1.4.6-1.4.8 Gas Laws
Heat and Temperature
Heat is random particle motion while temperature is a measure of the average kinetic energy of
particles. A regular thermometer uses the expansion of a fluid to measure temperature. When the
liquid (mercury or alcohol) in a thermometer is heated the average kinetic energy of the liquid
particles increases, causing the particles to take up more space expanding them up the tube.
There are three types of particle motion. Translational - whole atom or molecule changes its
location, Rotational - whole molecule spins on its axis and Vibration - motion that changes the
shape by causing the stretching, bending, or rotation of bonds. Translation and rotation occurs in
liquids and gases and vibration only happens in solids. At 0K there is no motion (translation,
rotation) or vibration of particles so the average kinetic energy is zero. For an ideal gas the average
kinetic energy is proportional to the absolute temperature. Therefore the gas with the greatest
kinetic energy will be the one with the greatest absolute temperature in Kelvin.
KE α Absolute temp (K)
When describing the behavior of gases an artificial scale called the absolute temperature or Kelvin
scale is used. This is because Celsius scale is based on the behavior of water molecules, with 0oC
being its freezing point of water or the point where the motion of the water molecules ceases. The
Celsius scale has limited use when describing the motion of gases whose motions can cease at
much lower temperatures. The mathematical conversion between oC and Kelvin is
°C + 273 = K
K -273 = °C
An ideal gas is a model of how a perfect gas would behave according to the gas laws. They obey
the ideal gas laws (Charles, Boyles, Gay-Lussacs, Avogadros, Combined). Gas that don’t exactly obey
the ideal gas laws are called real gases. No real gas can meet the ideal gas models criteria.
Kinetic Theory
Kinetic theory is a model used to describe the characteristics of a gas. According to kinetic theory
gas particles (atoms/molecules):
1) are in constant random motion. There is no order.
2) have mass.
3) have no or negligible intermolecular forces between their particles.
4) have elastic collisions. This means that no attractive or repulsive forces are involved during
collisions. Also, the kinetic energy of the gas molecules remains constant since there are no
(negligible) intermolecular forces between them (IMF’s).
5) do not have a fixed volume and will expand to fill the volume of the container.
6) the volume and pressure decreases proportionally with a decrease in temperature until
both reach absolute zero.
7) the average K.E of the particles α absolute temperature (K).
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8) the spaces between the particles is large so they can spread out and fill the container they
occupy.
9) are in constant random motion they can create pressure when they collide with one another
and the walls of the container.
10) have low densities.
11) diffuse (spread out) easily because of their relatively small masses and high velocity.
12) compress easily because the space between them and the particles is large. The volume
occupied by the gas is greater than the volume occupied by the particles due to the large
spaces between them.
13) expand on heating. Will expand without limit if they are not in a sealed container.
Pressure occurs when gaseous molecules /
atoms collide with the walls of the container.
Many different experiments in the 17th and 18th
centuries were carried out using kinetic theory to
provide further evidence of how gases behave. The
results of these experiments lead to the Boyles,
Charles and Gay-Lussac/Pressure Laws. These laws
explain the relationship between pressure, volume
and temperature of an ideal gas mathematically.
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Boyles Law
P α 1 when the temperature is constant
V
Equation
P1 V1
=
P2 V2
Explained at a molecular level using kinetic theory, as the volume increases the gas particles have
more space and so collide with one another and the walls of the container less frequently, causing
the pressure to decrease.
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Solving Gas Law problems
The Steps:
1. Identify the law used to solve each problem
2. Identify the constant (P, V or T)
3. Identify the unknown
4. Do unit conversion where necessary
5. Show all the calculations/steps
6. Write the answer using the correct number of significant digits and the proper units
Units
Pressure, P in Pa (or atm) (1 atm = 1 x 105 Pa ; 1 Pa = 1÷1000 KPa)
Volume, V in m3 or dm3 (1m3 = 1000 dm3)
Moles, n in mol
Temperature, T in K (°C + 273 = K)
Ideal Gas Constant, R is 8.31 J K-1mol-1 (this unit is for when P is in KPa, V in dm3 , T in K and n in
mol)
NOTE: When using the ideal gas equations ensure that the correct units are used. If V is given in L
or dm3 convert to m3 by dividing by 1000.
