# Kinetic Particle Theory, Gas Law

## Notes

(Credits to Mustafa Asif)

### Kinetic Particle Theory

The kinetic particle theory states that

• all matter is made up of small particles that cannot be seen directly with the naked eye

• there are spaces between particles in all matter but the amount of space in each state of matter is different

• particles are in constant random motion, but the speed of movement differs in each state

• particles possess kinetic energy that varies with temperature

• the average kinetic energy of all particles is directly proportional to the absolute temperature.

### Change of State  Melting • Melting is change from solid to liquid by absorbing heat to break force of attraction holding particles together.

• The temperature at which solid melts is melting point.

• From the graph:

• A-B: the temperature of solid increases to melting point. At this point, the particles are closely packed in a solid state with only the ability to vibrate about fixed positions.

• B-C: the temperature remains constant as heat is absorbed to break forces of attraction instead for raising temperature. Solid and liquid are present. The substance exist as solid-liquid states.

• C-D: the particles are in liquid state, gaining more heat energy and rising in temperature.

Freezing

• Freezing is the change of liquid to solid by cooling down of liquid.

• Freezing point is the temperature at which liquid freezes.

• From graph

• A-B: liquid temperature decreases to freezing point.

• B-C: heat energy is released as particles slow down to take up fixed and orderly position of a solid. The temperature remain constant release of energy compensates for loss of heat to surroundings.

• C-D: solid cools to the temperature of surroundings.

Boiling • Boiling is the change of liquid to gas by absorbing heat to break the forces holding them together.

• Boiling point is the temperature at which liquid boils.

• From graph

• P-Q: liquid temperature rises to boiling point. The particles are quite packed in a liquid state with only the ability to slide over each other.

• Q-R: heat energy is absorbed by particles to break the attractive forces so that they move freely and far apart as gas particles. That’s why the temperature remains constant.

• R-S: the particles are in a gaseous state gaining more heat energy and rising in temperature.

Evaporation

• Evaporation is change of liquid to gas without boiling, occurs below boiling point on water surface. It gives cooling effect – heat energy absorbed from surroundings.

Condensation

• Condensation is the change of gas to liquid. Heat energy is given out as gas particles slow down and move closer to one another to form liquid.

Sublimation

• When solid changes into a gas directly without going through liquid phase

• This happens because particles at the surface of the solid have enough energy to break away from the solid and escape as a gas and particles of the liquid are too weak to remain in that state

• Eg. iodine, ammonium chloride sublime

• Reverse of sublimation: Condensation

• Application: Dry ice can be used to keep food cold and change into a gas without leaving any liquid.

### Diffusion

• It is the spreading of molecules on their own accord without any external aid.

• Occurs in liquids and gases Occurs as particles are in random motion

• Depends on temperature and density (concentration) of fluid.

• The lower the density, the more space for particles to move into.

A. Diffusion of gases

• Experiment

• Bromine drops are placed into a jar.

• Another jar full of air is placed on top of jar with bromine, separated with cover.

• Cover is removed and bromine evaporates, filling both jars with dense reddish-brown bromine vapour.

• Explanation:

• Bromine particles move from lower jar into spaces between air particles in upper jar.

• At the same time, air particles move down from upper jar to mix with bromine particles in lower jar.

• Eventually, bromine and air particles are mixed completely.

B. Diffusion of liquids

• Experiment

• CuSO4 crystals placed in beaker of water, blue particles of the crystals is spread throughout the water to form uniformly blue solution.

Factors Affecting Rate of Diffusion

• Temperature

• The higher the temperature, the more particles of matter absorb energy making them move faster, the higher the rate of diffusion; the lower the temperature, the slower the rate of diffusion

• Mass of particles

• Greater mass, the slower it diffuses; Smaller mass, the faster it diffuses

• Experiment

• A cotton soaked in aqueous ammonia and another soaked in hydrochloric acid are placed on opposite sides of the tube.

• NH4OH vapor and HCl vapor diffuses in the tube and a compound is produced inside the tube closer to HCl soaked cotton as the particles are heavier.

• The greater mass, the slower particles diffuse.

• The smaller mass, the faster particles diffuse.

Differences between properties of matter and particles in them.

1. Matter can be coloured (e.g. sulphur is yellow) but particles are not.

2. Substances feels hot/cold but particles don’t get hot/cold. The temperature is due to speed of movement of particles. If hot, particles move fast.

