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.

Answer

10

Explanation

No. of balloons that can be filled
`=("V of" H_(2) "available")/("V of one balloon")`
Calculation of total volume of hydrogen in the cylinder at N.T.P.
`(P_(1)V_(1))/T_(1) = (P_(2)V_(2))/T_(2)`
`p_(1)=1` atm, `p_(2) = 20 atm`
`V_(1)=?`, `V_(2)^(2) = 2.82`l
`T_(1) = 273 K`, `T_(2)^(2) = 273 + 27 = 300 K`
`therefore V_(1)=(20 xx 2.82 xx 273)/(300 xx 1) = 51.3241 = 51324` mL
Actual volume to be transferred into balloons `=51324 = 2820 mL = 48504` mL
`[therefore 2820 "mL of" H_(2) "will remain in cylinder"]`
Volume of the balloon `=4/3 pir^(3) = 4/3 xx 22/7 xx (21/2)^(3)` [`therefore r=("diameter")/2]`
=4851 mL = 4.85 1 L
No. of ballons that can be filled up
`=(48504)/(4851) = 9.999=10`