1. D. GASES
General Gas Law
Kinetic Theory

2. General Gas Law Boyle’s law general gas law Absolute zero Pressure law
Charle’s law
pressure
temperature
volume
Kelvin (K)

3. Existence of gas pressure
The molecules in a gas possess energy and hence they are continually at the container’s walls. The walls of the container are at all times subjected to a
syringe
If the smooth piston is not held, what would happen?
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4. Definition of gas pressure
The gas pressure of a gas in a container with fixed volume is the pressure force exerted by the gas per unit .
Unit of pressure:
Factors affecting gas pressure
The pressure of a gas can be increased by
the molecular speed of the gas, as both the impact force and the frequency of impact would , so the pressure force would .
the volume of the container, as the total area is .
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5. Macroscopic and microscopic quantities
The macroscopic quantities of a gas are / are not measurable while the microscopic quantities are / are not easily measurable.
Are the following quantities macroscopic?
Temperature Pressure Volume Mass
Molecular mass Molecular velocities
Unit and measuring devices of commonly used quantities
P: of the gas, with the unit , which can be measured by a .
V: of the gas, with the unit , which can be measured by a .
T: of the gas, with the unit , which can be measured by a .
Absolute zero corresponds to oC and K.
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6. Boyle’s law This relates the and of a gas by the following experiment:
Why should the tube be narrow?
The pressure of a fixed of gas is to its volume if the is constant, that is or V p
TAS
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7. Example
In the experiment to study Boyle’s law, the initial pressure and volume of the gas are 1 atm and 10 cm3 respectively.
Sketch the pV graph during the change.
How can T be kept constant practically?
Sketch the pV graphs for
(i) double temperature.
(ii) less gas used.
(d) What does the constant pV depend on?
p / 105 Pa 1 2 3 4 5
V / cm3 6 7 8 9 10
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8. More on Boyle’s law
When a graph of p against 1/V is plotted, a should be obtained.
How can we ensure the temperature remains constant?
1. By changing the volume slowly / quickly.
2. By using conducting / non-conducting vessel.
3. By holding / avoiding to hold the vessel.
How should the above graph be modified if the temperature of the gas is increased?
1/V p
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9. Relation between V and T
This relates the and of a gas by the following experiment:
The volume and temperature (in oC) of the gas are related by
The absolute zero can be obtained by V T
TAS
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10. In Kelvin scale V T
If the VT graph is drawn with thermodynamic temperature which is in scale, a straight line passing through the centre can be obtained.
The volume of a fixed of gas is proportional to its temperature in if the is constant, that is or
Is the pressure the same as atmospheric pressure? Why?
Sketch the VT graphs for
(i) higher pressure. (ii) more gas used.
(c) What factors does the constant (V/T) depend on?
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11. Relation between P and T
This relates the and (in Kelvin) of a gas by the following experiment:
The pressure of a fixed of gas is to its temperature if the is constant, that is or
(a) Sketch the PT graphs for
(i) smaller volume. (ii) less gas used.
(b) What factors does the constant (p/T) depend on? T p
TAS
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12. Ideal gas equation In conclusion, we have by
what is the unit of this constant?
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13. Ideal gas equation
If n is the number of mole of the gas, then N (number of molecules) = , where NA = is the
In terms of n (number of mole), the ideal gas equation becomes
where R is the
In terms of the molar mass  and total mass of the gas M, the number of mole n can be expressed as .
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14. Examination questions
Solving problems involving pV = nRT
Examination questions
1995-IIA-20
The pressure of an ideal gas in a container is P. If the number of gas molecules is halved, the volume of the container is doubled and the temperature is kept constant, the pressure will be
A. P/ B. P/ C. P D. 2P E. 4P
1993-IIA-17
An inexpansible vessel contains air at 50 oC. What percentage of air remains in the vessel if it is heated to 100 oC under constant pressure? (You may take the ice point to be 273 K)
A. 87 % B. 85 % C. 73 % D. 63 % E. 50 %
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15. A. the gas pressure in X is 100 kPa.
