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A He balloon is such that it can rise to...

A He balloon is such that it can rise to a maximum height of 50 km above the Earth's surface. When the balloon rises to this height, its expansion reaches maximum with a volume of `10^(5)L`. If the temperature and pressure of the air at this height are `-10^(@)C` and 1.8 mm Hg, respectively, then what mass of He gas will be required for the maximum expansion of the balloon?

Text Solution

Verified by Experts

Given, `P=1.8" mm "Hg=(1.8)/(760)=2.368xx10^(-3)atm`,
`T=(273-10)K=263K,V=10^(5)L and =?`
`therefore n=(PV)/(RT)=((2.368xx10^(-3)atm)xx(10^(5)L))/((0.0821L*atm*mol^(-1)*K^(-1))xx263K)`
`therefore 10.96` mol `He=10.96xx4=43.84g` of He [`because` 1 mol of He=4g He]
`therefore `43.84g of He will be required for the full expansion of the balloon.
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