Ideal gas vs real gas and Ideal gas equation

 Ideal gas vs real gas

      Ideal gases obey Boyle’s law, Charles’ law and Avogadro’s law. Actually, these are based on the assumption that intermolecular forces are not present between the molecules of an ideal gases

    while real gases do not obey these laws (as Boyle’s law, Charles’ law and Avogadro’s law)

 Ideal gas equation

Ideal gas equation is derived by combining of Boyle’s law, Charles’ law and Avogadro’s law that gives the simultaneous effect of the change of pressure and temperature on the volume of gas. this is also known as combined gas law

Boyle’s law     V α 1/P   ------(1)              (at constant T and n)

Charles’ law V α T -----------(2)               (at constant P and n)

Avogadro’s law V α n   ------(3)               (at constant T and P)

By combining of these three equations (1), (2) and (3)

Then, Equation may be-

V α n T/P ----------------(4)

V = R n T/P            Or   

PV = n RT -------------(5)

Here, P= pressure of gas

           V= volume of gas

           n= number of moles of gas

           R= gas constant           

Eq (5) is known as ideal gas equation or combined gas equation for n mole gas.

Numerical value of R (gas constant) in different units are as-

S.No.	When unit of V	And unit of P	R value
1	L	atm	0.0821 L atm K-1 mol-1
2	ml	atm	82.1 ml atm K-1 mol-1
3	L	bar	0.08314 L bar K-1 mol-1
4	dm3	bar	0.0821 dm3 bar K-1 mol-1
5	m3	Pa or N/m2	8.314 Pa m3 K-1 mol-1   8.314 Nm K-1 mol-1 Or 8.314 J K-1 mol-1

At STP, volume of gas is taken as

In litre = 22.4 L

In ml   = 22400 ml

In m3   = 22.7 x 10^-3 m³

In dm3 = 22.7 dm³