A vessel of volume $5$ litre contains $1.4 g$ of nitrogen at a temperature $1800 K$ . The pressure of the gas if $30$ % of its molecules are dissociated into atoms at this temperature is :

4.05 a t m

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2.025 a t m

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3.84 a t m

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1.92 a t m

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Solution

The correct option is A $1.92 a t m$
The reaction involved, dissociation of nitrogen gas

$N_{2} ⇌ 2 N$

mass of nitrogen $= 1.4 g$

$\Rightarrow m o l e s = 1.4 / 28 = 0.05$

moles after dissociation of $N_{2} = 0.05 \times \frac{70}{100}$

and after dissociation of $2 N = 0.05 \times 2 \times \frac{30}{100}$

total moles involved $= 0.065$

applying ideal gas equation $(P V = n R T)$

$P = \frac{(n R T)}{V}$

$= 1.92 a t m$

So, the correct option is $D$

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