GAS LAWS

THE GAS LAWS

The 3 properties of a gas that are necessary to describe the state of the gas are the pressure, the volume and the temperature. For a given mass of a gas the above quantities are found to be related through gas law.

Properties of Gases

i.                      The molecules possess a weak cohesive force.

ii.                     The molecules are negligible

iii.                    They fill the entire container in which they are.

iv.                   They have the highest kinetic energy compared to solid and liquid.

v.                    The degree of randomness is high.

Kinetic Theory Of Gases (Postulates)

1.        Gases are tiny particles that move in a straight live and collide with one another and also with the wall of the container.

2.        The collision between the gases is perfectly elastic.

3.        The cohesive force of the gases is also negligible.

4.        The temperature of the gas is the measure of the average kinetic energy of the gas.

 (I) Boyle’s Law

Boyle’s law states that the pressure of a fixed mass of a gas is inversely proportional to its volume, provided that the temperature is kept constant. P       or    PV = constant,  i.e P1V1 = P2V2 where P is the pressure and V is the volume of a fixed mass of gas.

Kinetic Theory explanation of Boyle’s law

Consider a fixed mass of gas at constant temperature. if the gas volume is decreased, the molecules take less time to travel between the piston and the wall opposite. The molecules therefore hit the walls of the container more often in unit time. Therefore the gas pressure increases as more impacts per second are made. 

Example

If the volume of a fixed mass of Helium in a container is 30cm3 at a pressure of 50 mmHg. Find the pressure if the volume is 25 cm3 at constant temperature.

Solution

V1 = 30 cm3, P1= 50 mmHg, P2 =?, V2 = 25 cm3. P1V1 = P2V2;  T2 =  =  = 60 mm Hg.

 (Ii) Charles’s Law

Charles’ law states that the volume of a fixed mass of gas increases by 1/273 of its volume at 0oC per degree celcius rise in temperature, provided its pressure remains constant. V  T,  = Constant;    = .

Cubic expansivity of gas at constant pressure,  =

  =    or   Vt = Vo (1 + ) = Vo ( ) = Vo ( ) . since  is a constant, we can state that V  T.

Kinetic Theory explanation of Charles’ law

When the gas is heated at constant pressure, the molecules gain kinetic energy and hit the walls of the container more often in a second. This leads to an increase in pressure. In order, that the molecules would travel a longer distance before striking the walls of the container. Thus an increase in temperature at constant  pressure would lead to an increase in the gas volume.

Example

A fixed mass of gas of volume 600 cm3 at a temperature of 27oC is cooled at constant pressure to a temperature of 0oC. What is the change in volume?

Solution

V1= 600cm3, T1= 273 + 27 =300K,  T2= 273 +0 = 273K, V2=?

   = ,   V2 =  =  = 2 x 273 = 546 cm3.

 (Iii) The General Gas Law

The combination of the Boyle’s law and Charles’ law gives this law.  =Constant. Or  =  . where P1, V1 are the gas pressure and volume at temperature T1 and P2, V2 are the gas pressure and volume at temperature T2. The gas law does not hold good when a gas is near its liquefying temperature.

Example

A mass of gas occupies 20 cm3 at 5oC and 760 mm Hg pressure. What is its volume at 30oC and 800 mm Hg pressure?.

Solution

V1 = 20cm3 , T1 = 273 +20 = 293K , P1 = 760 mm Hg, V2 = ?, T2= 273 + 30= 303K,  P2= 800 mm Hg

 =  ,     V2 =  =  =  =  20.71 cm3.

Assignment

Calculate the final centigrade temperature required to change 20 litres of gas at 120oC and 1 atmosphere to 25 litres at 2 atmosphere. 

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