UPSC Chemistry Vanderwaals Equation

1. Write down the equation of state for van der Waals gases with symbolic significances and And the dimension of van dcr Waals constants.

Answer:

The van der Waals equation corrects for the volume of, and  forces between, gas molecules: ((P + a/V²) (V - b) = RT

The van der Waals equation of state approaches the ideal gas law PV = nRT as the values of these constants approach zero. The constant a provides a correction for the intermolecular forces. Constant b is a correction for finite molecular size and its value is the volume of one mole of the atoms or molecules.

(P + a/V²) (V - b) = RT
P is pressure, V is volume and T is temperature.
[P] = [F/A]  = [MLT ⁻²/L²] = [ML⁻¹T ⁻²]
[V] = [L³]

We cannot add or subtract quantities of different dimensions. Therefore,
[P] = [a/V²] ⇒ [a] = [PV²] = [ML⁻¹T ⁻² L⁶] = [M L⁵ T ⁻²]
∴ [a] = [M L⁵ T ⁻²]

Similarly,
[b] = [V] =  [L³]