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Derive Van der Waals equation of state.

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1. Consider the effect of intermolecular forces on the pressure exerted by a gas form the following explanation.

2. The speed of a molecule that is moving toward the wall of a container is reduced by the attractive forces exerted by its neighbours. Hence, the measured gas pressure is Q lower than the pressure the gas would exert, if it behave ideally.

Where ‘a’ is the proportionality constant and depends on the nature of the gas and n and V are the number of moles and volume of the container and respectively an/ V2 is the correction term

3. The frequency of encounters increases with the square of the number of molecules per unit volume n2 / V2 . Therefore an2 / V2 represents the intermolecular interaction that causes non-ideal behaviour.

4. Another correction is concerned with the volume occupied by the gas molecules. ‘V’ represents the volume of the container. As every individual molecule of a real gas occupies certain volume, the effective volume V- nb which is the actually available for the gas, n is the number of moles and b is a constant of gas.

5. Hence Van der Waals equation of state for real gases are given as \(\big(P+\frac{an^2}{V^2}\big)\) (V – nb) = nRT Where a and b are Van der Waals constants.

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