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## Summary

### Pressure-Volume Relationship of a Gas • Increasing the volume of the container lowers the pressure
• Decreasing the volume of the container increases the pressure
• Increasing the pressure of a gas sample decreases its volume
• Decreasing the pressure of a gas sample increases its volume

#### Boyle's Law

• States that for a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume
• P1V1 = P2V2
• Explanation
• When randomly moving gas molecules hit the wall of the container, they exert a force on the wall.
• Since pressure is defined as force per unit area, a gas exerts pressure.
• If the volume of the gas is halved by halving the volume of the container, the number of molecules per cm3 in the container will be doubled.
• The number of collisions of molecules with the wall in one second will also be doubled. Thus the pressure is doubled

#### Example 1

An air bubble at the bottom of a lake 40m deep has a volume of 1.5cm3. What is the volume of the air bubble when it rises to the surface of the lake?
(1 bar of pressure is approximately equivalent to the pressure exerted by 10m of water)

Solution

Pressure at surface = p1 = 1 bar = pressure exerted by 10m of water

Pressure at bottom = p2 = p1 + pressure exerted by 40m of water = 50m of water

Volume at surface = v1
Volume at bottom = v2 = 1.5cm3

Boyle's Law:
P1V1 = P2V2
10 x v1 = 50 x 1.5
v1 = 7.5cm3

## MCQ Questions

1. Brownian motion provides evidence that
a. smoke particles consist of molecules
b. smoke particles are lighter than air molecules
c. air molecules are in continuous random motion
d. air molecules attract smoke particles

2. At room temperature the particles in a solid are best described as
a. stationary and far apart
b. stationary and close together
c. vibrating and close together
d. moving randomly and far apart

3. Liquids have a definite volume because
a. the molecules are held in fixed positions
b. forces between the molecules do not allow them to leave the liquid
c. the molecules do not vibrate
d. the molecules are packed close together in a regular pattern

4. The volume of a certain gas in a piston is reduced to 2/3 of its original value. What happens to the pressure of the gas?
a. increases by 2/3
b. increases by 3/2
c. decreases by 2/3
d. decreases by 1/3

5. The pressure of a gas in a piston is 1.5 bar when the volume is 10cm3. The volume is increased and the pressure falls to 1.2 bar. By how much was the volume increased?
a. 2.5cm3
b. 12.5cm3
c. 8.0cm3
d. 1.8cm3

6. In one minute, a diver breathes 1 litre of air at an atmospheric pressure of 100 kPa. To breathe in the same mass of air in one minute, how much air would he need to breathe when the total pressure on him under water is 300 kPa?
a. 1/3 litre
b. 1/2 litre
c. 1 litre
d. 2 litres
e. 3 litres

7. The air in a large paper bag is heated. The bag is then found to rise through the surrounding cold air. This is because
a. the air in the bag has become less dense
b. the mass of the paper bag has decreased
c. heat always rises
d. the mass of air in the bag has increased
e. the chemical compositions of the air in the bag has changed

8. The motion of the molecule of two gases causes them to mix. What is this motion called?
a. Brownian motion
b. conduction
c. diffusion
d. evaporation

9. A student observes the Brownian motion of smoke particles in air with a microscope. She sees moving points of light. These points of light come from
a. air particles only moving randomly
b. air particles only vibrating
c. smoke particles only moving randomly
d. smoke particles only vibrating
e. both smoke and air particles moving randomly

10. Some gas trapped in a cylinder is compressed at constant temperature by a piston. Which of the following will not change?
a. density
b. mass
c. molecular spacing
d. pressure
e. volume

11. A given mass of air occupies 12 m3 at normal atmospheric pressure. If the pressure is increased to 4 times the original value without changing the temperature, what volume will the air occupy?
a. 3 m3
b. 6 m3
c. 24 m3
d. 48 m3
e. 192 m3

12. When the temperature of a gas rises at constant volume, its molecules
a. move closer together
b. move with greater average speed
c. collide with one anther less often
d. exert smaller forces on one another
e. expand

13. What is a property of both liquids and gases?
a. they always fill their containers
b. they are incompressible
c. they can flow
d. they have molecules in fixed positions

14. Which of the following is the correct explanation for the expansion of a substance when it is heated?
a. The particles of the substance increase in number
b. The particles of the substance vibrate faster
c. The particles of the substance push each other further away
d. The particles of the substance expand

15. In the Brownian motion experiment, the evidence of the movement of molecules is inferred by observing
a. the air particles moving randomly
b. the molecules moving randomly
c. the smoke particles moving randomly
d. the air particles colliding with the smoke particles

1. c
2. c
3. b
4. b
5. a
6. a (use v1p1 = v2p2)
7. a
8. c
9. c
10. b
11. a
12. b
13. c
14. c
15. c