3. Matter expands when heated but particles don’t. They increase distance between particles during expansion.

### Pressure exerted by a gas

• Randomly moving gas molecules collide with one another and with the inner surface of the container which the gas fills. The collisions produce forces.

• The force acting on each unit area of the inner surface of the container is the gas pressure exerted on it

• When the volume of gas is halved by halving the volume of its container, the number of molecules per unit volume in the container will be doubled.

• The number of collisions between the gas molecules and the inner surface of the container will double the force produced.

• Hence, the force acting on each unit area of the inner surface of the container, that is the gas pressure, will be doubled.

• The relationship between the pressure and volume of a gas at constant temperature and fixed mass is stated in Boyle's Law as follows

• For a fixed mass of gas at constant temperature, the pressure is inversely proportional to its volume p = k(1/v) --> pV = k

where k is a constant  • Pressure increases when:

• Volume of container decreases at constant temperature

• Temperature of gas increases at constant volume

• Number of gas molecules increase, total pressure exerted increases.

Equation: p1V1 = p2V2

## MCQ

1. Which property of gas affects the rate at which it spreads throughout a laboratory?

a. boiling point

b. molecular mass

c. reactivity

d. solubility in water

2. Four identical gas jars are filled with different gases. The lids are taken off the gas jars and they are left open to the air for a few hours. Which gas jar will then have the most air in it? 3. The conical flask contains compound X which is present in the solid, liquid and gaseous states. Which statement is correct? a. energy is released when X changes from liquid to solid

b. a gaseous X molecule has a lower mass than a liquid X molecule

c. liquid X is at a higher temperature than solid X

d. liquid X molecules vibrate about fixed positions

4. The table shows the boiling points of some of the gases present in air.

When air is cooled to -200oC, some of these gases liquefy. Which gases liquefy?

a. argon, helium, neon

b. argon, nitrogen, oxygen

c. helium, neon, nitrogen

d. helium and neon

5. By which process does the smell of cooking spread to all the rooms in a house?

a. decomposition

b. diffusion

c. displacement

d. distillation

6. What can be deduced about two gases that have the same molecular mass?

a. they have the same solubility in water at room temperature

b. they have the same boiling point

c. they have the same number of atoms in one molecule

d. they have the same rate of diffusion at room temperature and pressure

7. The cover-plates were removed from the gas jars as shown in the diagram. After several days, the colour of the gas was the same in both jars. Which statement explains this change?

a. oxygen and bromine gases have equal densities

b. oxygen and bromine molecules are in random motion

c. oxygen and bromine molecules diffuse at the same rate

d. equal volumes of oxygen and bromine contain equal numbers of molecules

8. Which of the following would diffuse most rapidly?

a. Cl2

b. CO2

c. CH4

d. N2

9. The kinetic theory of matter states that all matter is made up of

a. a small number of tiny particles

b. a large number of tiny particles

c. a small number of large particles

d. a large number of large particles

10. Which one of the following conditions increases the rate of movement of particles in matter?

a. increase in density

b. decrease in mass

c. increase in volume

d. increase in temperature

11. Ice is less dense than water because the ice molecules

a. are smaller than the water molecules

b. are different from the water molecules

c. are more loosely packed than the water molecules

d. move faster than the water molecules

12. Boyle's Law is valid for a gas at constant

a. volume

b. pressure

c. density

d. temperature

13. The volume of a certain gas at constant temperature is reduced by 1/2. The pressure of the gas will be

a. 1/4 of its original value

b. 1/2 of its original value

c. twice its original value

c. four times its original value

14. A balloon filled with hydrogen expands as it ascends because

a. its surrounding pressure decreases

b. its surrounding pressure increases

c. its temperature increases

d. its temperature decreases

15. 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

16. 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

17. 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

18. What can be deduced about two gases with the same relative molecular mass?

a. They have equal solubility in water at room temperature.

b. They have the same number of atoms in one molecule.

c. They have the same rate of diffusion at room temperature and pressure.

d. They have the same melting point.

19. One way to remove toxic nitrogen monoxide (NO) from motor vehicle exhaust is to inject a stream of ammonia gas into the exhaust vapour.

