Identify the correct statements from the foll | vedclass

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(C) $I$. Compressibility factor $(Z)$ is defined as the ratio of $PV$ to $nRT$. For an ideal gas,$PV = nRT$,therefore $Z = 1$ at all temperatures and

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$I, III$ only

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(C) $I$. Compressibility factor $(Z)$ is defined as the ratio of $PV$ to $nRT$. For an ideal gas,$PV = nRT$,therefore $Z = 1$ at all temperatures and pressures. Thus,statement $I$ is correct.$II$. The average kinetic energy of one mole of an ideal gas is given by $K.E. = \frac{3}{2}RT$. Since it depends only on the temperature $(T)$ and the gas constant $(R)$,it is independent of the molar mass of the gas. Therefore,the kinetic energy of $NO_{(g)}$ and $N_2O_{4(g)}$ at the same temperature $T$ must be equal. Thus,statement $II$ is incorrect.$III$. According to Graham's law of diffusion,the rate of diffusion $(r)$ of a gas is inversely proportional to the square root of its density $(d)$,i.e.,$r \propto \frac{1}{\sqrt{d}}$. Thus,statement $III$ is correct.Conclusion: Statements $I$ and $III$ are correct.

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