I’m bothered because I can’t get a grip on the Root Beer Pressure story.  Let’s see what we can do with common sense.

The Mentos/Diet Coke experiment is well known.  It produces a fountain of schaum – some ghastly concoction of gas and Diet Coke/Mentos liquor – that appears to sky up to perhaps fifteen feet in the air.  Perhaps more.  Mythbusters achieved 34 feet by substituting rock salt for Mentos.  20 meters has been claimed, but not well documented.

One bar is 32 feet (about ten meters) of water pressure.  Liquids at one bar pressure will squirt vertically to 32 feet, if all of the pressure is efficiently transferred into kinetic energy.  For no particular reason, one can say that the transfer is efficient, and the pressure in the Diet Coke/Mentos liquid is therefore one-half of a bar.

From Coke (see previous post):

Coca-Cola classic with 3.7 volumes of carbon dioxide dissolved in the product at a temperature of 75°F has an internal pressure of about 55 psi. (That’s 380 kPa)

The reason that the internal pressure is 55 psi is that the vapor phase in the top of the bottle is 55 PSI.  The real pressure is 480,536 Pa, or 480 kPa.  It would suggest that the efficiency of Diet Coke/Mentos is only about 10% efficient (otherwise it would sky out to 150 feet!)

The reason for the kinetic inefficiency, is that converting all the CO₂ from liquid to gas phase does not represent the entirety of the CO₂ load in the liquid.  It seems as though only 10% of the CO₂ is in solution.  The remainder is chemically converted into H₂CO₃ or carbonic acid.  The chemical exchange between carbonic acid and CO₂ is very slow in vitro, but very fast in vivo due to a specific enzyme, carbonic anhydrase. The first-order half-life in vitro is in the 15-second range.  This explains why the CO₂ capacity is so high, but the mole fraction is so low.  The acid ionizes immediately. The ratio (H2C03) : (CO2) at equilibrium is very small ( < 0.002)) and at all pH values in our experiments, the ratio (H2CO3:HC03-) is 0.005 or less. Therefore, H2CO3 can be neglected in the over-all reaction…(THE JOURNAL OF BIOLOGICAL CHEMISTRY Vol. 238, No. 10, October 1963)

Coke’s v/v partition in water is 3.7 volumes of CO₂, or 78% volume fraction at CO₂, at a pressure of 480 kPa, or 4.8 bar in the top (vapor) mixture of CO₂/Water/air/etc.    This should be pretty much linear.  The number would be 0.77 volumes in the liquid phase per bar in the gas phase.  At that temperature, 1 bar pressure should require 0.77 volumes of CO₂.

Kimmey, R. Pepsi Brooklyn Bottling Center. Fax. 25 May 2000, reports (ref. cit):

“At 60 F, the gauge pressure in the container is approximately 40 psi.”

The gauge pressure would not account for atmospheric, so that’s about three bar.  The v/v estimate using the Coke formula would be about 2.3 volumes CO₂.  The molecular weight of water is 18g/m, and that of CO₂ is 50 g/m.  The equivalent mass of H₂O and CO₂ in a liquid represents a mixture which is 73% water, and 26.4% CO₂.  This is relevant because gas pressures are based on moles, not grams.

So for Pepsi, 2.3 volumes of CO2 in 1 volume of water represents a molar ratio of 6.4 grams of CO₂ in a 1 gram equivalent of H₂O.  That’s an 86% gram equivalent of the liquid as CO2.  No doubt that no matter how the H₂O dissolves the CO₂, the  CO₂ is responsible for most of the weight of a soft drink like Pepsi, and more so for Coke – perhaps 91%.

If all the volume of Diet Coke flashed into CO₂ in a 2L bottle, it would make for 20L of CO2 (ignoring the water) or 10 bar.  That should produce a prodigious jet over 300 feet.

I would see if Mythbusters takes it on, were they continuing.

Intelligent Root Beer Fermentation

OK, so after all that yammer, what do we have left?  It’s best to lager-ferment root beer, as it will allow for the slow hydration of the CO₂ to carbonic acid, and thus “pack” the root beer with a molecule that does not directly equilibrate with gaseous CO₂ and produce instant bubbles.  HOWEVER tempting that solution might be, there is some peril to the concept of injecting CO₂ into liquids by 20 PSI overpressure, and then dropping it to 5 PSI upon bottling.  Unless the liquid is somewhat alkaline to begin with, the carbonic acid will re-equilibrate to a head pressure of 20 PSI of CO₂.  And if it’s heated, even more CO₂ will be produced, as the solute phase of CO₂ will come out of solution.

Even More Intelligent Root Beer Fermentation

Well, the maltose polymer is in, but where’s the bubblies?  Perhaps the answer is to come from the world of Champagne.  A second fermentation might just be the ticket.  Using the Coke formula, halving it for safety, a volume of flat root beer should produce two volumes of CO2 in a secondary fermentation.  Again, by the molar ration, that’s about 66% volume fraction of CO2.  A liter of flat root beer should produce two liters of CO2 (STP) to properly carbonate.  That’s 90 mmol. of CO2 per mol of water.  or 15g glucose equivalent per mol of water.  Remember each glucose gives two CO2 per molecule So I’ll take my 2L flat stuff and add ~30g of glucose equivalent to it.  Since it’s about twelve grams per tablespoon (12.68g, see LINK) then two tablespoons in, decant to bottles, and go for a second lager ferment.

1/27 PM Addition

The secondary ferment at room temperature is done; the lager temperature has finished in two out of four bottles.

The room temperature ferment is successful – very bubbly and with a robust head.  Apparently the maltodextrin was not eaten up by the yeast.  The flavoring is powerful but balanced – more like a root-beer concentrate that needs to be diluted 2:1 with club soda, perhaps I shall.  It is sweet, with an overwhelming taste of sarsaparilla, which was added directly in, and floats on the surface as chips.  It must be strained out with cheesecloth, I expect.  I should call it SassGorilla were I looking for a marketing label.