A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP from a cylinder containing the gas at 20 atm. at 27 degree celcius. If the cylinder can hold 2.82 litres of water, calculate the numbers of balloons that can be filled up ?

Volume of 1 balloon to be filled = 4/3 r3

= 4/3 * 22/7 * (21/2)3 = 4.851 litre

Let n balloons are filled, then total volume of H2 used in filling balloons = 4.851 * n litre

Cylinder of H2 used in filling balloons will also H2, after n balloons are filled:

Volume of cylinder = 2.82 L

Therefore total volume of H2 at NTP = Volume of n balloons + volume of cylinder

= 4.851*n + 2.82 - 1

The volume of H2 at NTP can be found out using this data:

P1V1/T1 = P2V2/T2 or 1*V/273 = 20*2.82/300

Therefore:

V = 20*2.82*273/300 - 2

Both 1 and 2 should be same:

4.851*n + 2.82 = 20*2.82*273/300

Thus, n = 10