O lvl Phy: Kinetic Model of Matter

Dec 1989 P2 Q8a, 8b(i)

(a) A sealed flask contains a gas.

(i) Describe the motion of the gas molecules
(ii) Explain how the motion of the gas molecules results in a pressure exerted by the gas on the walls of the flask.

(b) Explain what is meant by Brownian motion.

*************************

Answer:

(a)
(i) The gas molecules move at a high speed in random directions.

(ii) The moving molecules bombard all parts of the wall of the flask. This bombardment causes a force on the wall, and hence a pressure on the wall. The pressure of the gas is dependent on the frequency of collisions and the speed of the molecules.


(b) Brownian motion is the random movement of light particles within a fluid. An example is smoke particles in air.

O lvl Phy: Kinetic Model of Matter

June 1988 P2 Q8a

A sample of air exerts a pressure on the walls of its container. Use your knowledge of the kinetic theory to answer the following questions:

(i) The pressure exerted on each part of the walls is the same. What deductions about the motion of the molecules in the air sample can be made from this fact?

(ii) How does the motion of the molecules of the air sample change when the container and the air inside it are heated?

State and explain how the change affects the pressure exerted by the gas.

(iii) How does the expansion of the container affect the change in pressure you describe?

*************************

Answer:

(i) The air molecules are moving in all directions with the same average speed. Their frequency of collisions per unit area of the wall are the same.

(ii) When the container and the air inside it are heated, the average energy of the air molecules increases. This results in the molecules moving faster in every direction, and causes a higher frequency of collisions of the molecules with the walls of the container. Hence, the pressure exerted by the air increases.

(iii) The expansion of the container results in an increase in the space for molecules to move about. Hence, the frequency of collisions of the molecules with the walls of the containers will be slightly less than in (ii) because the average distance travelled before collision is now further. The pressure exerted is thus lesser.

O lvl Phy: Kinetic Model of Matter

Mayflower Sec Sem 1 2005 P2 Q3

Using the kinetic model of matter for part (a) and (b),

(a) Explain how gases exert pressure.

(b) Explain how the pressure exerted by a gas changes when its volume is increased.

(c) A carbon dioxide cylinder contains gas at a pressure of 4.5 * 10⁵ Pa. The volume of the cylinder is 0.015 m³.
Calculate the volume occupied by the gas at atmospheric pressure, 1.5 * 10⁵ Pa.

*************************

Answer:

(a) Gas molecules move randomly, and they bombard the walls of the container they are in. During the bombardment, the gas molecules exert a force on the walls. The force per unit area on the walls from the bombardment of these gas molecules is the pressure exerted by the gas on the wall.

(b) When volume is increased, the pressure decrease. This is because although the number of gas molecules remain the same, the frequency of collisions with the walls of the container decreases. This results in a decrease in pressure.

(c) P₁V₁ = P₂V₂
(4.5 * 10⁵) (0.015) = (1.0 * 10⁵) * V₂
V₂ = 0.0675

Thus, the volume occupied by the gas at a.t.m. is 0.0675 m³

O lvl Phy: Kinetic Model of Matter

RI 1998 Sec 3 EOY P2 Q6

The figure below shows a gas jar full of air at atmospheric pressure. The jar is connected to a small reservoir containing a dark brown liquid which evaporates very easily.

The tap connecting the jar to the reservoir is then opened.

Nothing seems to happen for some time but gradually a brown gas is seen to move very slowly into the air in the jar.

Eventually, the whole jar is filled with the brown gas although the process began with only a small volume of liquid.

(a) Name the process described and explain the above observations in terms of simple kinetic molecular model of matter.

(b) State and explain how the pressure exerted by the contents of the gas jar changes as the process goes on, assuming that the temperature remains constant.

*************************

Answer:

(a) The process is diffusion.

As the dark brown liquid evaporates, the brown liquid molecules become brown gas molecules. These brown gas molecules move randomly, colliding with air molecules. Slowly, the gas molecules move into the gas jar because of their random motion. After some time, there will be a uniform mixture of air molecules and brown gas molecules in the gas jar.

(b) As the process goes on, more and more brown gas molecules are present in the gas jar. Since there are more gas molecules, there is a higher frequency of collisions on the wall of the gas jar. This results in an increasing pressure.

O lvl Phy: Kinetic Model of Matter

Catholic High Prelims 2004 P2 Q5

The figure below shows a metal can with a tight fitting lid. The can is heated.

Use the simple kinetic theory of gases to answer the following:
(a) What happens to the pressure in the can when the temperature increases?
(b) If a little water is put into the bottom of the can before heating, explain how this would affect the pressure in the can when the temperature increases?

*************************

Answer:

(a) The pressure increases since the molecules gain kinetic energy and move faster, making more collisions per unit area per second with the walls of the container.

(b) The pressure would be greater as there will be more gas molecules due to the vapourisation of water. In the can, there will thus be higher frequency of collisions per unit area of the walls, and this results in the higher pressure.

