The Kinetic Theory of Matter & Gases

The Kinetic Theory of Matter postulates that matter is made up of tiny particles that are continuously in motion and so possess kinetic energy. It is also known as the Molecular Theory. The particles may be atoms, molecules or ions. Recall that matter exists in three common states, namely solid, liquid and gaseous states; although, we also have plasma and Einstein-Bosé condensate as additional states of matter. However, these are beyond our scope of discussion. The major differences in the properties of solid, liquid and gas are the degrees of intermolecular forces of attraction and average kinetic energy of the particles.

While the intermolecular force is strongest in the solid state, which confers upon a solid its rigidity in shape and form, it is weakest in the gaseous state, which explains why a gas is formless and takes the shape and volume of the containing vessel. The intermolecular force of attraction is however, mild (not very strong and not very weak) in the liquid state. This is why a liquid has a definite volume, but takes after the shape of the containing vessel.

Conversely, the average kinetic energy of the particles is lowest in the solid state and highest in the gaseous state. This is why a solid always tends to remain where it is, except it is acted upon by a force which results in its motion. It also explains why a gas can readily spread across a large room within seconds, and why a liquid tends to flow slowly when poured on a surface, because of the moderate average kinetic energy of its particles.

Change of State

It is possible for a substance to exist in the three different states of matter discussed above with the absorption or evolution of heat. This is known as change of state of matter and it can be explained using the Molecular Theory. The heat involved in a change of state is known as latent (hidden) heat because it cannot be detected by the thermometer. The various changes of state of matter include:

a) melting - solid to liquid
b) freezing/solidification - liquid to solid
c) vaporization - liquid to gas
d) condensation/liquefaction - gas to liquid
e) sublimation - solid to gas

Phase Diagram for Change of State of Water

Melting
This is the conversion of a solid to liquid through the application of heat. Given that the temperature of a substance is a measure of the average kinetic energy of its molecules, when the solid is heated, the particles at the point where the heat is applied, acquire kinetic energy in the form of heat energy and start vibrating about their axes. They translate this energy to the nearby particles. This continues until all the particles begin to vibrate about their axes.

When a solid (say ice) is heated, there are two forces contending with each other - the vibrational force driven by the applied heat and the intermolecular force of attraction, which holds the particles together. As the temperature increases (as recorded by the thermometer), the force of vibration increases, until a point is reached, when the force of vibration of two adjacent particles is greater than their intermolecular force of attraction. This will cause the latter to give way, allowing the particles to move about 'freely' as water molecules. At this juncture, melting is said to begin. No further heat applied will be recorded by the thermometer, until all the intermolecular forces of attraction holding the solid particles together are broken or melting is completed. The heat absorbed during melting is known as the latent heat of fusion, and the fixed temperature at which the process occurs is the melting point of the substance.

Freezing
This is the opposite of melting as it is the change in state of a liquid (like water) to solid (say ice). It is also known as solidification. During freezing, there is a loss of heat, which is marked by a drop in temperature as recorded by the thermometer. This decrease in temperature leads to a decrease in the average kinetic energy of the liquid, and this in turn increases the intermolecular forces of attraction existing between the molecules. At this point, the particles which were farther apart start getting closer until a bond is formed between any two adjacent particles. Immediately this occurs, no temperature change is further detected by the thermometer until all the molecules are linked together by the intermolecular forces of attraction peculiar to solids. During freezing, the latent heat of fusion is evolved, and the fixed temperature at which this occurs is the freezing point of the substance. It is important to note that the melting and freezing point of a pure sample of a substance are always the same. While the former is associated with the solid state, the latter is with the liquid state.

Vaporization
This is change in state of a substance from its liquid to gaseous state with the application of heat. Using water as an example, it is the stage at which the water molecules become water vapour (steam) molecules. It can also be said to be gasification. There are two different forms of vaporization - evaporation and boiling, and we shall look at each in details.

Evaporation: When the temperature of the liquid increases due to the applied heat, different particles of the liquid acquire different amounts of kinetic energy. This rise in temperature is recorded by the thermometer. As the temperature of the system keeps increasing, many particles acquire more kinetic energy and rise to the liquid surface. On getting there, they are prevented from breaking free by the surface tension of the liquid and the intermolecular attraction of its neighbouring particles. This continues until the molecules acquire sufficient energy to overcome the surface tension and the intermolecular force of attraction to exist as free gaseous molecules in the space above the liquid surface. At this point, evaporation is said to occur.

