A spherical balloon of 21cm diameter is to be filled up with ${\mathrm{H}}_2$ at NTP from a cylinder containing the gas at 20atm at 27⁰c  .The cylinder can hold 2.82 lts of water at N.T.P. Calculate the no. of balloons that can be filled up. 
 

Volume of one balloon $\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{21}{2}\right)}^3=4.851 \mathrm{ltrs}$ Let ’n’ balloons are filled, then total volume of ${\mathrm{H}}_2$  used in filling balloons $=4.851\times \mathrm{n}$

The cylinder of ${\mathrm{H}}_2$ used in filling balloons will also have ${\mathrm{H}}_2$ in it, after $\mathrm{n}$ balloons are filled. Also volume of cylinder $=2.82 \mathrm{lts}$.
Total volume of ${\mathrm{H}}_2$ at $\mathrm{NPT}=$volume of $\text{'}\mathrm{n}\text{'}$ balloons + volume of cylinder

$4.851\times 2.82\to 1$ From the data $\frac{{\mathrm{P}}_1{\mathrm{V}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{P}}_2{\mathrm{V}}_2}{{\mathrm{T}}_2} \frac{1\times \mathrm{V}}{273}=\frac{20\times 2.82}{300}$        $\mathrm{V}=51.32\to 2$ volume in 1 and 2 both are same $4.851\times \mathrm{n}+2.82=51.32 \mathrm{n}=10$