A spherical ballon of `21 cm` diameter is to be filled with hydrogen at `STP` from a cylinder containing the gas at `20 atm` and `27^(@)C` . If the cylinder can hold `2.82 L` of water, calculate the number of balloons that can be filled up .

Explanation

Volume of the balloon `=(4)/(3)pi r^(3)=(4)/(3)xx(22)/(7)xx((21)/(2))^(3)=4851 cm^(3)`
Volume of the cylinder =2.82 litres=2820 `cm^(3)`
Pressure =20 atm. Temperature =300 K
Converting this to the volume at NTP,
`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2)) :. (20xx2820)/(300)=(1xxV_(2))/(273)" or "V_(2)=51324" cm"^(3)`.
When the pressure in the cylinder is reduced to one atmosphere,no more `H_(2)` will be released and hence 2820 `cm^(3)` of `H_(2)` will be left in it. Hence, volume of `H_(2)`used in filling the balloons
`=51324-2820 cm^(3)=48504 cm^(3)`.
Number of balloons filled =48504/4851=10