Why do soda cans blow up when you put them in the freezer?

This is something that I found in my old computer files. I originally wrote it sometime around the mid-1990s, in response to some people on an email mailing list wondering why cans of soda often exploded messily when frozen, leaving “stalactites” of frozen slush all over the inside of the freezer. I updated it a bit when re-posting it here, though, so the reference to Wikipedia near the end isn’t the anachronism that it looks like

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A popular way of rapidly chilling a can of soda is to put it in the freezer for a short time. However, if the can is allowed to freeze, it will often explode, depositing interesting stalagmite-like icy structures on the sides of the freezer. This effect does not occur with cans of non-carbonated liquids, which generally just crack open and ooze.

There has been some question of exactly what causes the cans to explode the way they do, and so I’d like to present here an analysis of two questions:

1. Do frozen soda cans explode primarily because of the gas pressure, or primarily due to the expansion of the ice?

2. What is the origin of the stalagmite-like structures on the sides of the freezer afterwards?

1. What makes the soda can explode?
The critical item is the solubility of CO2 in ice as compared to the solubility in water. According to _Seidell’s Solubilities_ (fourth edition):

At -5 deg. C, the solubility of CO2 in ice is 1/20th of the solubility of CO2 in 0 deg. C water at the same CO2 pressure.

At -20 deg. C, the solubility in ice drops to only about 1/200th of the solubility in 0 deg. C water.

So, upon freezing, water initially expels about 95% of the CO2 from the crystal structure. The next question is, how much CO2 is that?

Seidell gives the solubilities of CO2 in cc of gas per gram of water (volume measured at 0 deg. C and 1 atm. pressure). I’ve added values in moles of CO2 per kg of water, which we will be wanting a bit later. We are interested in the values at the freezing point of water, so at 0 deg. C we have the values given in Table 1.:

Solubility of CO2 in water at 0 deg. C

Pressure

CO2 content

CO2 content

1 atm.

1.80 cc/g

0.08 mols/kg

5 atm.

8.71 cc/g

0.387 mols/kg

10 atm.

15.89 cc/g

0.706 mols/kg

In experiments using soda bottles as oxygen tanks for a rocket (Wenzlaff, 1994, personal communication), the bottle ruptured at a bit over 5 atmospheres above ambient (6 total). I don’t know how much pressure is normally used in soda cans, but let’s assume 1.5 atmospheres above ambient, or 2.5 atmospheres absolute pressure (note: the Kirk-Othmer Encyclopedia of Chemical Technology says that colas are bottled at higher pressure than sodas pretending to be fruit-juice based, but they didn’t give any hard numbers).
Now, the head space. I found a Mountain Dew can lying around, which says on it that it holds 355 grams of soda. When it was completely filled to the top with water, there were 371 grams of water in it, so the nominal head space is 16 ml, or 4.5% of the volume of the soda.

So, let’s say that the soda can is put into the freezer at an absolute internal pressure of 2.5 atm. Doing a little interpolation between the 1 atm. and 5 atm. values, there should be about 3.6 cc CO2 per gram of liquid, or 1,284 in 355 g of liquid. Now, say that half of the soda freezes. Allowing 5% of the CO2 to stay in the ice, that still leaves us with 610 ml of CO2 that has to go somewhere. If this is all forced into the 16 ml of headspace, then we’ve just increased the amount of gas in that 16 ml by a factor of about 38, so (2.5 atm.) x 38 = 95 atmospheres, or about 1400 psi.

Of course, I didn’t account for the CO2 being forced into solution in the remaining liquid by the pressure. Going back to Seidell, the equation for solubility of CO2 in water at 0 deg. C is:

S = 1.84*P – 0.025*P^2

where S is the solubility in cc/gram water, and P is the pressure in atmospheres. So, now we can put together a formula for the pressure of CO2 in the can as a function of the fraction of the liquid in the can that freezes. Variables are:

X = Fraction of the liquid that is frozen (maximum value 1.0)
V = Volume of liquid in the can (355 ml in this case)
Po= initial pressure in the can (take as 4 atmospheres absolute pressure)
T = Initial quantity of CO2 dissolved in the liquid, which is calculated from:
T = V*S = 355*(1.84*4 – 0.025*4^2) = 2470.8 cc CO2
D = Quantity of gas dissolved in remaining liquid after freezing begins:
D = V*(1-X)*(1.84*P – 0.025*P^2) (I decided not to worry about the 5% of the CO2 that stays in the ice for this calculation)
H = Headspace. I calculated the pressure both assuming a constant headspace of 16 cc, and assuming that the headspace was reduced as the water froze, according to the formula:
H = 16 – 0.097*X*V

