Calculate the pressure of one mole of nitrogen gas in a 10 L cylinder at $50^{\circ} C$ using the Van der Waals equation.Also find the value of ideal gas pressure.(Van der Waals constants a and b for nitrogen are $1.4 L^{2} a t m m o l^{- 2} a n d 0.04 L^{2} m o l^{- 1}$ respectively) .

2.18 atm

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2.965 atm

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2.652 atm

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None of these

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Solution

The correct option is D
None of these

From the Van der Walls equation ,

$⟮ p + \frac{a}{V^{2}} ⟯ ⟮ V - b ⟯ = R T$

We get ,

$⟮ p + \frac{1.4}{100} (10 - 0.04) = 0.0821 \times 323 \Rightarrow p = 2.648 a t m$
From ideal gas equation, we have
$p = \frac{R T}{V} = \frac{0.0821 \times 323}{10} = 2.652$
$P_{i d e a l} = 2.648 a t m P_{r e a l} = 2.652 a t m$

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