A spherical balloon with a diameter of 21 cm is to be filled with hydrogen gas at STP from a cylinder of `H_(2)` gas at 20 atm pressure and `27^(@)C`. If the cylinder can hold 2.82 L of water, how many balloon can be filled with the hydrogen gas from the cylinder?

Explanation

Volume of each balloon`=(4)/(3)pixx((21)/(2))^(3)=4851cm^(3)=4.851L`
Since the cylinderr can hold 2.82 L of water, the volume of the cylinder is 2.82 L and hence the volume of `H_(2)` gas at 20 atm and `27^(@)C` is 2.82 L.
Let, volume of `H_(2)` gas in the cylinder at `STP=V_(2)L`
We know, `(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`
Given, `P_(1)=20atm,P_(2)(STP)=1atm,V_(1)=2.82L`,
`T_(1)=(273+27)K=300K,T_(2)(STP)=273K and V_(2)=?`
`therefore V_(2)=(T_(2))/(T_(1))xx(P_(1))/(P_(2))xxV_(1)=(273K)/(300K)xx(20" atm")/(1 " atm")xx2.82L=51.324L`
After the balloon are filled with `H_(2)` gas, the cylinder will contain `H_(2)` gas with a volume equal to its own volume i.e., 2.82 L. hence, the vaolume of `H_(2)` gas available for filling up the balloons will be=(51.324-2.82)L=48.504L.
thus, no of balloons that can be filled up `=(48.504)/(4.851)=10`