6NO (g) + 4NH3 (g) ---> 5N2 (g) + 6H2O (g)

A car emits 3 dm3 of nitrogen monoxide for each kilometre it moves. If it is driven 40,000 km a year, what is the volume of ammonia gas needed per annum to clean up te exhaust gas?

a. 40,000 dm3

b. 60,000 dm3

c. 80,000 dm3

d. 120,000 dm3

20. The particles in the gas can be described as

a. expanding in fixed directions

b. moving randomly in all directions

c. vibrating about a fixed position

d. rising upwards

21. In an air-conditioned bus, water is slowly collected on the glass window panes. This process is best described by

a. melting

b. boiling

c evaporation

d. condensation

22. Which of the following atoms has a nucleus which does not contain any neutrons?

a. aluminium

c. chlorine

d. hydrogen

23. Which of the following groups consists of mixtures only?

a. chlorine, water, salt

b. chlorine, water, sand

c. salt, water, salt

d. salt, air, brass

24. During the formation of ionic bond, the atoms taking part

a. gain protons

b. lose and gain protons

c. lose and gain electrons

d. gain electrons

25. Which of the following compounds are formed as a result of sharing electrons?

a. calcium chloride

b. oxygen gas

c. iron(III) oxide

d. aluminium

26. Which of the following solids does not contain any covalent bonds?

a. diamond

b. ice

c. copper

d. graphite

27. Which of the following would diffuse most rapidly?

a. CI2

b. CO2

c. CH4

d. N2

1. b

2. c

3. a

4. b

5. b

6. d

7. b

8. c

9. b

10. d

11. c

12. d

13. c

14. a

15. a

16. a

17. b

18. c

19. c

20 b

21. d

22. d

23. d

24. c

25. b

26. c

27. c (it has the smallest relative molecular mass)

## Structured Question Worked Solutions

1. The table shows some information about three gases.

a. complete the table by filling in the boxes.

A student heated some solid ammonium chloride, NH4Cl in a test-tube. Ammonia and one other gas were formed. He tested the gases coming out of the tube with litmus paper. The red litmus quickly turned blue. A few seconds later, both pieces of litmus paper turned red.

b. name the process which caused the gases to move along the tube

c. which gas turned red litmus paper blue?

d. which gas turned the litmus paper red?

Solution

1a.

1b. diffusion

1c. ammonia

1d. hydrogen chloride

2. In both liquids and gases, the molecules present are moving.

a. compare the movements and the spacing between the molecules in a gas with those in a liquid

b. how do these movements change as the temperature is increased?

c. how does your answer in (a) explain how the rates of chemical reactions change as the temperature of the reaction mixture is increased?

Solution

2a. The molecules in a gas move very vigorously at random. The molecules are far apart. In a liquid, the molecules are closer and move less vigorously. They only slide between the layers. There are still forces of attraction between the liquid molecules.

2b. As temperature is increased, the movement of molecules speeds up and they move further apart. For gases, this causes an expansion while in liquids expansion also occurs but when enough energy is obtained by the particles, they will break away from the forces holding them in liquid state and will change to gas. These particles will collide more often.

2c. The rates of chemical reactions corresponds with the rate of collision of the particles in the reactants. Hence the chemical reaction is faster.

3a. The diagram represents the arrangement of the particles in a solid. i. describe the movement of the particles in the solid

ii. how does this movement alter as the temperature of the solid is increaseD?

iii. how does this movement alter as the solid melts?

b. Samples of the gases carbon dioxide, Mr = 44, and hydrogen, Mr = 2, are at the same temperature. Compare the speeds of the molecules in these two gases.

c. Equal masses of steam and of water contain the same number of molecules. Explain why the volume of the steam is much greater than that of the water.

Solution

3ai. Particles in the solid are fixed in orderly arrangement and they vibrate about fixed positions.

3aii. They vibrate more vigorously as energy is absorbed.

3aiii. They move about as the forces holding the particles together break.

3b. The average molecular speeds of hydrogen molecules are higher.

3c. In steam, the molecules are more energetic and are further away from one another. The volume of steam is thus higher.

4. A tyre contains 1500 cm3 of air at pressure p. The volume of air in the pump is 500 cm3 at the same pressure p. What will be the pressure in the tyre after one stroke of the pump, assuming the volume of the tyre and the temperature of the air do not change?

