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# Compressibility factor (Z) for $N_2$ at $-50^{\large\circ}C$ and 800atm pressure is 1.95. Calculate mole of $N_2$ gas required to fill a gas cylinder of 100mL capacity under the given conditions.

$(a)\;22408\qquad(b)\;22.40\qquad(c)\;2240.8\qquad(d)\;2040$

We have $Z = \large\frac{PV}{nRT}$
mole of $N_2 = \large\frac{PV}{ZRT}$
$\;\;\;\;\;\;= \large\frac{800\times100}{1.95\times0.0821\times223}$
$\;\;\;\;\;\;\;\;\;=2240.8$