1999-IIA-37
Two metallic containers X and Y of volume V and 4V respectively are connected by a narrow tube as shown. Initially the tap S is closed and an ideal gas is contained in X at a pressure of 400 kPa while container Y is evacuated. The tap S is then opened and when equilibrium is finally reached
A. the gas pressure in X is 100 kPa.
B. there are still gas molecules moving through the tap S.
C. the product of pressure and volume of the gas in X is equal to that in Y.
D. the density of gas molecules in X is greater than that in Y.
E. the gas molecules in Y on average move faster than those in X.
V V X Y S
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16. Kinetic Theory ideal gas real gas Kinetic theory
random molecular motion
bombardments with containers
molecular kinetic energies
temperature
gas pressure
gas expansion

17. Random motion of gas molecules
Molecules in a gas are in continuous random motion due to their At any instant, different molecules move with the same / different speed.
Let the speed of the i th molecule of a gas be vi, then the root mean square speed c2 of the gas can be obtained by
1. taking of speeds of every molecules,
2. then finding the of results in (1),
3. then taking of the result in (2).
r.m.s. speed c2 =
Write down the expression for the total kinetic energies of the gas molecules.
Root mean square speed
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18. Basic assumptions in kinetic theory for ideal gas
An ideal gas is defined microscopically by the followings:
1. The are negligible except during a . Therefore, the velocity of the molecules are between
2. All collisions invovled (including those between molecules and those between molecules and the wall of container) are .
3. The time of impact of collision between a molecule and the wall is compared to the times between two such successive collisions.
4. The of the molecules themselves is negligible compared to the occupied by the gas.
What can you say about the total kinetic energies of molecules of a gas from assumption (2)?
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19. Condition when real gas behaves as ideal gas
A real gas behaves as an ideal gas when:
1. at high / low temperature and
2. at high / low pressure.
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20. Total and average internal energy for ideal gas
Immediately from assumption (1), the potential energy (due to intermolecular interaction between molecules) is for ideal gas.
The total internal energy U of an ideal gas is therefore due solely to the energy, thus
U =
The average internal energy EK of an ideal gas is then given by
EK =
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21. Kinetic theory L x y z
Consider a cube of dimension L  L  L containing N molecules each of mass m.
In order to provide a microscopic interpretation of ideal gas laws stated previously, the exerted by the gas on the container should be found.
In order to do this, the acting on the (shaded) wall by a particular (the ith) molecule should be found first.
Note that force causing a pressure on the shaded wall is along the direction only, and hence only the component of velocity in the direction is considered.
The force experienced by the shaded wall due to the ith molecule fix varies with time as shown. t fx
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22. Time average force acting on the wall by the ith molecule
Change of momentum in x-direction of the ith molecule during the collision
Time average force acting on the wall by the ith molecule
Total time average forces acting on the wall by all molecules
Pressure acting on the wall
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23. Temperature and kinetic theory
From kinetic theory:
From ideal gas equation:
To combine, we have the total internal energy of the gas given by
For one mole of gas, therefore, U = , average internal kinetic energy of an ideal gas is
which is its temperature.
From the above results, it can be shown that the root mean square speed can be expressed as
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24. Examination questions
Solving problems involving kinetic theory
1991-IIA-10
Which of the following properties of molecules of an ideal gas is/are the same on the moon as on earth, if the temperature and volume of the gas are unchanged?
(1) The average momentum change when a molecule of the gas rebounds from a wall of the container.
(2) The average kinetic energy of a molecule of the gas.
(3) The weight of a molecule of the gas.
A. (1), (2) and (3) B. (1) and (2) C. (2) and (3)
D. (1) only E. (3) only
1991-IIA-17
A fixed mass of ideal gas at S.T.P. occupies a volume of 2 m3. The gas is heated and allowed to expand to a final volume of 4 m3 with its pressure doubled. The root mean square speed of the gas molecules is
A. reduced to one quarter of its value. B. halved.
C. unchanged. D. doubled. E. increased four times.
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25. Given: Avogadro constant = 6  1023 mol-1
1992-IIA-13
Given: Avogadro constant = 6  1023 mol-1
Boltzmann constant = 1.38  J K-1
Molar gas constant = 8.31 J mol-1 K-1
If 1 mole of an ideal gas is heated under constant pressure from 20 oC to 70 oC, the total kinetic energy of the gas molecules is increased by
A J B J C J D J E J
1992-IIA-14
The relative atomic mass of oxygen is 16. What is the ratio of the average speed of oxygen molecules to that of hydrogen molecules at room temperature?
A. 1/ B. 1/4 C D E. 16
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26. (1) the number of gas molecules is the same;
1993-IIA-18
Identical containers A and B contain oxygen (O2) and hydrogen (H2) respectively.
