Single Choice

At low pressures, the van der Waals equation is written as $$\displaystyle \left [ P+\frac{a}{V^2} \right ]V=RT$$ The compressibility factor is then equal to :

A$$\displaystyle \left [ 1-\frac{a}{RTV} \right ]$$
Correct Answer
B$$\displaystyle \left [ 1-\frac{RTV}{a} \right ]$$
C$$\displaystyle \left [ 1+\frac{a}{RTV} \right ]$$
D$$\displaystyle \left [ 1+\frac{RTV}{a} \right ]$$

Solution

$$\displaystyle \left [ P+\frac{a}{V^2} \right ]V=RT$$ $$\displaystyle PV + \frac{a}{V}=RT$$ $$\displaystyle \frac{PV }{RT}+\frac{a}{RTV}=1$$ $$\displaystyle \frac{PV }{RT}=Z \:(compressibility \:factor)$$ $$\displaystyle =\left [ 1-\frac{a}{RTV} \right ]$$

SIMILAR QUESTIONS

States of Matter - Gas and Liquid

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States of Matter - Gas and Liquid

If $$ Z$$ is a compressibility factor, van der Waals equation at low pressure can be written as:

States of Matter - Gas and Liquid

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States of Matter - Gas and Liquid

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States of Matter - Gas and Liquid

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States of Matter - Gas and Liquid

At very high pressures, the compressibility factor of one mole of a gas is given by :

States of Matter - Gas and Liquid

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States of Matter - Gas and Liquid

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States of Matter - Gas and Liquid

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States of Matter - Gas and Liquid

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