Question

Compressibility factor $\left(Z\right)$ for $N_2$ at $-{23}^{\circ }\text{C}$ and $821\text{atm}$ is $1.25$. Calculate the number of moles of nitrogen gas needed to fill a gas cylinder of $100\text{litre}$ capacity under given condition.

• A. $2060$
• B. $2500$
• C. $3000$
• D. $3200$

Answer 1

The correct option is D $3200$

We know,
$Z=\frac{P{V}_{\text{real}}}{nRT}$
where,
$V_{\text{real}}$ = Volume of real gas
$n=$ Number of mole
$Z=$ compressibility factor
So,
$n=\frac{P{V}_{\text{real}}}{Z\times R\times T}$
$\Rightarrow n=\frac{821\times 100}{1.25\times 0.0821\times 250}$
$\Rightarrow n=3200\text{moles}$