Derive van der Waal.s equations.

Explanation

Molecules of gases interact with each other this type of attraction ..changes pressure and repulsion can change volume...
Interaction attraction process at higher temperature and correction in pressure : At high pressures molecules of gases are very close to each other. Molecular interactions start operating. At high pressure, molecules do not strike the walls of the container with full impact because these are dragged back by other molecules due to molecular attractive forces. This affects the pressure exerted by the molecules on the walls of the container. Thus, the pressure exerted by the gas is lower than the pressure exerted by the ideal gas.
`therefore p_("ideal")=(p_("real"))+((an^(2))/(V^(2)))" "` ....(Eq. - i)
`= (("Experimental observed"),("Pressure"))+(("Correction in pressure of"),("interactive molecules"))`
where, a = constant + (Van der Waals constant as correction of pressure.)
= magnitude of measurement of Alteraction force of gas.
`therefore` Value of a is independent to pressure.
Value of a is independent to temperature and pressure.
Interaction repulsive forces and correction of volume high pressure : Repulsive forces also become significant. Repulsive interacrtions are short - range interactions and are significant when molecules are almost in contact. This is the situation at high pressure. The repulsive forces cause the molecules to behave as small but impenetrable spheres. The volume occupied by the molecules also becomes significant because instead of moving in volume V, these are now restricted to volume (V - nb) where (nb) is approximately the total volume occupied by the molecules themselves. Effect volume of gas = (V - nb) .....(Eq. - ii)
(real volume) (correction of volume)
Van der Waals equation :
Equation of common ideal gas pV = nRT
For equation of pressure (i) and volume (ii), put in ideal gas equation then equation can be written as under,
`(p+(an^(2))/(V^(2)))(v-nb)=nRT " "` .....(Eq. - iii)
This equation is known as van der Waals equation.
Where,
p = real pressure, V = real volume a, b = van der Waal.s constant.
Value of a, b is depend upon characteristics of gas.
Value of a, b are magnitude of measurement of intermolecular attraction and repulsive force respectively.
They are independent to temperature and pressure.