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UPSC Chemistry Vanderwaals Equation

Nidhi T.
28/08/2017 0 0

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]

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