Question

A spherical balloon of 21 $cm$ diameter is to be filled with hydrogen at $NTP$ from a cylinder containing the gas at 20 atmosphere at ${27}^{\circ }C$. If the cylinder can hold 2.82 litres of water, the number of balloons that can be filled up is _____.

Answer 1

Number of moles of hydrogen present in the cylinder,

$n=\frac{PV}{RT}=\frac{20atm\times 2.82L}{0.0821L.atm/mol.K\times 300K}=2.289$ $mol$

Now calculate the volume of the balloon,

$V=\frac{4}{3}\pi {\left(\frac{D}{2}\right)}^3=\frac{4}{3}\times 3.1416\times {\left(\frac{21cm}{2}\right)}^3=4849mL=4.849L$

Now calculate the number of moles present in one balloon.

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2};$ $V_2=n\times 4.849+2.82$ where, $n=$ no. of ballons

$\frac{20\times 2.82}{300}=\frac{1\times (n\times 4.849+2.82)}{273}$

$\Rightarrow n=10$

Thus, 10 balloons can be filled from the cylinder.