Factors Affecting the Rate of Evaporation
Before we discuss the factors that affect the rate of evaporation, it is important to know that evaporation occurs at every temperature, and only at the surface of the liquid.

a) For evaporation to occur, the liquid must be in an open vessel. The openness of the containing vessel will determine how rapid the particles at the surface will transit from the liquid to the gaseous phase.

b) The rate of evaporation is affected by humidity. Humidity is a measure of the amount of water vapour present in the atmosphere at a given time. A large amount of water vapour in the atmosphere around a liquid will reduce the kinetic energy of the liquid molecules, thereby reducing the rate of their vaporization. Hence, the higher the humidity, the lower the rate of evaporation and vice versa.

c) The windiness of the environment also affects the rate of evaporation. Evaporation is faster on a very windy day, than a less windy one. This is because as long as the space above the liquid surface is not saturated by vapour, there will always be room for other molecules of the liquid to break free and exist as gaseous molecules. The space above the liquid surface can only remain unsaturated, if there is sufficient wind to blow away the existing vapour molecules.

d) Evaporation is also affected by surface area. The larger the surface area of the material, the higher the rate of evaporation will be. This is because with a larger surface area, more particles of liquid are exposed to vaporization at the surface.

The above factors explain why the oceans cannot boil, why clothes dry faster on a dry and windy day and why a completely spread towel dries faster than a folded one.

Boiling: This is an advanced form of evaporation, except that it occurs at a fixed temperature and throughout the liquid. As the molecules rise to the surface of the liquid and break free as gaseous particles, some of the vapour molecules still return into the liquid. This continues as the temperature increases until an equilibrium is reached, when the number of molecules leaving the liquid as gaseous molecules equals the number of gaseous particles returning into the liquid. At this point, the space above the liquid surface is said to be saturated with vapour. The saturated vapour starts exerting pressure on the liquid surface, and this is known as the saturated vapour pressure (s.v.p) of the liquid. It varies with temperature.

The saturated vapour pressure of the liquid increases as the temperature increases, until a temperature is reached when its s.v.p equals the atmospheric pressure. At that point, an air bubble rises from the bottom of the liquid to its surface, and this marks the beginning of the boiling process. No further temperature rise will be detected by the thermometer until all the intermolecular forces of attraction are broken. Just like evaporation, the latent heat of vaporization is absorbed during boiling, but unlike it, the whole liquid is seen to be bubbling. Also, the temperature at which this occurs is the boiling point of the liquid. In other words, the boiling point of a liquid is the temperature at which its saturated vapour pressure equals the atmospheric pressure.

Condensation
This is the opposite of vaporization. It is the change in state of a gas to liquid, and involves the evolution of the latent heat of vaporization. It is also known as liquefaction. The loss in heat is accompanied by a decrease in temperature, which also leads to a decrease in the average kinetic energy of the gas molecules, and a subsequent decrease in their randomness. As they get closer to one another, the effect of the intermolecular forces of attraction begin to increase, until a bond is formed between two adjacent gaseous particles. At this point, the thermometer stops recording any further change in temperature until all the intermolecular bonds (forces of attraction) are formed. These bonds restrict the excessively random nature of the particles, and as a a result, they become liquid. The constant temperature at which this change occurs is called the condensation point of the gas.

The Heating Curve

The above graph is the heating of curve of water. It is a plot of the changes water undergoes when heated from the solid state (ice) to the gaseous state (steam). Between the solid and liquid phases is the melting point, where you have the solid-liquid (ice-water) equilibrium. Similarly, at the boiliing point, the water exists in a liquid-gas (water-steam) equilibrium. As seen from the diagram, these two temperatures are constant over periods of time, and the temperature changes only occur after the melting and boiling processes had been completed.

The fixed melting and boiling points are typical properties of crystalline substances such as water. Non-crystalline or amorphous substances like wax, melt and boiling over a range of temperatures, and as such their heating curve will not be as sharp as that of crystalline substances.

The Kinetic Theory of Gases

This is the extension of the kinetic theory of matter aimed at describing the behaviour of an ideal gas. It is the basis for the study of the Gas Laws, and it states the following:

1. The gas molecules move randomly in a straight line colliding with themselves and with the walls of the containing vessel. The collisions of the gas molecules on the walls of the vessel account for the gas pressure exerted in the container.

2. The volume of each gas molecule is negligible compared to the volume of the containing vessel.

3. The forces of cohesion existing between the gas molecules is negligible. This explains the wide distances between the gas molecules, which makes it easy for a gas to be compressed. It also explains why a gas opened from a container rapidly spreads to fill a room.

4. The collisions of the gas molecules between themselves and the walls of the containing vessel is perfectly elastic. In other words, when two molecules collide, they rebounce like elastic balls because their total kinetic energies remain the same, as there is no loss of energy or conversion of kinetic energy to heat energy.

5. The temperature of the gas is a measure of the average kinetic energy of the molecules. This holds true not only for gases, but for all states of matter. An increase in the temperature of a body leads to a corresponding increase in its average kinetic energy.

Do These

Question 1
Using water as an example, distinguish between the three common states of water.

Question 2
Using a heating curve, differentiate with explanation, the following changes in state of matter - melting and freezing, boiling and liquefaction.

Question 3
a) Differentiate between boiling and evaporation.
b) What do you understand by the terms, vapour pressure and saturated vapour pressure?

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