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

Step I. Volume of hydrogen available for filling
`V_(1) = 2.82 L , V_(2) = ?`
`P_(1) = 20 atm ` , `P_(2) = 1` atm
`T_(1) = 27 + 273 = 300 K` , `T_(2) = 273 K`
According to gas equation, `(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2))` or `V_(2) = (V_(1)P_(1)T_(2))/(P_(2)T_(1))`
`V_(2) = ((2.82 L) xx (20 atm) xx (273 K))/((1 atm) xx (300 K)) = 51.324 L = 51324 mL`.
Capacity of the balloon `= 2.82 L = 2820 mL`.
`:.` volume of hydrogen available for filling up .
Radius of balloon `(r) = (21)/(2) = 10.5` cm
Volume of balloon `(v) = (4)/(3) pir^(3) = 4/3 xx 22/7 xx (10.5 cm)^( 3) = 4851 cm^(3) = 4851 mL`.
`:.` No. of balloons to be filled `= (48504 mL)/(4851 mL) = 10`.