# Real Gases

As you are heading towards the end of january, you might be in need of many important tips for your revision process…

Here are few such in the topic Real Gases.

Gases that don’t obey PV = nRT equation are known as “Real gas”.

Compression factor = (Z) = $$\frac{V}{V(ideal)}=\frac{nRT}{P}$$

For ideal gas, Z = 1 and for non-ideal gas Z ≠ 1.

If Z < 1, there exists net attraction between gas molecules

If Z > 1, there exists net repulsion between the gas molecules.

Vander waal’s equation: The gas which obeys Boyle’s law, charle’s law for all values of temperatures and pressure is “Ideal gas”. But no gas is ideal or perfect in nature. So, for real gas this theory was given.

$$\left( P+\frac{a{{n}^{2}}}{{{V}^{2}}} \right)(V-nb)=nRT$$

Where a and b are characteristics constants of a real gas.

a → Pressure correction

b →Volume correction

Volume correction: Vander waal’s assumed that molecules of real gas are rigid spherical particles which posses a definite volume. Thus, the volume of real gas i.e., volume available for compression or movement is actual volume minus volume occupied by gas molecule.

Note: As V → ∞, z → 1, i.e., at very high temperature and very low pressure, a non-ideal gas becomes an ideal gas.

If ‘b’ is effective volume of the molecules per mole of the gas, the ideal volume for the equation is (V –  b) not V.

Corrected volume = V – b for 1 mole of a gas for n moles, corrected volume = V – nb.

$$b=\left[ \frac{4}{3}\pi {{r}^{3}} \right]\times 4N$$

Where, r is the radius of gas molecule

Pressure correction: A molecule in the interior of the gas is attracted by other molecules on all sides. A gas molecule which is just going to strike the wall of the vessel experiences an inward pull due to attractive forces.

Hence, it strikes the wall with less momentum and the observed pressure will be less than the ideal pressure.

Pideal = PObserved + P’

P’ is the pressure correction = $$\frac{a{{n}^{2}}}{{{v}^{2}}}$$.

Therefore, after this two corrections, we get,

$$\left( P+\frac{a{{n}^{2}}}{{{v}^{2}}} \right)(V-nb)=nRT$$

This equation is called real gas equation depending on a and b the gas behavior changes.

Units of a and b:

1. Pressure correction = $$P’\,=\,\frac{a{{n}^{2}}}{{{v}^{2}}}$$.

∴ $$a=\,\frac{P'{{V}^{2}}}{{{n}^{2}}}$$

$$a=\frac{(pressure\,\,correction)\times {{(volume)}^{2}}}{{{(moles)}^{2}}}$$

Units of a:

S.I. units of a = (atm) (litre)² (Moles)⁻²

Unit of b:

Volume correction = V’ = nb.

$$b=\frac{V’}{n}$$

Unit of b = m³ mol⁻¹.