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

Options

A. 5
B. 2
C. 10
D. 12

Answer

C

Explanation

Volume of balloon `= (4)/(3) pi r^(3) = (4)/(3) xx (22)/(7) xx ((21)/(2))^(3) = 4851` ml
Volume of the cylinder containing gas = `2.82 L = 2820 mL`
Volume at STP , = `V_(1) = (p_(1) V_(2) T_(1))/(T_(2) p_(1)) = 2820 xx (273 xx 20)/(300 xx 1) = 51324` mL
Volume of the gas that will remain in the cylinder after filling balloons is equal to the volume of cylinder i.e., 2820 mL
Available hydrogen for filling = `51324 - 2820 = 48504` mL `therefore` Number of balloons = `(48504)/(4851) = 10`