[yabbadabbadoodoodoo]

Hi everyone, I'm attempting to teach chemistry to 11-13 yr olds. I've tried to research this but have struggled, probably because the answer lies far beyond my (and my students level)

I am planning an experiment to test the thermal expansion of different liquids, e.g water, honey, ketchup, etc (they will measure the different heights risen in capillary tubes placed within a water bath). Am I right in thinking there is no single answer to explain why one liquid will expand more than another, other than to say it involves the structure of the particles in different substances, and that some require more energy in order to expand. I myself learnt Chemistry up to the age 18 so Highschool level, so my Chemistry (and Physics) isn't particularly strong; I imagine entropy and other concepts that I am not particularly versed in come into play?

I have researched that increased salt concentration in water leads to increased coefficents of thermal expansion, I am not clear on the reason why and whether this rule can be applied to most solutes in most solvents?

Does viscosity of the substance come into play? It appears from a preliminary that the thermal coefficient of honey is greater than that of water.


(P.S If anyone has a rule of thumb and an explanation suitable for a 11-13 year olds that would be amazing! )

[Corribus]

This is a very interesting question actually. Unfortunately, I don't think you're going to find a simple, general answer to this question, and certainly not one you'll be able to explain to 11-13 year olds.

Cards on the table, I don't know the answer, and a cursory search around the ol' internet isn't very helpful. I found a few old JACS articles that treat the problem semi-empirically, but that's not very helpful to get at a fundamental answer.

I think we can fairly say that (most) substances expand when heating because they vibrate more, because they have more kinetic energy, so there's a pushing force between molecules. For almost the same reason, gasses expand. I suppose you could invoke some entropy arguments but I don't think it's really necessary to do so. In condensed phases (liquids, solids), intermolecular forces are very important to determining bulk properties, and at higher temperatures these forces will be weakened. (Well, weakened, plus there is simply the fact that there's a lot more thermal energy around to break them apart.) This will also, I think, tend to favor expansion.

So what types of substances are more likely to have larger thermal expansion coefficients?

My first thought is that thermal expansion will be larger in (a) smaller molecules and (b) molecules that have weaker intermolecular forces. Smaller molecules because for a certain volume of liquid, there will be more molecules when molecules are smaller, so there will be more particles (if you want to think of them that way) pushing each other apart. (That is to say, I'm thinking the volume of actual molecules doesn't change as temperature is raised as much as the volume of the space between molecules does.) Wrt to strength of intermolecular forces - if the forces are weaker between molecules, they won't be able to stick together as well when the temperature rises, so molecules with weaker intermolecular forces should expand more readily as temperature raised. 

So, that was my prediction. The next step is to look for data. Sadly, I had a hard time finding good tables of data. Even the CRC wasn't very helpful.... or at least, I didn't see them in there.

I did find kind of a brief list here:

http://www.engineeringtoolbox.com/cubical-expansion-coefficients-d_1262.html

We can make a few comparisons that seem to indicate my predictions may be at least generally true.

Compare the volumetric thermal expansion coefficients of methanol, ethanol, and isobutyl alcohol: 0.00149, 0.00109, and 0.00094. Also compare pentane (0.00158), heptane (0.00124), octane (0.00114) and olive oil (0.0007). The units here are in K-1 and a large value indicates that the substance expands more as temperature is raised (a value of 0 means no change in volume as temperature is increased).

In both of these sets of molecules, we can approximate the intermolecular forces to be more or less on the same order of magnitude with respect to strength. Thus in these sets we are looking at the effect molecular size has one thermal expansion. Notice that for the hydrocarbons, as the molecules get bigger, the thermal expansion coefficient gets smaller. Same thing for the organic alcohols.

What about strenght of intermolecular forces? With such a small selection of molecules it's hard to find suitable comparisons. What we're looking for are two molecules that have the same approximate size but very different polarity (intermolecular forces). One that I think might be relevant is diethyl ether and isobutyl alcohol, both of which feature four carbons and an oxygen. The expansion coefficient of ether is 0.0016 and that of the alcohol is 0.00094. Ether would be expected to have much weaker intermolecular forces than the alcohol, which is borne out in their respective boiling points (34.6 C vs 107 C). The weaker intermolecular forces of ether may mean that there's not as much holding together the structural integrity of the liquid  as there is in the alcohol, which doesn't expand nearly as much as it's heated. Another suitable comparison that shows this effect is toluene (0.00108) versus phenol (0.0009) or aniline (0.00085).

Anyway, that's a very superficial treatment but maybe it gives you some ideas. One thing to bear in mind is that thermal expansion is temperature dependent and can also behave very weirdly for a number of substances (namely, water), so the simplistic treatment I've provided here should be taken with a truckload of salt.

Happy to hear other ideas.

[curiouscat]

Will the capillaries be sealed at one end? I'm not sure I understand your setup exactly. Could you draw a sketch?

[yabbadabbadoodoodoo]

The set up is a test-tube with a bung filled with the liquid, 'sealed' with a perforated bung with a capillary tube threaded through, the capillary tube will extend past the height of the test-tube.

The test-tube will then be placed into a beaker of warm water, along with test-tubes of other liquids, the distance that the liquid rises will be recorded.


@Corribus

Thank you for the input, similarly I've found tables of expansion coefficients, but very little scientific explanation. Your explanation of intermolecular forces and size of molecules makes sense to me and is probably enough, perhaps this practical would be useful for a lesson on polymers too potentially, though I need to have a think about that.

[curiouscat]

So in addition to expansion there's cappilary rise. Surface tension enters that eq. & σ is a function of Temp.

Not sure if that effect's small or big but maybe some compensation will be needed?

[yabbadabbadoodoodoo]

Ah cheers, I didn't even consider that, I won't mention that to this class since I don't want to over-complicate things - but maybe for a lesson with older children, I'll just have to gloss over that flaw to the experiment!

[Corribus]

If your capillary is sealed, an even bigger issue is vapor pressure, which works to push the liquid back down. This is why mercury is traditionally used for thermometers even though it has a relatively low thermal expansion - almost no vapor pressure.

[curiouscat]

If your capillary is sealed, an even bigger issue is vapor pressure, which works to push the liquid back down. This is why mercury is traditionally used for thermometers even though it has a relatively low thermal expansion - almost no vapor pressure.

For this expt. why would one want to seal the capillary?

[Corribus]

If the substances being heated are toxic.

But I see from the opening post that these will be common household items. So, fine. But the OP should be aware that most of those are water-based "solutions" with very complex chemical profiles. In this case it may be even harder to draw meaningful conclusions about why some expand more than others.