If methane follows normal van der Waal’s equation of state. Calculate the pressure (in atm) exerted by 1 mole of CH4 at temperature 240.821K if volume occupied by CH4 molecule is negligible .(Given a=2atm Lit2mol−2). R=0.0821 L atm/mol K

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If methane follows normal van der Waal’s equation of state. Calculate the pressure (in atm) exerted by 1 mole of ${CH}_{4}$ at temperature $\frac{24}{0.821} K$ if volume occupied by ${CH}_{4}$ molecule is negligible .
$(G i v e n a = 2 a t m L i t^{2} m o l^{- 2}) . R = 0.0821 L a t m / m o l K$

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answer is 0.72.

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Detailed Solution

$(P + \frac{a}{V_{m}^{2}}) (V_{m}) = R T P V_{m}^{2} - R T V_{m} + a = 0 F o r r e a l g a s t h i s e q u a t i o n m u s t h a v e o n l y o n e r o o t . D = 0, b^{2} - 4 a c = 0, {(2.4)}^{2} - 8 P = 0 \Rightarrow (P = 0.72 a t m)$

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