Helium in an old mylar balloon

Question

As a sealed mylar foil balloon ages, it deflates. I assume that this is mostly due to the monoatomic helium escaping through the envelope material. (In much the same manner as hydrogen can escape sealed tanks.)

Because commercially available helium is cut with air, (to reduce costs, conserve supply, and prevent asphyxiation.) the larger molecules that make up air are left behind inside the balloon envelope when it deflates.

If I want to find the helium content by volume after some time t, I assume that I can play around with the ideal gas law a bit. A problem arises, however, because I don't know how fast I'm losing helium ($frac{dn}{dt}$) or pressure ($frac{dP}{dt}$, although I generally know the starting pressure).

Does anyone know where to find or how to find those numbers without laboratory or industrial equipment?

dmckee --- ex-moderator kitten · Answer

Asymptotically the balloon should contain only air. The ratio of initial to final volume gives you the air fraction (by number). Once you know that it is easy to fit an exponential plus constant to the measured volume as a function of time.

You can attempt the free fit of both the exponential and the constant with data from a limited period, but the fitting error will necessarily be worse and the covariance matrix will be non-trivial until you get out to several lifetimes.

Helium in an old mylar balloon

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