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Question

At a given temperature $$T$$, gases $$Ne, Ar, Xe$$ and $$Kr$$ are found to deviate from ideal gas behaviour. Their equation of state is given as $$p = \dfrac {RT}{V - b}$$ at $$T$$.
Here, $$b$$ is the van der Waals constant. Which gas will exihibit steepest increase in the plot of $$Z$$ (compression factor) vs $$p$$?

A
$$Ne$$
B
$$Ar$$
C
$$Xe$$
D
$$Kr$$
Solution
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Correct option is C. $$Xe$$
$$Z= 1 + \dfrac{b}{RT}P$$
$$Y=mX+C$$

As $$b\uparrow\ \Rightarrow slope \downarrow$$
We know that the 'b' is the volume occupied by the particles of the gas.
Xe has the highest size so it occupies the highest volume for a certain amount of gases.

Hence, $$Xe$$ will have the highest slope.

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