What is the new volume of a balloon, and how many moles of air does it contain?

Question

If the balloon contains 4.0 L of air, internal pressure is 1.25 atm, and temp is 21.2 degrees Celsius and is carried down to the bottom of a lake (ignore the unlikelihood of that) where the pressure is 5.95 atm and temp is 10.9 degrees Celsius?

I understand that when pressure increases then volume decreases. I don't understand how the number of moles would change - seems like that should stay the same, just while occupying less space?

Roger the Mole · Accepted Answer

Ignoring the trouble about being given the internal pressure originally, then the external pressure at the lake bottom:
(4.0 L) x (1.25 atm / 5.95 atm) x (10.9 + 273) K / (21.2 + 273) K = 0.81 L

You are correct -- the moles don't change.  So calculate the number of moles in either state.  (I prefer to use the initial state.)
n = PV / RT = (1.25 atm) x (4.0 L) / ((0.08205746 L atm/K mol) x (21.2 + 273) K) = 0.207 mol

What is the new volume of a balloon, and how many moles of air does it contain?

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