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 1 balloon which has to be filled `=4"/"3pi (21"/"2)^(3)`
`=4851 mL=4.851` litre
Let n balloons be filled, then volume of `H_(2)` occupied by balloons `=4.851xxn`
Also, cylinder will not be empty and it will occupy volume of `H_(2)= 2.82` litre.
Total volume occupied by `H_(2)" at "NTP=4.851xxn +2.82` litre
At STP
`P_(2)=1 " atm Available "H_(2)`
`V_(1)=4.851xxn+2.82" "P_(2)=20 atm`
`T_(1)=273K" "T_(2)=300K`
`P_(1)V_(1)"/"T_(2)=P_(2)V_(2)"/"T_(2)" "V_(2)=2.82` litre
or `1xx(4.851n+2.82"/"273)=20xx2.82"/"300" ":. n=10`