Why doesn't liquid propane in a closed coke bottle burst?

Question

I was watching this YouTube video in which the original experiment was to make a small rocket out of liquid propane and Coke. When that failed, the person doing the experiment decided to try pouring liquid propane into the Coke bottle and closing the cap on it to see what would happen.

I would have expected (and I believe he did too) that the bottle eventually would build up enough pressure to explode. However, that did not happen and along with that not happening, the liquid appeared to warm up to about air temperature and stopped boiling. When he opened the lid of the bottle, it quickly depressurized, the liquid began boiling and returned to its normal, cold state.

My guess is that once the propane vapors filled the bottle and expanded sufficiently, it put enough pressure on the liquid to keep it from boiling. So my question here is, is my guess correct and, along those lines, if it had been warmer outside, would that bottle have built up enough pressure to explode?

Note: Even if my guess is correct, I want to see the hows and whys of it in an answer.

Answer 1

Yes, based on what we can see in the video, your guess appears to be correct: as the propane-filled bottle warmed up, just enough propane evaporated to keep the pressure inside the bottle equal to the equilibrium vapor pressure of the liquid propane.

According to the video, the ambient temperature outside at the time it was recorded was "about 45 °F", or about 7 °C. Using the formula given here, I calculate the vapor pressure of propane at that temperature to be about 4400 mm_Hg, or about 590 kPa or about 5.9 bar.

Meanwhile, according to this page, the pressure inside a warm can or bottle of Coke can reach at least 380 kPa, or about two thirds of the vapor pressure of propane on a cold day. As the bottles are certainly designed with a considerable safety margin, to make sure that they won't burst even if handled carelessly or slightly damaged, it's not surprising that they can easily withstand the pressure of the propane in the video.

BTW, this is exactly how aerosol spray cans work: they contain a mixture of the liquid being sprayed and a propellant substance (quite often propane) that has a boiling point at 1 atm only slightly below room temperature (or, equivalently, that has an equilibrium vapor pressure only slightly above 1 atm at room temperature). Thus, as the can is drained, the partial boiling of the propellant maintains the pressure inside the can at the propellant's vapor pressure, which is high enough to propel the spray out of the nozzle, but not so high that it would require an excessively sturdy and expensive can to contain it.

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As for what would happen at higher temperatures, at room temperature (i.e. 25 °C), the vapor pressure of propane would be about 7100 mm_Hg or 950 kPa (according to the formula, or about 7600 mm_Hg or 1000 kPa according to the table, which seems to be taken from a different source). According to this random forum post, the small ½ liter Coke bottles used in the video can apparently withstand at least 180 psi, or 1250 kPa, so the propane-filled bottle probably wouldn't burst even at room temperature (unless it happened to be damaged or otherwise particularly weak). If the temperature was raised to, say, 45 °C (113 °F, a very hot day), the vapor pressure of the propane would rise further to about 1500 kPa, which just might be enough to make the bottle fail. Also, elevated temperatures will soften and weaken the plastic somewhat, making failure more likely.

In any case, in my personal experience, the weakest point of such bottles seems to be the relatively thin and weak cap, which would likely fail at some point before the bottle itself did. I wouldn't be surprised if that was by design, to make the typical failure mode relatively safe and predictable.

Answer 2

The person in the video said it was about $\pu{45^oF}$. At this temperature propane has a vapor pressure of about 8 atm, so that is the pressure that built up inside the Coke bottle. Once this pressure had built up, it quit boiling.

The fact that he could still fairly easily squeeze the bottle suggests that it was probably not very close to bursting from the pressure, and I very much doubt that even a hot day would have caused enough pressure for it to burst. I once saw the aftermath of a similar experiment with a bottle like that in which the lucky-to-be-alive idiot had used liquid nitrogen to blow it up. The bottle had badly deformed and stretched out before bursting.

Bonus Answer: Why it didn't work
Since propane is less dense than, and immiscible with, water (or Coke), it just floated on top and was the first thing to pour out when the bottle was inverted. If he had held his glove-covered hand over the opening and inverted it so that the propane was on top inside the bottle, rapidly expanding in a confined space, it would have at least had a chance of working.