# Gas laws , Boyle’s law and properties of gaseous materials

Particles of any material are moving in a continuous random motion , this type of motion differs according to the state of matter , So , we find that Solid molecules move in vibrational motion only , Liquid molecules move in translational and vibrational motion and Gas molecules move in random translational motion .

### Properties of gaseous materials

1. Gas molecules are in a continuous random motion called Brownian motion after a Scottish scientist called Brown .
2. There are intermolecular spaces between gas molecules which are more or less constant for different gases .
3. Gases are compressible .

Brown motion is a group of random motion of fluid particles ( liquid or gas ) in all directions for short distances , Brown ( Scottish scientist ) discovered in 1827 that tiny pollen grains suspended in water move in a random motion .

Air ( gas ) molecules move in haphazard ( random ) motion in all directions with different velocities , During their motion they collide with each other and collide with the walls of the box , The reason for this is that the gas molecules are in a free motion and in continuous collision , so , they change their direction randomly .

Gas molecules move in random motion , During this motion , they collide with each other and collide with the walls of the container which contain them .

#### The compressibility of gases

If the gas is compressible , The large intermolecular spaces between molecules decreases , thus the volume occupied by the gas decreases , The volume of a gas is affected by changes in pressure as well as in temperature or both while in case of solids or liquids , Volume changes as the temperature changes but not the pressure as they are incompressible , thus :

The experiments performed to evaluate the thermal expansion of a gas are complicated , In order to make a full study of the behavior of a gas , The relations between three variables which are the volume , pressure and temperature , which are known as ( Gases laws ) .

##### Gas laws
1. Boyle’s law : Study the relation between the volume and the pressure at constant temperature .
2. Charles’s law : Study the relation between the volume and the temperature at constant pressure .
3. Pressure law or Jolly’s law : Study the relation between the pressure and the temperature at constant volume .
4. the relation between pressure , volume and temperature .
##### Boyle’s law

The relation between the volume and the pressure of a gas at constant temperature ( Boyle’s law ) .

Apparatus structure : It consists of a burette ( A ) connected by a rubber tube to a glass reservoir ( B ) containing a suitable amount of mercury ( A ) and ( B ) are mounted side by side onto a vertical stand with a ruler attached to a base where the stand is adjusted vertically .

The reservoir ( B ) is movable along the stand either upwards or downwards and can be fixed at any desired position , The two tubes contain a suitable amount of mercury .

The following factors should be constant to verify Boyle’s law : temperature , mass of the gas and atmospheric pressure , The burette ( A ) should be of uniform cross-sectional area so that the length of a trapped air column be a measure of a gas volume .

1. Determine the atmospheric pressure ( Pa ) using mercuric barometer in cm Hg .
2. Open the tap ( A ) and move the reservoir ( B ) up and down until the mercury levels in the two tubes are at the same horizontal level .
3. Close the tap ( A ) to trap a volume of air ( Vol )1 , Pressure P1 =  Pa .
4. Move the reservoir ( B ) upwards so that the trapped air volume in the reservoir ( A ) decreases to ( Vol )2 and its pressure becomes P2 = Pa + h .
5. Move the reservoir ( B ) downwards so that the trapped air volume in the reservoir ( A ) decreases to ( Vol )3 and its pressure becomes P3 = Pa − h .
6. Repeat steps 4 , 5 several times and each time determine P , Vol then tabulate the results .
7. Draw a graphical relation between ( Vol ) on the ( X- axis ) and ( 1/ ρ ) on the ( Y- axis ) , So you get a straight line .

As the pressure of gas increases , the volume of the gas decreases and vice versa , So , the relation between the volume and the pressure of gas is an inverse proportionality relation .

Vol ∝ 1 / P

At constant temperature , the product of ( Vol ) and ( P ) of any given mass of gas is constant .

P Vol = Constant

##### Boyle’s law statement

The volume of a fixed mass of a gas is inversely proportional to the pressure , at constant temperature .

Or at constant temperature , the product of a certain volume of any given mass of a gas and its pressure is constant .

P1 / P2 = ( Vol )2 / ( Vol )1

Or     P1 ( Vol )1 = P2 ( Vol )2

PV = Constant = P1 V1 = P2 V2 = P3 V3

The gas does not obey Boyle’s law in very high or very low pressures , The gas obeys Boyle’s law in the straight portion only of the graph .

If two gases are mixed with each other , we can calculate by using the following relation at constant temperature :

P Vol ( mix. ) = P1 ( Vol )1 + P2 ( Vol )2

Where : P1 , P2 represent the pressure of the two gases before mixing .

If there is air bubble under water surface then it is raised at the surface of water at constant temperature .

P1 ( Vol )1 = P2 ( Vol )2

( Pa + ρgh ) ( Vol )1 = Pa ( Vol )2

Where h is the depth of bubble inside the liquid .

If a capillary tube containing a column of mercury of length ( h ) trapped a certain volume of air of length ( l ) .

When the tube is placed horizontally , then held vertically with the open end downwards .

P1 ( Vol )1 = P2 ( Vol )2

Pa l1 = ( Pa − h ) l2

When the tube is placed horizontally , then held vertically with the open end upwards .

P1 ( Vol )1 = P2 ( Vol )2

Pa l1 = ( Pa + h ) l2

Factors affecting the force of viscosity and Applications on the viscosity

Steady flow , Turbulent flow and Applications on the continuity equation

Charles’s law , Jolly’s law and General gas law