There, I think that’s everything. Now, the pressure should be equal to the number of volumes of CO2 squeezed into the headspace, divided by the volume of the headspace, so: P = (T-D)/H

All of which we have expressions for above. Unfortunately, pressure terms crop up all through the resulting equation, so I just went to a spreadsheet and solved it by successive approximations. The results I got were:

Fraction Frozen

Constant Headspace

Varying Headspace

0.1

4.34 atm

4.37 atm

0.2

4.90 atm

4.98 atm

0.3

5.64 atm

5.77 atm

0.4

6.63 atm

6.90 atm

0.5

8.05 atm

**headspace negative**

1.0

146.7 atm (after everything is frozen, and all but 5% of the gas is in the headspace)

So, what we see here is a race between the gas pressure rupturing the can, and the expanding ice using up all the headspace and rupturing the can. If the can fails at less than 8 atmospheres absolute pressure (about 100 psi gauge pressure), which we would expect from Bob Wenzlaff’s soda bottle experiments, then the CO2 pressure will do it. If it manages to hold out until then, it will likely rupture when the can runs out of headspace. Of course, if the bottom domes out enough that we get about another 16 ml of headspace, then the ice expansion still won’t be enough, but it will blow sometime before all the water freezes and the gas pressure peaks at something over 2000 psi.

2. What makes the “stalagmites”?
One last thing to consider, is why the soda sprays out of the can as mostly liquid, but then freezes almost instantly. While it is true that increasing the pressure will decrease the freezing point of water, a 100 atmosphere pressure increase will only drop the freezing point by about 0.75 deg. C (according to my Physical Chemistry book, here), so that effect is small. Another, larger effect is the freezing point depression due to dissolved material (there are lots of dissolved materials other than CO2 here, but they aren’t going to seriously affect the conclusions because they don’t come out of solution when the pressure drops).

The molal freezing-point depression constant for water is 1.86 K for every 1 mole of material dissolved per kg of water, and we have the molalities (moles/kg) for saturated CO2 solutions above, so our freezing-point depressions at different pressures are approximately:

Pressure

Freezing Point Depression

1 atm.

-0.15 deg. C

5 atm.

-0.72 deg. C

10 atm.

-1.3 deg. C

And then, finally, we have what is probably the biggest effect. When you quickly reduce the pressure of a compressed gas, the expanding gas gets colder. you get a significant amount of adiabatic cooling which will help freeze the stuff. If Wikipedia is to be believed, then the temperature change for typical gases can be estimated from:

T2 = T1(P2/P1)^0.2857

where T1 and P1 are the initial pressure and temperature, T2 and P2 are the final temperature and pressure, and 0.2857 is calculated from the value of “gamma” for common gas molecules (it is actually for diatomic molecules, like O2 and N2, but it is still probably at least in the ballpark for CO2). Using this equation, if we start at 273 Kelvin (the freezing point of water) and assume that the pressure at can rupture is 8 atmospheres, then assuming there is no source of heat, the temperature should plummet to only 150 Kelvin (about -123 C, which is really, really cold). Even granting that this is a very crude estimate, and that it won’t get that cold because the freezing water gives up its heat of crystallization as it flies through the air, we can see that the adiabatic cooling probably dominates the temperature drop in this case.

The CO2 that is still in solution when the can ruptures will also quickly leave the solution and become a gas, causing evaporative cooling, but I think we can just consider this to be included in the crude estimate of the adiabatic cooling.

So, what happens? First, our can pressurizes up as small amounts of the soda freezes, while the rest of the liquid stays liquid because of the CO2 depressing its freezing point. Eventually, the can just can’t take it any more, and explodes. As the liquid (which is a bit colder than the freezing point of water) flies through the air, the pressure has crashed to atmospheric, and it is now supersaturated with CO2.

So, the CO2 boils away, with the combination of evaporative cooling and adiabatic expansion reducing the temperature of the liquid still further, while allowing the freezing point to pop back up to what you would expect with pure water (well, OK, sugar syrup with flavors). This all happens in a fraction of a second, so it is already slush-on-its-way-to-ice by the time it hits the side of the freezer. Instant stalactites.

This agrees very well with observation, so I guess we could take this as explained. If anyone wants to try it out, it occurs to me that just throwing a full soda bottle into a salt/ice bath should get it cold enough, so this could be done outdoors instead of in Somebody Else’s Freezer (you could actually watch it this way, too, instead of just opening the freezer to look at the aftermath).

One of the things that I was a bit surprised by in this whole exercise is just how much CO2 is put into carbonated beverages. According to the Kirk-Othmer Encyclopedia, 18% of the CO2 used commercially, goes to soft drink carbonation. Yikes!

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