A spherical balloon of 21 cm diameter is to the filled up with `H_(2)` at NTP from a cylinder containning the gas at 20 atm at `27^@`C . The cylinder can hold 2.82 litre of water. The number of balloons that can be filled up

Answer

`10`

Explanation

Volume of balloon `= (4)/(3) pi r^(3) = (4)/(3) xx 3.14 xx ((21)/(2))^(3) cm^(3) = 4847 cm^(3) ~~ 4.85 L`
Now, when volume of in cylinder is converted into NTP volume, then `(p_(1) V_(1))/(T_(1)) = (p_(2) V_(2))/(T_(2))`
`rArr (20 xx 2.82)/(300) = (1 xx V_(2))/(273), V_(2)=` NTP volume `rArr V_(2) = 51.324 L`
Also, the cylinder will into empty completely, it will hold 2.82 L of `H_(2)` (g) when equilibrium with balloon will be established.
Hence, available volume of `H_(2)` for filling into balloon is `51.324 - 2.82 = 48.504L`
`rArr` Number of balloons that can be filled `=(48.504)/(4.85) = 10`