCH 2 CH 2 N H 2 (aq) ➝ HOCH 2 CH 2 N H 3+ (aq) + H OCH 2 CH 2 N HCO2­ (aq)
A sailor exhales 125 mL of CO2 per minute at 23°C and 1.02 atm.
a. How many moles of CO2 are exhaled by the sailor in 1 min?
b. How many moles of CO2 are exhaled by the sailor in 1 day
c. Use the stoichiometry of the chemical equation to determine the volume of 4.0 M
2-aminoethanol is needed per sailor in a 24-hour period.
22. A gas mixture with a total volume of 1.00 L contains 0.700 mol of N2, 0.200 mol of H2, and
0.100 mol of CH4.
a. What is the mole fraction of H2 in the mixture?
b. What is the total pressure of the gasses at 10.0oC?
c. What are the partial pressures of each gas at 10.0°C?
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