Some chemical whimsy: How much helium?

Helium is pretty cool.  For a number of reasons.  As a gas, it’s lighter than air, and incredibly inert, so you can use it to lift stuff (like balloons or blimps).  As a liquid, helium is exceedingly cold.  Clocking in at 4 Kelvin (-452 °F), it’s the coldest refrigerant available.

So much technology would not be possible without helium.  Ever had an MRI taken at the hospital?  Not possible without liquid helium to cool the superconducting magnet inside the MRI.  My NMR spectrometer (which has been talked about, in depth, before) uses liquid helium for the same reason.  Every six weeks or so, the helium supply of the instrument needs to be replenished.  An NMR spectrometer uses considerably more helium than a balloon.

ALL THE HELIUM

60 liters of helium is quite a bit.

That got me thinking…  If you vaporized all the helium inside a 60 L dewar, just how many balloons could you fill up?  Remember, this isn’t the same helium you buy at a party supply store; liquid helium is many, many times more dense than gaseous helium.

One of my undergraduate professors was fond of brain-teasers called Fermi problems named after the Italian physicist Enrico Fermi, who was renowned for his ability to rapidly estimate answers to incredibly complex problems.  This type of problem solving relies on rounding and the use of simple assumptions to reach approximate solutions (often called a “sanity check”).

Let’s assume the following: gaseous helium is an ideal gas (it’s not, really), and a large party balloon has a volume of about 10 liters.

The tare weight printed on the side of the helium dewar tells me there are 17 pounds of helium in the canister.  Let’s call it 20 for simplicity’s sake.  One pound is about half a kilogram, so there are about 10 kg (10000 grams) of helium.  The molar mass of helium is 4.00 g/mol.  Therefore I have 2500 moles of helium (liquid).  As per the ideal gas law, one mole of a gas occupies 22.4 liters of space.  Call it 20 for round numbers.  So vaporizing my 2500 moles of liquid helium gives me 50000 liters of (now gaseous) helium.

At 10 liters per balloon, my original 60 liter dewar can fill 5000 balloons.  That’s a lot of balloons.  Enough to lift a child off the ground, a la Pixar’s “Up.”  However, that’s only 1% of the helium required to fill the Goodyear blimp.

According the manufacturer’s data, the actual number of balloons we could fill would be closer to 4500.  That number accounts for the the fact that helium isn’t really an ideal gas.  And they didn’t round off all their numbers.

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