Question

A spherical balloon of $21cm$ diameter is to be filled up with $H_2$ at NTP from cylinder containing the gas at $20atm$ at $27^{\circ }C$. The cylinder can hold $2.82$ litre of water a NTP. Calculate the number of balloons that can be filled up.

Answer 1

Answer: 10

Volume of one balloon (to be filled)
$\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times {\frac{21}{2}}^3$
$=4851mL=4.851$ litre
Let ' $n$ ' balloons are filled, then total volume of
$H_2$ used in filling balloons $=4.851\times n$ litre
The cylinder of $H_2$ used in filling balloons will
also have $H_2$ in it, after $n$ balloons are filled.
Also volume of cylinder $=2.82$ litre
Hence, Total volume of $H_2$ at NTP = volume
of ' $n$ ' balloons $+$ volume of cylinder
$=4.851\times n+2.82\dots$...(i)
The volume of available $H_2$ at NTP can be
derived by the data
Given $P=1atm,V=?,T=273K$
and $P=20atm,V=2.82$ litre, $T=300K$
$\therefore \frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$
or $\frac{1\times V}{273}=\frac{20\times 2.82}{300}$
$\therefore V=\frac{20\times 2.82\times 273}{300}=51.32$...(ii)
From equation (1) and (II)
$4.851\times n+2.82=51.32$
$n=10$