﻿ Gas Laws

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## Gas Laws

Background

In the form one syllabus, you must have learnt about the particulate nature of matter where it was observed that matter is made of small particles. In this topic, we shall discuss more about the behavior of gases as a constituent of matter and their behavior under different conditions.

Background

In the form one syllabus, you must have learnt about the particulate nature of matter where it was observed that matter is made of small particles. In this topic, we shall discuss more about the behavior of gases as a constituent of matter and their behavior under different conditions.

#### By the end of the topic, you should be able to

:

• State the gas laws
• Verify experimentally the gas laws
• Explain how absolute zero temperature can be obtained from a graph
• Explain the gas laws using the kinetic theory of gases

Introduction

Inflated balloons are likely to burst on a sunny (hot) day and shrink at night when it is cold. When a bicycle tyre is inflated in a cold morning it is likely to burst when temperature rises later in the day. All these show the inter-relationship between pressure, volume and temperature of a gas.

Kinetic theory of gases.

The kinetic theory of gases assumes that gases are made up of small particles which are in random continuous motion. In this theory, the following assumptions are made.

a. Collisions between the gas molecules and the walls of the container are perfectly elastic.

b. Pressure of the gas is due to the impact of the molecules upon the walls of the container.

c. The gas molecules exert no attraction forces towards each other. To visualize this theory, click on the play button and make your observations.

Boyle's law

The animation below shows how pressure varies with volume. Click the play button and observe what happens as the pressure is increased gradually.

Observations

As pressure increases volume decreases.

Explanation

When the gas is compressed, its volume decreases leading to an increase in particle vibration. This increases the rate of collision between the gas molecules and the walls of the container causing an increase in gas pressure. This shows that the pressure of the gas increases with a decrease in volume. When the pressure of the gas is plotted against I/V, a straight line graph is obtained. This implies that Pressure is DIRECTLY proportional to the reciprocal of Volume or INVERSELY proportional volume.

Conclusion

Boyle's law states that for an ideal gas of fixed mass, Pressure is inversely proportional to volume provided that temperature is kept constant.

PA1/V

P = K/V

PV = K Where P - pressure , V-volume and K - a constant of proportionality

Charles' law

The following animation can be used to demonstrate the relationship between volume and temperature of a fixed mass of a gas at constant pressure. Click the play button and make your observations.

Observations

As the temperature increases, volume of the gas increases.

Explanation

As the temperature increases, the volume of the trapped gas also increases. This is because; the kinetic energy of the gas molecules increases their collisions and thus increasing the volume that they occupy. When a graph of volume against temperature on the Kelvin scale is plotted, a straight line graph is obtained which passes through the origin when extrapolated (extended). Similarly, when a graph of volume against temperature on the Celsius scale is plotted, a straight line graph is obtained but does not pass through the origin. When extrapolated, it cuts the temperature axis at -2730C. This temperature 0K (-2730C) is known as the absolute zero temperature. This is the temperature at which a gas is assumed to have zero volume.

Conclusion

This implies that as temperature increases, volume also increases. Charles' law states that 'volume of a fixed mass of gas is directly proportional to its absolute temperature provided that the pressure is kept constant'. Mathematically: V A T or V = kT

Pressure law

The set up below demonstrates the relationship between the temperature and pressure of a fixed mass of gas. Click on the play button of the animation below about pressure law and make your observations.

Discussion

From the activity it is observed that, when the temperature of a fixed volume of a gas is raised, pressure also increases. From the experiment, if the volume of the gas is kept constant, an increase in temperature causes an increase in the rate of collision between the gas molecules and the walls of the container which leads to an increase in pressure since the gas is not allowed to escape/expand. A graph of pressure versus temperature is drawn as the one shown below.

The graph is a straight line cutting temperature axis at -2730C, which is the absolute zero. Pressure is directly proportional to absolute temperature.

P AT

P=KT

P/T=K

The pressure law

The Pressure law states that: pressure of a fixed mass of gas is directly proportional to its absolute temperature provided that the volume is kept constant.

Gas Laws

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Gas Laws

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Gas Laws

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