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Q)

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

$(a)\;2.92atm\qquad(b)\;1.92atm\qquad(c)\;3atm\qquad(d)\;1atm$

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A)
$N_2\iff 2N$
Initial Moles of $N_2 = \large\frac{1.4}{28}$
Initial Mole of 2N = 0
Mole after dissociation of $N_2 = \large\frac{1.4}{28}\times \large\frac{70}{100}$
Moles after dissociation of 2N = $\large\frac{1.4}{28}\times \large\frac{2\times30}{100}$
Total Mole = $\large\frac{1.4}{28}\times\large\frac{70}{100}+\large\frac{1.4\times60}{100\times28}$
$=\large\frac{1.4}{28}\times[\large\frac{130}{100}]$
$P\times5 = \large\frac{1.4\times130}{28\times100}\times0.0821\times1800$
P = 1.92 atm
Hence answer is (b)
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