Example 1
A perfectly elastic balloon has a volume of 1.2 dm3 at a pressure of 0.987 atm. Assuming the
temperature remains constant, what volume will the balloon occupy if the pressure is reduced to
0.816 atm.
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Charles Law
Charles law states that V α T when the pressure is constant
Equation
V1
T1
=
V2
T2
Explained at a molecular level using kinetic theory, as the temperature increases the average kinetic
energy of the gas particles increases making them take up more space. The volume increases in
order to keep the pressure constant.
Example 2
A partially filled party balloon contains 2.6 dm3 of helium gas at atmospheric pressure and a
temperature of 12°C. Calculate the volume the balloon will occupy if it warms to a temperature of
20°C at atmospheric pressure?
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Gay Lussacs Law (Pressure Law)
Gay-Lussacs law states that P α T when the volume is constant
Equation
P1
T1
=
P2
T2
Explained at a molecular level, as the temperature increases the average kinetic energy of the gas
particles increases. The particles collide with one another and the walls of the container with more
force increasing the pressure.
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Ideal Gas Equation
PV=nRT
d = m (g) ÷ v (dm3)
Formula for density
(gdm-3)
Determining the volume of an ideal gas
of known m or n, M, T, and P:
n = m (g)
M (gmol-1)
(mol)
PV = nRT
V = nRT
P
V =
mRT
MP
Example 3
Determine the volume 52.0g of carbon dioxide will occupy at a temperature of 24°C and 206 KPa?
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Determining the molar mass, M of an ideal gas
of known P, T, m or n and V:
n = m (g)
M (gmol-1)
(mol)
PV = nRT
n = PV
RT
m =
M
PV
RT
Molar Mass, M = m R T
PV
(Mr is relative molar mass)
Example 4
125 cm3 of an unknown gas has a mass of 0.725 g at 25°C and 0.97 atmospheres. Determine the
molar mass of the gas?
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Determining the density of a gas
of known T, P, M and m or n:
PV = nRT
and
d = m
V
V = nRT
P
m = nRT
d
P
d = Pm
nRT
or since
n=m
M
d = Pm
mRT
M
d = PmM
mRT
d = PmM
mRT
d = PM
RT
(M can also be Mr)
The Combined Gas Law
A combination of Boyles, Charles and Gay-Lussacs laws. Is used to determine the fixed mass of an
Ideal gas.
P1 V1
T1
=
P2 V2
T2
Boyles, Charles and Gay-Lussacs laws can be obtained from this law by holding one quantity (P, V or
T) constant.
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Example 5
An expandable balloon contains 95.0dm3 at 1.0 atm and 24°C. What volume will the balloon occupy
when the pressure drops to 0.236 atm and the temperature is 11°C.
Questions
1. Which change in conditions would increase the volume of a fixed mass of gas?
A.
B.
Pressure/kPa
Doubled
Halved
Temperature/K
Doubled
Halved
C.
D.
Doubled
Halved
Halved
Doubled
2. All of the following are characteristic properties of gases EXCEPT
A. They can expand without limit.
B. They diffuse readily.
C. They are easily compressed.
D. They have high densities.
3. Which pressure expression represents the density of a gas sample of relative molar mass, Mr, at
temperature, T, and pressure, P?
A. PMr
T
B. RT_
PMr
C. PMr_
RT
D. RMr
PT
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4. The molar mass of an unknown gas is to be determined by weighing a sample. As well as its
mass, which of the following must be known?
I. Pressure
II. Temperature
III. Volume
A.
B.
C.
D.
I only
II only
I and II only
I, II, and III
5. Which of the following best accounts for the observation that gases are easily compressed?
A. Gas molecules have negligible attractive forces for one another.
B. The volume occupied by the gas is much greater than that occupied by the molecules.
C. The average energy of the molecules in a gas is proportional to the absolute
temperature of the gas.
D. The collisions between gas molecules are elastic.
6. In which gas sample do the molecules have the greatest average kinetic energy?
A. H2 at 100 K
B. CH4 at 273 K
C. H2O at 373 K
D. CH3OH at 353 K
7. The temperature in Kelvin of 2.0 dm3 of an ideal gas is doubled and its pressure is increased by a
factor of four. What is the final volume of the gas?
