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

We must first understand that the gas in the cylinder is at `20 atm` and `27^(@)C`, while it has to be filled in the balloon at `STP` conditions. First we calculate the volume of the gas at `STP` using Boyle's law, we have
`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`
where `P_(1)=20atm`, `V_(1)=2.82 L`, `T_(2)=273 K`,
`P_(2)=1 atm`, and `T_(1)=300K`.
`:. V_(2)=(P_(1)V_(1))/(T_(1))xx(T_(2))/(P_(2))=(20xx2.82)/(300)xx(273)/(1)=51.324 L`
This volume `V_(2)` of the gas is used to fill the balloon.
Volume of one balloon `=(4)/(3)pir^(3)=(4)/(3)xx(22)/(7)xx((21)/(2))^(3)`
`=4.851 L`
Therefore, the number of balloon filled up is
`=((51.324-2.82)/(4.851))=10`
The numbr of balloons that can be completely filled in only `10`.