How does carbonation, salt, and fresh (filtered) water affect the cooling rate in different environments?

As an undergraduate I majored in chemistry and biology. I am currently working on a graduate degree in chemistry.

I'd just like to clarify the difference between freezing point and freezing rate before I start answering your question. When we add salt or any solute (including carbon dioxide) to water, we lower its freezing point, or the temperature at which it freezes. When we talk about rates, however, it is ultimately a question of thermal conductivity, or how quickly we can add/remove thermal energy (note that I don't say heat! -- heat is a process, not a "thing") from the system. The higher the thermal conductivity, the faster we can cool or heat a substance.

As a disclaimer, I would like to say that the answer to your questions is somewhat involved. Let's start with the simplest case: distilled (pure) water. Thermal conductivity depends on temperature. I believe the trend is that at higher temperatures thermal conductivity is higher. But I would like to say that thermal conductivity only changes very slightly with temperature. What does this mean? As an example, if we start cooling one cup of water at 90F and another cup starting at 40F, the rate at which the 90F water cools will be slightly greater. Note that if we were trying to freeze the two cups of water the 40F would probably still freeze first, but only because it was closer to the freezing point. You can think about it in terms of the slopes of the lines that you would get from plotting temperature vs. time. The slope of the 90F water would probably be slightly steeper (i.e. have a faster rate) than the 40F water.

However, we need to be careful here. At a certain point, water will boil and become steam/vapor. The thermal conductivity of a vapor will be much lower than that of a liquid. In this case, the difference is not slight at all -- it is about an order of magnitude (10 times)! You can think about it like this: the molecules in the liquid are much closer together, so they can transfer energy (and thus heat or cool) more easily. But the molecules in the vapor are far apart, and will not "bump into each other" as often, so energy won't be transferred as quickly as in the liquid.

That said, let's think about what this means. When you say "how does carbonation, salt and fresh water affect cooling rate in different environments?" I understand "different environments" to mean different temperatures. You should be very careful here, because a good experiment usually only changes one variable at a time. Here, you're talking about two variables: (1) type of solute (salt, carbon dioxide, or none), and (2) temperature. If we only consider liquid distilled water, then at a lower temperature, thermal conductivity is lower, and cooling rates will probably be marginally slower. Does this make sense? Remember the definition of thermal conductivity!

OK. So now let's discuss the other two cases, where we include solutes (carbon dioxide or salt). When we add impurities to water, we very slightly decrease the thermal conductivity of the water. I believe this is true if we keep all other things constant. So what does that mean? Compared to pure water, cooling rates would probably be slower. If we stay within the constraint of liquid water and starting the cooling/freezing process from different temperatures, I think the cooling rates of the water with solutes will still be slower, due to lower thermal conductivity. But remember, it's a small decrease in thermal conductivity, and thermal conductivity does not change drastically with temperature -- so the differences may be hard to discern!

I think it would also be a good idea to try the experiment if you haven't already. Take three cups, fill all three with the same amount of water, but one will be distilled water, one will be salt water, and one will be carbonated water. Put them in the freezer at the same distance from where cool air comes into the freezer. Be very sure to try and make all the conditions equal, except the fact that they have different solutes -- having other conditions be different could introduce experimental errors! Check on them periodically to see which freezes first. And do it a few times to verify that you're getting the same results.

One other important thing to note is that I think the experimental conditions to observe what I think would be very slight differences would have to be very pristine and precise. Most household environments are probably not ideal for this. Furthermore, your definition of when water is considered "frozen" would have to be very consistent. This is difficult, even in an ideal experimental setting. To give you an idea: do we consider it frozen when the first few molecules on the outside begin to have a crystalline structure? Or is it something else? It can be complicated ... But please don't let this discourage you! Try the experiment out, just to see. There are so many amazing discoveries and advancements in science that happened because people were curious and tenacious about it.

I hope this helps. I realize it was a rather involved answer, so if you still have questions feel free to ask.