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.

Options

A. 5
B. 10
C. 15
D. 20

Answer

B

Explanation

Volume of one balloon
`= (4)/(3) pi r^(3) = (4)/(3) xx (22)/(7) xx ((21)/(2))^(3) = 4851 cm^(3)`
`= 4.851` litre
Let `n` balloon be filled, thusm total volume of hydrogen used in filling balloons
`= 4.851 xx n` litre
Total volume of hydrogen in the cylinder at NTP,
`V = (20 xx 2.82 xx 273)/(300 xx 1) = 51.324` litre
Actual volume of `H_(2)` to be transferred to balloons
`= 51.324 - 2.82` (2.82 litre retained in the cylinder)
`= 48.504` litre
No. of balloons filled `'n' = (48.504)/(4.851) ~~ 10`