A spherical balloon of 21 cm diameter is to be filled up hydrogen at NTP from a cylinder containing the gas at 20 atmosphere at 27^(@)C. If the cylinder can hold 2.82 litres of water, calculate the number of balloons that can be filled up.

A spherical balloon of 21 cm diameter is to be filled up hydrogen at N

1.	A spherical balloon of 21 cm diameter is to be filled up hydrogen at NTP from a cylinder containing the gas at 20 atmosphere at 27^(@)C. If the cylinder can hold 2.82 litres of water, calculate the number of balloons that can be filled up.
Answer» Solution :Volume of the balloon `= (4)/(3) pi r^(3)` `= (4)/(3) xx (22)/(7) xx (10.5)^(3) c c ""("radius" = (21)/(2) = 10.5)` = 4851 cc. Balloon is at a temperature of 273 K and 1 atm pressure, i.e, pressure `= 1 xx 76 xx 3.6 xx 981 = 1.014 xx 10^(6)` dynes/`cm^(2)`. `therefore` no. of moles of `H_(2)`, the balloon can CONTAIN at NTP `=(pV)/(RT)` `= (1.014 xx 10^(6) xx 4851)/(8.314 xx 10^(7) xx 273) = 0.2167`. No. of moles in the cylinder `= ((20 xx 76 xx 13.6 xx 981) xx 2820)/(8314 xx 10^(7) xx 300)` = 2.2929. While filling the last balloon, when the pressure ofthe cylinder will drop to 1 atm, gas cannot be withdrawn. Now, no. of moles of `H_(2)` remaining in the cylinder unused `= (1.014 xx 10^(6) xx 2820)/(8.314 xx 10^(7) xx 300) = 0.1146` `therefore` no. of balloons that can be filled `= ("no. of moles of " H_(2) " in the cylinder that can be used")/("no. of moles of " H_(2) " one balloon can contain")` `= (2.2929 - 0.1146)/(0.2167) = 10`