Question

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

Answer 1

Volume of balloon $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times 3.14\times {\left(\frac{21}{2}\right)}^{3}c{m}^3=4847c{m}^3\approx 4.85L$
Now, when volume of $H_2(g)$ in cylinder is converted into NTP volume, then
$\frac{p_1{V}_1}{T_1}=\frac{p_2{V}_2}{T_2}$
$\Rightarrow \frac{20\times 2.82}{300}=\frac{1\times V_2}{273},V_2=$ NTP volume
$\Rightarrow V_2=51.324L$
Also, the cylinder will not empty completely, it will hold $2.82L$ of $H_2(g)$ when equilibrium with balloon will be established. Hence, available volume of $H_2(g)$ for filling into balloon is
$51.324-2.82=48.504L$
$\Rightarrow$ Number of balloons that can be filled $=\frac{48.504}{4.85}=10$