It's been hot in the coastal foothills of California (afternoon highs ranging from 102 to 107F), and we've been cooling off in the pool and with a steady supply of cold drinks. But the search for truth marches on, even on vacation, and in that spirit we did a little experimentation this afternoon. Does Diet Coke ™ really float, while the high calorie stuff sinks? Not having any on hand, we substituted Diet 7-Up and Sierra Mist (non-diet) and dropped away. Sure enough the diet stuff floats.

Why? The cans are the same size, but the non-diet soda weighs more. Why? Do calories have mass? One of my brothers suggested it was because sugar is a heavier molecule than aspartame (NutraSweet ™). This is true - sucrose weighs in at 342.3 daltons while aspartame comes in just under 300 (294.3 daltons), but not the solution to the mystery. The relative sweetness of the two molecules is the key. You need less than 100 mg of aspartame to equal the sweetness of the roughly 40 g of sugar in the regular soda. Both have the same volume of solution, the sugar one is denser than water and sinks. But wait...why isn't the diet stuff denser than water, too? It should be just a little heavier than just plain water not? True, but the air bubble in the top of the can is just enough to offset it.

Tolman, “The Principles of Statistical Mechanics, Chapter 1, Part 1

4 weeks ago in The Curious Wavefunction

This is interesting.

ReplyDeleteIn retrospect, it is predictable that soda with a sweetener many times sweeter than sucrose should float. But, post-predictions don't count, do they?

The ordinary soda can I just measured was approximately 12 cm high and had a diameter of 6.6 cm. Assuming that it is a perfect cylinder (in reality it is not) and ignoring the thickness of the can, its volume is approximately 410 cm3. The label gives the volume of soda inside as 355 ml.

Therefore, a full can of soda will float if [355 g + weight of can] =< 410 g. [I don't have an empty can to weigh.] If we add to that about 40 g of sucrose (ignoring the weights of flavors and CO2), but subtract the weight of water that sucrose is displacing so that the total volume stays 355 ml, we will have the total weight of a can of ordinary soda, which is probably slightly higher than 410 g. Thus, such a can will sink.

On the other hand, because aspartame is much sweeter than sucrose, there is probably very little of it is used and once again ignoring the weights of flavors and CO2, I will guess that the weight of a can of diet soda is probably close to [355 g + weight of can]. Therefore, it will swim.

Hey, I should have posted this on my own blog!

I like the quantitative analysis!

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