Chemistry for a dummy
May 18, 2006 7:56 AM   Subscribe

When I pour sugar in my coffee the total volume in my mug increases. What happen to the volume when the sugar dissolves (decreasing or stable ?) ?
posted by vincentm to Science & Nature (9 answers total) 1 user marked this as a favorite
I just want to poke my head in, and point out that this kind of question is non-trivial in general for arbitrary substances dissolving in water.

The physical chemistry involved is horrendous (when I last checked a few years back), and the modeling is still relatively crude.

The volume changes can actually depend on the concentrations nonlinearly, as I remember. The other fun bit of trivia is that there are substances (magnesium salts, I think?) that one can add to water, that make the total volume decrease. (i.e. add a spoonful of magical substance X to a liter of water, end up with 0.97 liters total volume!)
posted by NucleophilicAttack at 8:02 AM on May 18, 2006

I believe that with the amount of sugar that you would normally put in coffee, you'll see the volume decrease as it dissolves, but end up slightly above the volume of the coffee sans sugar.
posted by Dipsomaniac at 8:12 AM on May 18, 2006

Is this a homework problem type question or something you've actually observed? If the latter, is it possible that the act of stirring the coffee and/or waiting for the sugar to dissolve allows enough steam to come off the top to lower the amount of water in the mug?
posted by underwater at 9:01 AM on May 18, 2006

Best answer: Yes about the non-linear solution. Sugar water has a different (greater) density than water; The water will fit in the spaces between sugar molecules resulting in a denser solution.

You can also observe this if you add 1 litre of water to 1 litre of alcohol, you will see that the result is less than 2 litres.
posted by dobie at 9:46 AM on May 18, 2006 [1 favorite]

Yes, for an exact answer, this is hard, also considering the fact that you've got water, coffee stuff, and sugar.

Qualitatively, I believe Dipsomaniac is correct. I guess you can think of it as mixing together a tub full of marbles and a tub full of baseballs, except with molecules. They will pack together and you will not wind up with two tubs, but you'll have more than one tub. If you wanted a numerical answer it is quite a bit beyond just adding and subtracting volumes. Don't remember much more than that, as it isn't my thing.
posted by TheOnlyCoolTim at 9:49 AM on May 18, 2006

I'm no physicist, nor even a scientician. Doesn't the addition of the sugar change the surface tension of the coffee. In a mug, wouldn't this difference appear pretty large.
posted by Classic Diner at 10:54 AM on May 18, 2006

CD - Surface tension may change, because all colligative properties will change, but this should in no way affect the volume of the liquid in the mug. Surface tension will only affect the miniscus, or how the liquid "grabs onto" the walls of its container. At worst, the miniscus would be less severe, causing the "legs" of the coffee to be shorter, which might make the volume *appear* smaller.
posted by schmordelia at 12:57 PM on May 18, 2006

Another way to think about the answer to the original question. Think of a mug mostly filled with sugar. When you add a small amount of hot coffee to the mug (say 1/4 vol), what happens? Not only does the mug not overflow, but you can probably watch the level of the sugar drop as the crystals dissolve into the hot liquid. Baseballs and marbles indeed.
posted by schmordelia at 1:01 PM on May 18, 2006

Best answer: Solution chemistry is very poorly understood. There is no formula to calculate how density will change for any solution. There do exist ad hoc formulas for, for example, sugar and salt in water, or a mixture of salts, but for a system as complex as coffee with milk and sugar: no way.

It's a pretty safe bet to guess that the solution will contract though. That's what sugar in water does. How much? I dunno. The "answer" would be to measure and find out.

I do take issue with dobie's answer. It's not as simple as void filling. Water is the exception to every "rule" in solution chemistry. Water can take multiple forms around dissolved particles and is said to 'flicker' between them. One of these forms has a density lower than regular water. Some solutes, usually non-polar ones, can force water to prefer this configuration, causing the solution to expand. The intricacy of water solution chemistry is why fancy layered drinks like a pousse cafe is possible, for example.

Side questions:
Surface tensions do change, and usually drop, when reducing the polarity of a water (air is non-polar).

The change in the meniscus is almost impossible to see with the naked eye, however. I was just trying something similar last week. Couldn't really see a meniscus change even under much more favourable conditions than a coffee cup.
posted by bonehead at 1:24 PM on May 18, 2006

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