Assuming the same pressure in each case, calculate the mass of hydrogen required to inflate a balloon to a certain volume at `100^(@)C` if 3.5 g He is required to inflate the balloon to half the volume at `25^(@)C`.

Explanation

Volume of 3.5g He at `25^(@)C` and pressure P is
`V=(nRT)/(P)=(3.5)/(4)xx(RT)/(P)=(3.5xx298R)/(4P)` . .[1]
To fill the balloon with `H_(2)` at 373 K, the volume of `H_(2)` gas required, `V_(H_(2))=2V`. Hence,
`2V=(nRT)/(P)=(w)/(2)xx(Rxx373)/(P)` . . [2]
Dividing [2] by [1] gives
`2=(wxx373)/(2)xx(4)/(3.5xx298) or, W=2.796g`