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Perfect (ideal) gases

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Suppose your balloon has a radius of 3 m and that it is a spere when inflated.
a.) how much H is needed to inflate it to a pressure of 1 atm at an ambient T of 25 celsius @ sea level?
b.) what mass can the balloon lift @sea level, where the density of air is 1.22 kg m^-3 ?
c.) what would be the payload if helium were used instead of hydrogen?
d.) would you and a companion on board, the balloon ascends to 30,000 feet where pressure is 0.28 atm. Assume no volume change, what is the temp (in celsius) at 30,000 feet?

PLEASE- detailed steps, I need to know not just the answer, but understand how you got there- much thanks.

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Solution Summary

The solution calculates mass, volume, temperature using ideal gas equations

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a.)how much H is needed to inflate it to a pressure of 1 atm at an ambient T of 25 celsius @ sea level?

radius of balloon= 3 m
Volume of balloon= (4/ 3 ) pi r ^3 = 113.10 m^3

Volume=V= 113.10 m^3
Pressure=P= 1 atm= 101350 N / m^2
Temperature= T= 25 C= 298.15 K =273.15+25

Ideal gas Law is PV=nRT
or n=PV/RT
R= Gas constant= 8.3145 J.mol ^-1K ^-1
No of moles=n= 4623.97 moles =(101350*113.1)/(8.3145*298.15)

No of moles required to inflate the balloon= 4623.97 moles
1 mole of Hydrogen ...

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