Question

A spherical balloon of $21cm$ diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at $20atm$ and ${27}^{\circ }C$. The cylinder can hold $2.82litre$ of water at NTP. Calculate the number of balloons that can be filled up.

Answer 1

Volume of one balloon :

$=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{21}{2}\right)}^3=4851c{m}^3$

$=4.851litre$

Let $n$ balloons be filled; thus, total volume of hydrogen used in filling balloons

$=4.851\times n$ litre

Total volume of hydrogen in the cylinder at NTP,

$V=\frac{20\times 2.82\times 273}{300\times 1}=51.324litre$

Actual volume of $H_2$ to be transferred to balloons

$=51.324-2.82(2.82$ litre retained in the cylinder)

$=48.504litre$

No. of balloons filled ${}^{\prime }{n}^{\prime }=\frac{48.504}{4.851}\approx 10$.