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I want to brew beer using helium instead of $\ce{CO2}$.

Most beers use about 2.5 grams of $\ce{CO2}$ per litre except stout like Guinness which uses nitrogen as it allows bubbles for much longer hence a frothy head on the stout.

So, perhaps a blend of helium and nitrogen would work? Helium is more soluble and if used in place of $\ce{CO2}$, as soon as the seal broke on a can it would escape rendering the cartoon voice idea useless.

How much helium can I squeeze into a litre of beer with or without compounding it to get the chipmunk voice?

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    $\begingroup$ Since you are not inhaling your beer, I don't think you'll get a cartoony voice. $\endgroup$ – Martin - マーチン Aug 15 '15 at 6:15
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    $\begingroup$ Oh I know some who seem to inhale their beer $\endgroup$ – user15489 Aug 15 '15 at 6:18
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    $\begingroup$ Might be better on homebrew.stackexchange.com Still don't get why you want to use helium $\endgroup$ – paparazzo Aug 15 '15 at 8:30
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    $\begingroup$ That would be a waste of good helium! $\endgroup$ – Gimelist Aug 24 '15 at 14:00
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    $\begingroup$ CO2 is needed to draw beer from a tap on the counter, but not for brewing. Brewing makes carbon dioxide! $\endgroup$ – Karl Feb 1 '17 at 7:19
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To correct one point in the question, helium has the lowest water solubility of all gases. At one atmosphere and $\mathrm{25^oC}$, $\ce{CO2}$ is 100 times more soluble than $\ce{He}$ and $\ce{N2}$ is about twice as soluble as $\ce{He}$. This is why deep-divers prefer helium to nitrogen.

At 45 psi, which is 3.1 atmospheres pressure, you could dissolve about 0.005 g $\ce{He}$ or roughly 30 mL when fully degassed. A typical adult breath is around 500 mL, and of course the $\ce{He}$ will not degas instantly.

The bottom line is that pressurizing beer with helium will not make you talk like Donald Duck. And the biggest difference you would see between $\ce{N2}$ and $\ce{He}$ would be in your bank statement.

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