Question

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

Answer 1

Volume of balloon $=\frac{4}{3} \pi r^{3}$
$=\frac{4}{3} \times 3.14 \times\left(\frac{21}{2}\right)^{3} cm ^{3}=4847\, cm ^{3} \approx 4.85\, L$
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
$\Rightarrow V_{2} =51.324 \,L$
Also, the cylinder will not empty completely, it will hold $2.82\, L$ of $H _{2}(g)$ when equilibrium with balloon will be established. Hence, available volume of $H _{2}(g)$ for filling into balloon is
$51.324-2.82=48.504 \,L$
$\Rightarrow$ Number of balloons that can be filled $=\frac{48.504}{4.85}=10$