The equation of state, corresponding to $8 g$ of $O_{2}$ is?

P V = 8 R T

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P V = \frac{R T}{4}

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P V = R T

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P V = \frac{R T}{2}

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Solution

The correct option is B $P V = \frac{R T}{4}$
$A s p e r i d e a l g a s e q u a t i o n P V = n R T w h e r e n = n u m b e r o f m o l e s A l s o n u m b e r o f m o l e s (n) = \frac{T o t a l m a s s}{M o l a r m a s s} T o t a l m a s s o f o x y g e n = 8 g a n d m o l a r m a s s o f O_{2} = 16 \times 2 = 32 T h e r e f o r e n u m b e r o f m o l e s (n) = \frac{T o t a l m a s s}{M o l a r m a s s} = \frac{8}{32} = \frac{1}{4} T h u s P V = n R T P V = \frac{R T}{4}$

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Column A	Column B
(A) High pressure	(i) $P V = R T + P b$
(B) Low pressure	(ii) $P V = R T - \frac{a}{V}$
(C) $P \to 0$	(iii) $P V = R T$
(D) Neither $a$ nor $b$ is negligible	(iv) $(P + \frac{a}{V^{2}}) (V - b) = R T$

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