Bubble Trouble

To celebrate New Years this past week, I got myself a bottle of hard cider, fearing the looks I would get for buying cheap champagne in the country of its origin. Since I'm still outfitting my apartment here, I had no way to cork the bottle after opening, but I was impressed with how long it kept its carbonation in the refrigerator. I thought I'd look into some of the models for gas solubility at different temperatures to understand the contributing factors.

Carbonated drinks are so named because they consist of carbon dioxide dissolved in liquid. The bubbles you see (and taste) on opening a bottle are pockets of CO2 coming out of solution. The amount of CO2 that stays in solution is given by Henry's Law:

where p is the partial pressure of the gas outside the liquid, kH is a coefficient that changes with temperature, and c is the concentration of the dissolved gas. Partial pressure means the fraction of overall pressure due to the specific gas that's dissolved, in this case the amount of CO2 in the atmosphere. As with any model, we're making approximations here, like the assumption that the CO2 acts like an ideal gas, only interacting with itself.

We're trying to compare the amount of CO2 that stays in the cider when refrigerated and at room temperature, so we need to look at how kH varies:

where k0 is kH at reference temperature T0, and C is a constant that depends on the gas being considered. The link above gives for CO2 at room temperature k0 = 29.41 L atm/mol, C = 2400 K, and T0 = 298 K. A typical temperature for refrigerators is 40°F or 277.6 K. Plugging these in, we find that kH will be about 55% smaller in the refrigerator. Since the partial pressure is the same inside and out, that means the concentration in the refrigerator is 1/0.55 = 80% larger than at room temperature.

When I started looking into this, I thought I would be finding a time it took to lose a given amount of carbonation, and the process would be slower in the fridge, but this model suggests that the carbonation will stay indefinitely. I think that's because even though having the CO2 outside the liquid is a lower-energy state overall, it takes some energy to create the bubbles – That's why shaking a soda makes it fizz. Happy New Year!