A. 1.0 dm3
B. 2.0 dm3
C. 3.0 dm3
D. 4.0 dm3
8. When the pressure is increased at constant temperature, the particles in a gas will:
A. become smaller
B. become larger
C. move faster
D. be closer together
9. Which quantity will not change for a sample of gas in a sealed rigid container when it is
cooled from 100°C to 75°C at a constant volume?
A. The average kinetic energy of the molecules
B. The pressure of the gas
C. The density of the gas
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10. A sample of gas has a certain volume at a temperature of 60°C. What must the temperature be
in order to double the volume if the pressure is kept constant?
A. 120°C
B. 333°C
C. 393°C
D. 666°C
11. A 250 cm3 sample of an unknown gas has a mass of 1.42 g at 35°C and 0.85 atmospheres.
Which expression gives its molar mass, Mr? (R = 82.05 cm3 atm K-1 mol-1)?
A. 1.42 X 82.05 X 35
0.25 X 0.85
B. 1.42 X 82.05 X 308
0.25 X 0.85
C. 1.42 X 250 X 0.85
82.05 X 308
D. 1.42 X 82.05 X 308
250 X 0.85
12. Which one of the following changes in conditions would give the greatest increase in the rate at
which particles collide with the walls of the container?
A. Increasing the temperature of the gas and increasing the volume of gas.
B. Increasing the temperature of the gas and decreasing the volume of the gas.
C. Decreasing the temperature of the gas and decreasing the volume of the gas.
D. Decreasing the temperature of the gas and increasing the volume of the gas.
13. When a bicycle tire is pumped up with air at constant temperature, assuming any change in its
volume can be neglected, the pressure increase comes from the fact that:
A. The gas particles are moving faster.
B. The collisions with the wall occur at a greater frequency.
C. Each collision transfers more momentum to the wall than before.
D. Two or three of the changes mentioned in A, B, and C occur simultaneously.
14.
For which set of conditions does a fixed mass of an ideal gas have the greatest volume?
Temperature
Pressure
A.
low
low
B.
low
high
C.
high
high
D.
high
low
(1)
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15. M00/420/S(2)
(a) In hydrogen gas what happens to the average speed of the molecules if the temperature is
increased?
[1]
(b) Explain in terms of molecules, what happens to the pressure of a sample of hydrogen gas if
the volume is halved and the temperature is kept constant.
[3]
16. N01/420/H(2)
The mass of a gas sample is measured under certain conditions. List the variables that must be
measured and show how these can be used to determine the molar mass of a gas. [4]
17. Floating balloons are filled with helium. Explain why these always deflate more quickly
than those blown up with air. (2)
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Bibliography
Clugston, Michael and Rosalind Flemming. Advanced Chemistry. Oxford: Oxford University Press, 2000.
Derry, Lanna, Maria Connor and Carol Jordan. Chemistry for use for the IB Diploma Standard level.
Melbourne: Pearson Education, 2008.
Dombrowski, Eileen, Lena Rotenberg and Mimi Bick. Theory of Knowledge Course Companion. Oxford:
Oxford University Press, 2007.
Green, John and Sadru Damji. Chemistry for use with the International Baccalaureate Programme.
Melbourne: IBID Press, 2007.
Neuss, Geoffrey. IB Diploma Programme Chemistry Course Companion. Oxford: Oxford University Press,
2007.
—. IB Study Guides, Chemistry for the IB Diploma. Oxford: Oxford University Press, 2007.
Organisation, International Baccalaureate. Online Curriculum Centre.
<http://occ.ibo.org/ibis/occ/guest/home.cfm>.
—. "Chemistry Data Booklet." International Baccalaureate Organisation, March 2007.
—. "Chemistry Syllabus." International Baccalaureate Organisation, March 2007.
Organisation, International Bacclaureate. "Theory of Knowledge Subject Guide." International Baccalaureate
Organisation, March 2006.
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Answers
1. D
2. D
3. C
4. D
5. B
6. C
Temp ∝ average kinetic energy
7. A
8. D
9. C
10. A
11. D
12. B
13. B
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Charles law, when P is constant when you double the V the T will double