O lvl Phy: Kinetic Model of Matter

(a) Explain, by the molecular model,
(i) how the air inside a cylinder exerts a pressure on walls of the cylinder.
(ii) why the pressure in a cylinder increases as the cylinder gets heated
(iii) why the pressure in a cylinder increases as more air is pumped into the cylinder.
(iv) what happens to a block of ice when the temperature of ice is increased and the ice does not melt.


(b)The diagram shows a box with a partition which can be raised. The two parts of the box are filled with two different gases, gas A and gas B.

A long time after the partition has been raised, the gases are found to be completely mixed. Explain how this happened and why it takes a long time.

*************************

Answer:

(a)
(i) The air molecules collide with the inner walls of the cylinder and so air molecules exert a force on the walls. Since force is the product of pressure and area, the air molecules exert pressure on the walls when they exert a force on them.

(ii) As the temperature of the air increases, the average kinetic energy of the air molecules increases. This increases the frequency of collision between air molecules and the walls of the cylinder, causing the pressure to increase.

(iii) As the number of air molecules in the cylinder increases, the average separation between air molecules decreaes. This increases the frequency of collision between the air molecules and the walls of the cylinder, hence causing the pressure to increase.

(iv) The molecules in the ice vibrate with more energy but there is no change in the pattern of arrangement of the molecules.



(b) The unrestricted random continuous motion of gas molecules allows them to penertrate into the large spaces between molecules and mixing of gases takes place, As there are many gas molecules in the jar, the collisions with other gas molecules make the diffusion process slow.

O lvl Phy: Kinetic Model of Matter

Kinetic theory of matter attempts to explain macroscopic properties of matter by considering their molecular composition and motion.
(a) In a particular experiment, smoke particles in a transparent box are observed using a microscope. A small point of light is seen to move around as shown.

(i) What does this motion demonstrate about the air molecules?
(ii) State and explain the change in the motion of the smoke particles when:
--- (1) the size of the smoke particle increases
--- (2) the temperature of the surrounding increases

(b) During the process of boiling, heat is supplied to the liquid but there is no increase in temperature. Explain this process in terms of the molecular behaviour.

(c) Explain how the process of evaporation leads to a cooling of the liquid.

*************************

Answer:

(a) (i) It shows that air molecules are in continuous random motion.

(ii) 1.
The path of the particles are shorter.
The speed of particle is slower as it requires more molecules colliding on the particle to result in a change in motion.
There is less agitation as the number of collisions between particles and air molecules decreases

2. Higher temperature increase the kinetic energy of the air molecules. Hence the smoke particle will move faster and in a more random manner.


(b) Heat is used to increase the potential energy/ increase the distance between the molecules/weaken intermolecular forces. However, during boiling, the average kinetic energy of the molecules remained constant hence temperature remains the same.

(c) Molecules on the surface with higher kinetic energy will be able to break free from the surrounding water molecules. Resultant internal energy/average kinetic energy of molecules remaining in water decreases, and hence temperature decreases.

O lvl Phy: Kinetic Model of Matter

Question from http://www.sgforums.com/forums/2297/topics/330790
TYS D04/P1/Q15

Water of depth 10 m exerts a pressure equal to atmospheric pressure. An air bubble rises to the surface of a lake which is 20 m deep. When the bubble reaches the surface, its volume is 6 cm³. What was the volume of the air bubble at the bottom of the lake?

*************************

Answer:

Many of my tuition students asked this same question, so I think it would be great for me to post it here to share. It's an MCQ question, but I won't be posting out the choices, because it can easily be turned into a structured question anytime.

At the surface:
Pressure, P₁ = 1 atm (atmospheric pressure equivalent to 10m of water), V₁ = 6cm³

At the bottom of the lake:
pressure, P₂ = 3 atm (atmospheric pressure + 20 m of water), V₂ = unknown

Using Bolye's Law, P₁V₁ = P₂V₂

V₂ = 2 cm³

O lvl Phy: Kinetic Model of Matter

The diagram below shows the relative equilibrium positions of a piston, of negligible mass, in a container of air, at different temperatures.

Using the kinetic model of matter,

(i) explain why the piston at 25 °C does not sink to the bottom of the container.
(ii) calculate the pressure of the gas at 25 °C
(iii) calculate the pressure exerted by the gas at 50 °C
(iv) explain the reason the piston rises to a greater equilibrium height at 50 °C

*************************

Answer:

(i) The particles of air collide with the surface of the container, as well as the surface of the piston, and hence exerts a upward force on the piston. This prevents it from sinking to the bottom.

(ii) Since the piston is of negligible mass, it exerts negligible force on the air in the container.
Since the piston is in equilibrium,

pressure of gas = pressure of atmosphere
= 1.0 х 10⁵ Pa

(iii) Since the piston is still in equilibrium,
pressure of gas = pressure of atmosphere
= 1.0 х 10⁵ Pa

(iv) As the temperature is greater, the kinetic energy of the particles is greater. This increases the pressure of the gas, hence causing a net upwards force on the piston, causing the piston moves upwards.

As the piston moves upwards, the volume of the air increases, causing a corresponding reduction in the gas pressure according to Boyle's Law (P1V1 = P2V2). This continues until equilibrium is reached, when pressure of the gas equals the pressure of the atmosphere.

The end result is the greater equilibrium height for temperature at 50 °C