Question

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

• A. $11$
• B. $10$
• C. $8$
• D. $1$

Answer 1

The correct option is B $10$

Firstly we need to find the volume of a single balloon of hydrogen as diameter is given
Volume of 1 balloon= $V_{H_2}^{\prime }=\frac{4}{3}\pi r^3$
(given balloon is spherical)
So $V_{H_2}^{\prime }=\frac{4}{3}\pi (\frac{21}{2}{)}^3$
= 4846 $c{m}^3$
Vol. in lit. = 4.846 L
Now calculating volume of cylinder at NTP by using ideal gas equation as
$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$
where $P_1,V_1,T_1$ are 20 atm, 2.82 L , 300 K
and $P_2,T_2$ are 1 atm, 273 K
put up the values in equation we find $V_2$ = 51.324 L
since volume of empty cylinder is 2.82 L subtracting this gives total volume available for filling the balloons =51.324-2.82 L =48.504 L
So number of balloons that can be filled will be
= $\frac{totalvolume}{volumeof1balloon}$
= $\frac{48.504}{4.846}$ $\approx$ 10