Solution

p1V1 = p2V2

p1 x (1500 + 500) = p2 x 1500

p2 = 4/3 p1

5. An air balloon at the bottom of a pond has a volume of 5cm3. The depth of the pond is 40 m. Assuming that the temperature remains constant, calculate the volume of the balloon when it reaches the surface, where the atmospheric pressure is equal to 10 m water.

Solution

at the bottom of the pond, pressure acting on the balloon,

p1 = 40 + 10 = 50 m water

volume of balloon, V1 = 5 cm3

At the surface of the pond, p2 = 10 m water

volume of balloon, V2 = V

According to equation pV = constant

p1V1 = p2V2

50 x 5 = 10 x V

V = 25 cm3

6. A fixed mass of air occupies 9.0 litres at a temperature of 300 K and a pressure of 1.2 atmospheres. The volume is reduced to 5.0 litres by increasing the pressure to 2.3 atmospheres.

a. assuming that the air behaves as an ideal gas, calculate the temperature of the air after the reduction in volume

b. give one reason why the actual temperature may be different from that you have calculated.

Solution

6a. V1 = 9 cm3

V2 = 5cm3

P1 = 1.2 atmosphere

P2 = 2.3 atmosphere

T1 = 300 K

to find T2,

P1V1 / T1 = P2V2 / T2

(1.2 X 9) / 300 = (2.3 X 5) / T2

T2 = 319.4 K

6b. Air does not behave like an ideal gas.

7. A bubble of air at the bottom of a lake has a volume of 3.0 cm3 and the pressure on it is equivalent to 4.5 atmospheres. Assuming that the temperature remains constant, calculate the volume of the bubble when it reaches the surface, where the pressure is 1.0 atmosphere.

Suggest, in terms of the forces acting on it, why the bubble rises towards the surface.

Solution

let volume of bubble be V2

p1V1 = p2V2

4.5 x 3 = 1 x V2

V2 = 13.5 cm3

The weight of the air bubble is much smaller compared to the upthrust of water on it. This initial resultant upward force causes the bubble to move upwards.

8ai. Describe the motion of the molecules of a gas

8aii. What type of motion does a sound wave give to the molecules of air?

8aiii. What effect does a sound wave have on the pressure of air as the wave moves through it?

8b. A bicycle pump of volume 72 cm3 is filled with air at a pressure of 0.100 MPa. The volume is reduced to 30 cm3. No air leaks from the pump and the temperature stays constant. Calculate the pressure of the compressed air.

Solution

8ai. random and continuous

8aii. oscillatory

8aiii. An alternate series of high and low pressure regions is produced.

8b. Using Boyle's Law,

p1V1 = p2V2

0.100 x 72 = p2 x 30

p2 = 0.240 MPa

9. The graph below shows the heating curve of a pure substance. a. What is the melting point of the substance?

b. What happens to the temperature while the substance changes state? Explain your answer.

c. Explain why the substance cannot be water.

Solution

9a. 80ºC

9b. It remains at a constant temperature until the change in state is completed. At 80ºC, the solid particles absorb heat energy to break the forces of attraction between them. The amount of energy supplied at this point is equal to the amount of energy needed to break the forces of attraction holding the particles in fixed position. At 215ºC, the heat energy supplied is only sufficient to cause the liquid particles to move further apart into a state of randomness. No further rise in temperature will occur until all the forces of attraction in a liquid has been broken.

9c.Water has a melting point of 0ºC and a boiling point of 100ºC. The graph shows a substance that melts at 80ºC and boils at 215ºC.

10. In both liquids and gases, the molecules present are moving.

i. Compare the movements and the spacing between the molecules in a gas with those in a liquid.

ii. How do these movements change as the temperature is increased?

iii. How does your answer to (ii) explain how the rates of chemical reactions change as the temperature of the reaction mixture is increased?

Solution

10i. In a gas, the molecules are very far apart and they are moving randomly around the space available. In a liquid the molecules are still quite closely packed, with the molecules sliding over each other.

10ii. As temperature of a gas is increased, the particles will move more vigorously and further apart. In a liquid, the particles will move faster, eventually breaking the forces of attraction that hold them together at boiling point and moving into a state of randomness when a gas is formed.

10iii. The rate of a chemical reaction corresponds to the rate of effective collision between reactant particles. With an increase in temperature, the reactant particles will gain more kinetic energy and move faster, collide more often, leading to an increase in reaction rate.