A spherical balloon of `21` cm diameter is to be filled up with hydrogen at `1 atm`, `273 K` from a cylinder containing the gas at `20 atm` and `27^(@)C`. If the cylinder can hold `2.82` litre of water, calculate the number of balloons that can be filled up completely.

Explanation

`"Volume of balloon, V"=(4)/(8)pir^(3)`.
`r=(21)/(2)cm`
`V=(4)/(3)xx(22)/(7)xx((21)/(2))^(3)`
= 4851 mL.
Volume of hydrogen in the cylinder at N.T.P. can be calculated as :
`(p_(1)V_(1))/(T_(1))=(p_(2)V_(2))/(T_(2))`
Volume of the cylinder = 2.82 L = 2820 mL
`p_(1)="20 atm "p_(2)="1 atm"`
`V_(1)="2820 mL "V_(2)=?`
`T_(1)=273+27=300K" "T_(2)=273`
`V_(2)=(p_(1)V_(1)T_(2))/(p_(2)T_(1))`
`=(20xx2820xx273)/(1xx300)=51324mL.`
When the pressure in the cylinder is reduced to 1 atm, no more `H_(2)` will be released and hence 2820 mL of `H_(2)` will be left in the cylinder.
`therefore" Vol. of hydrogen available for filling balloons"`
`=51324-2820=4804mL`
`"No. of balloons to be filled "=(48504)/(4851)=10.`