# Gas law

Gases when heated will show a significant change in pressure volume and temperature unlike solids and liquids which show insignificant change in volume.
Gas laws are laws which express the relationships between Pressure, (P), Volume (V) and Temperature (T) of a fixed mass of a gas.

1. Boyle’s law
Boyle’s law states that the volume of fixed mass of gas at contact temperature is inversely proportional to its pressure.

Mathematically;

When pressure is doubled the volume is halved or vice versa

Experiment to verify Boyle’s law

Trap dry air in the capillary tube using the mercury column.
-The pressure is varied using a bicycle pump and its value, P read from the Bourdon gauge and recorded.
-For each vale of P, the length, l of the air column is measured from the scale and recorded. This is the volume of the air.
-The procedures are repeated for different values of P and the results tabulated.

Note: from the above example, it is found when pressure halved the volume doubles.

Example:2
The volume of a fixed mass of gas at constant temperature increases from 300cm3 to 500cm3 . Find the new pressure if the initial pressure was 70cmHg.

Solution

Example:3
The pressure of a fixed mass of 0.5litres of a gas is 30cmHg. Find the volume if the pressure increases to 70cmHg.

Solution

1. Charles’ Law
Charles’ law states that the volume of a fixed mass of a gas at constant pressure is directly proportional to the absolute temperature.

Experiment to verify Charles’s law

Trap dry air using the index of concentrated sulphuric acid in a capillary tube. Tie the tube on the metre-rule using a rubber band.
-Place the apparatus in a metal can containing water and heat the water slowly while stirring gently.
-Read and record the length, l of the trapped air column and the temperature, T.
-Repeat the procedures for different temperatures and tabulate the results.
-Plot a graph of l against temperature, T.

Conclusion:
-The graph shows that l (which is proportional to volume), is directly proportional to the
absolute temperature at constant pressure. This verifies charles’ law.

Absolute temperature is the Kelvin temperature scale which has zero value coinciding with -273 0C.
Absolute temperature is also called thermodynamic temperature. On this scale temperature is measured in Kelvin (K)

The volume-temperature and pressure-temperature graphs for a gas are straight lines. This is because gasses expand uniformly with temperature. So equal temperature increase cause equal volume or pressure increases.

Standard temperature and pressure (S.T.P)

This is the physical condition of temperature equal to 0℃ and pressure is equal to 76cmHg at S.T.P, one mole of any gas occupies a volume of 22.4l.

Gas laws and kinetic theory.

Kinetic theory of matter states that, matter is made up of small particles called atoms or molecules that are in a constant random motion and the speed of movement of the particles is directly proportional to temperature.
-The theory considers the molecules of a gas to be like elastic spheres.
-Each time one of the molecules strikes the wall of the container it rebounds.
-The force produced on the on the wall by a molecule is the momentum change per second. So the gas pressure due to all bombarding molecules is proportional to their average total momentum per second (Force) normal to the wall.

Kinetic theory can be used to explain the cause of; -Gas pressure
-Boyle’s law
-Charles’s law
-Pressure law

a) Causes of gas pressure.
-Gas molecules are in constant random motion colliding with each other and bombarding the walls of the container.
-As they bombard the walls of the container, they exert a force on the walls. These forces cause gas pressure.

Boyle’s law
-At constant temperature, the average speed of gas molecules is constant.
-When the volume of the container decreases, the rate of collision and bombardment increases resulting in increase of force exerted on the walls and increase in pressure.
-Likewise increase in volume at constant temperature result in decrease in pressure.

Charles ‘s law.
-When temperature of gas molecules increases, they move faster.
-To maintain the pressure constant, the volume of gas must increase so that molecules travel further between collisions with the walls.
-This results in fewer collisions per second.

Pressure law.

-When the temperature of gas increases, molecules move faster
-Raising the temperature of a fixed mass of gas at constant volume increases the average kinetic energy of the molecules so that the molecules make more frequent collisions with walls at high velocity.

This decreases the rate of bombardment (few molecules collide), resulting in decrease in gas pressure.

b) Effect of Temperature on pressure
-When a gas is heated and its temperature rises, the average kinetic energy of the molecules increases and the average speed of the molecules increases.
-The frequency of the collisions of the molecules with the walls of the container increases hence the pressure of the gas increases.
-If the container is flexible, the volume of the gas increases in order to maintain the pressure constant.
-If the volume of the gas is to remain constant the pressure of the gas increases due to more frequent and more violent collisions of the molecules with the walls.
-The above explanation is used to explain why a balloon inflated with air bursts when left in sunshine.
-This is because the temperature rises yet volume remains constant so the pressure increases due to more frequent and more violent collision of the molecules with the walls.

Absolute zero is the temperature at which the molecules have their lowest possible kinetic energy.