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. 10
B. 11
C. 20
D. 12

Explanation

Radius of balloon = `(21)/(2)` cm = 10.5
Volume of the balloon = `(4)/(3) pi r^(3) = (4)/(3) xx (22)/(7) xx (10.5)^(2) = 4851 c.c = 4.851 L`
Volume of cylinder = Volume of water it can be hold = 2.82 L
For hydrogen in the cylinder ,
`P_(1) = 20` atm , `T_(1) = 300 K , V_(1) = 2.82 L`
Foe hydrogen in the cylinder at STP , `P_(2)` = 1 atm , `T_(2) = 273 K , V_(2)= `?
From `(P_1 V_1)/(T_1) = (P_2 V_2)/(T_2)`
`V_2 = (P_1 V_1)/(T_1) xx (T_2)/(P_2) = (20 xx 2.82)/(300) xx (273)/(1) = 51. 324 L`
As the pressure drops to 1 atm , the gas from the cylinder can.t come out and it does not mean that cylinder is empty .
Hydrogen gas at STP available for filling the balloons = `(51.324 - 2.82) = 48.504 L`
`therefore` No. of balloons that can be filled is = `(48.504)/(4.851) = 9.998 = 10`