Both gases are at room temperature and atmospheric pressure. Which of the following statements is/are true?
In both containers,
(1) the number of gas molecules is the same;
(2) the r.m.s. speed of gas molecules is the same;
(3) the frequency of collision of gas molecules with the walls of container is the same.
A. (1) only B. (3) only C. (1) and (2) only
D. (2) and (3) only E. (1), (2) and (3)
1995-IIA-21
The r.m.s. speed of the molecules of a certain gas X is 341 m s-1 at 298 K. Find the molar mass of the gas X.
(Given : Universal gas constant R = 8.31 J mol-1 K-1)
A g B g C g D g E g O2 H2
Container A:
Container B:
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27. B. Half of the molecules travel at a speed higher than c.
1997-IIA-35
Two different ideal gases, A and B, are contained in two identical vessels. If the ratio of their absolute temperature and the ratio of the root-mean-square of the molecules are respectively 2 : 1 and 3 : 1, the ratio of their molecular mass is
A. 2 : B. 2 : 9 C. 1 : D. 9 : E. 3 : 2
1998-IIA-35
The root-mean-square speed of a sample of helium gas molecules, each of mass m, is c. Which of the following deductions is correct?
A. The percentage of molecules travelling at speed c is greater than at other speeds.
B. Half of the molecules travel at a speed higher than c.
C. All molecules travel randomly with speed c.
D. The average speed of the molecules is c.
E. The average kinetic energy of the molecules is ½mc2.
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28. Which of the following descriptions about ideal gas is/are correct?
1999-IIA-38
Which of the following descriptions about ideal gas is/are correct?
(1) An ideal gas obeys Boyle’s law only under high temperature and low pressure.
(2) The molecules of an ideal gas have no size.
(3) The internal energy of an ideal gas consists of kinetic energy only.
A. (1) only B. (3) only C. (1) and (2) only
D. (2) and (3) only E. (1), (2) and (3)
2001-IIA-32
Which of the following is NOT a basic assumption of the kinetic theory of an ideal gas?
A. All molecules are in random motion.
B. All molecules move with the same speed at a certain temperature.
C. All molecules are point particles that have no physical size.
D. All collisions are perfectly elastic.
E. All molecules do not exert force on one another except during collisions.
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29. (Given: Universal gas constant = 8.31 J K-1 mol-1
2002-IIA-39
What is the order of magnitude of the number of molecules in 1 cm3 of air in an atmospheric pressure of 105 Pa and at room temperature?
(Given: Universal gas constant = 8.31 J K-1 mol-1
Avogadro constant = 6.02 x 1023 mol-1)
A B C D
2002-IIA-40
At 80 oC, the r.m.s. speed of the molecules in a fixed mass of an ideal gas is c. If the temperature is increased to 160 oC, the r.m.s. speed of gas molecules would become
A. 2c B c C c D c
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30. B. The mass per unit volume of the gas
2005-IIA-20
Two vessels contain hydrogen gas and oxygen gas respectively. Both gases are assumed to be ideal and they have the same pressure and temperature. Which of the following physical quantities must be the same for the two gases?
A. The volume of the gas
B. The mass per unit volume of the gas
C. The r.m.s. speed of the gas molecules
D. The number of gas molecules per unit volume
2006-IIA-22
The ideal gas equation derived from the kinetic theory can be
expressed as In this equation, what does the product Nm represent?
A. the total mass of the gas
B. the mass of one mole of the gas
C. the number of molecules in unit volume of the gas
D. the number of molecules in one mole of the gas
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31. Examination questions
1999-IIA-38
Which of the following descriptions about ideal gas is/are correct?
(1) An ideal gas obeys Boyle’s law only under high temperature and low pressure.
(2) The molecules of an ideal gas have no size.
(3) The internal energy of an ideal gas consists of kinetic energy only.
A. (1) only B. (3) only C. (1) and (2) only
D. (2) and (3) only E. (1), (2) and (3)
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32. (2) The volume of the molecules cannot be neglected.
2000-IIA-39
Which of the following statements concerning a real gas is/are correct?
(1) Collisions between molecules and the wall of a container are not perfectly elastic.
(2) The volume of the molecules cannot be neglected.
(3) Intermolecular forces cannot be neglected.
A. (1) only B. (2) only C. (3) only
D. (1) and (2) only E. (2) and (3) only
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