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
- Gas molecules are in a continuous random motion called Brownian motion after a Scottish scientist called Brown .
- There are intermolecular spaces between gas molecules which are more or less constant for different gases .
- 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 ) .
- Boyle’s law : Study the relation between the volume and the pressure at constant temperature .
- Charles’s law : Study the relation between the volume and the temperature at constant pressure .
- Pressure law or Jolly’s law : Study the relation between the pressure and the temperature at constant volume .
- General ( universal ) law of gases : Study the relation between pressure , volume and temperature .
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 .
- Determine the atmospheric pressure ( Pa ) using mercuric barometer in cm Hg .
- 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 .
- Close the tap ( A ) to trap a volume of air ( Vol )1 , Pressure P1 = Pa .
- 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 .
- 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 .
- Repeat steps 4 , 5 several times and each time determine P , Vol then tabulate the results .
- 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 .
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