Gas laws - Boyle's law

 

The gaseous state

·      General characteristics are

a.     Shape and volume- gases neither has definite shape nor definite volume

b.     Highly compressible

c.      Gases exert pressure

d.     Have much lower density than the solid and liquids

e.     Diffusion- gases intermix completely in all proportions without any mechanical aid

f.       Liquefaction – can be liquified by cooling and by applying pressure.

This simplicity of gases is due to weak or  negligible force of interaction between gaseous particles

The gas laws

·      From the study of the behaviour of gases, certain generalisation were made. i.e the behaviour of gases are governed by some general laws, these generalisation are called gas laws.

·      These laws are related to measurable properties(pressure, volume, temperature and mass) of gases

These laws are as follows

a.     Boyle’s law(pressure-volume relationship)

b.     Charles’law (Temperature-volume relationship)

c.      Gay lussac’s law(pressure-Temperature relationship)

d.     Avogadro law(volume-Amount relationship)

a.     Boyle’s law (pressure-volume relationship)

·      In 1662 Robert Boyle proposed a relationship between Pressure and temperature. It is called Boyle’s law

·      The Pressure of a fixed amount of a gas are inversely related to its volume at constant temperature and.

                          P α 1/V   ---------(1)

           PV = K₁    ----------(2)      

     

 Let us consider  initial pressure and volume as P_1, V₁    After applying external pressure on gas, the final pressure and volume are as      P_2, V₂

   At constant amount of substance and Temperature

Then, according to Boyle’s law-

 P₁V₁ =K₁     ---------(1)

 P₂V₂ = K₁ ---------(2)

i.e.

    P₁V₁ = P₂V₂ =K₁     --------(3)

Graphical representation of Boyle’s law-

    ·      If graph is plotted between P and V we get curve called rectangular hyperbola)

   The curve clearly shows that when volume is increased, pressure decreases and vice versa.

   Similar curves are obtained at other temperature. Higher curve corresponds to higher temperature.

   Each curve corresponds to a different constant temperature, is known as isotherm (constant temperature curve) 

    ·      If the graph is plotted between P and 1/V, a straight-line graph is obtained passing through origin.

    ·      At high pressure, gasses deviate from Boyle’s law and so at high pressure, a straight-line graph cannot be obtained.

`            relationship between pressure and density

·      If density(d) = m/V    or V = m/d     Here m=mass of gas and V=volume of gas

Then we can give relationship between pressure and density by putting the value of volume (V) in Boyle’s equation as-

                              P m/d = K₁                                     (Boyle’s law  PV= K₁ )

                              So, P α d

Significance of Boyle’s law-

     ·      Gases are compressible      

     ·      Low pressure at high altitude, cause altitude sickness(anoxia) symptoms-uneasiness, sluggish feelings, headache

       Jet and aeroplanes fly at very high altitude with emergency oxygen supply in case of pressure falls