Math teacher here. I’m trying to teach about types of sets that when you add them together, their sizes don’t add (called non-measurable sets). I came across the chemistry experiment where you mix 50 ml water and 50 ml ethanol, and you get less than 100 ml total solution. Is there a more dramatic version of this experiment?


2 Answers 2


A quick glance at the graph $V^\mathrm{E}$ vs $x_1$ for the system water+ethanol typically show a minimum of around $\pu{-1.2 cm3 mol-1}$ at ambient temperature. This means that when we mix them, then the system contracts.

Ekezie et al. (2023) studied the excess volume and excess viscosity for methanol with several alkyl acetates at different temperatures:

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where $\ce{M}$ is methanol, $\ce{MA}$ is methyl acetate, $\ce{BA}$ butyl acetate, and $\ce{PA}$ pentyl acetate. The graph labelled with (a) is at $\ce{25 °C}$ whilst the one with (d) is at $\ce{40 °C}$. We stick with the latter.

The system $\pu{M+MA}$ presents an expansion of about $\pu{8 cm3 mol-1}$ when the molar fraction of methanol is around $\pu{0.3}$. The system $\pu{M+PA}$ presents a contraction of around $\pu{-9 cm3 mol-1}$ when again the molar fraction of methanol is around $\ce{0.3}$. Both values are are approximately $\pu{6.5}$ and $\pu{7.5}$ times higher, in absolute value, with respect to the system water+methanol.

As an aside, the authors argument with respect to the positive excess volumes that:

On mixing, methyl acetate appears to disrupt the self association of methanol hydrogen bonds leading to rupturing of the bonds and hence, the observed positive deviation. Positive deviation may also be attributed to weak dipole-dipole interaction dominant in the mixed system.

Conversely, for the negative excess volume:

It is possible that on mixing, methanol formed new hydrogen bonds with the dipolar oxygen of the esters. This behavior may be attributed to inductive effect which increased the electron density and thus, the proton accepting ability of the alkyl acetate. Increase in alkyl chain length of acetates increase the inductive effect.


Ekezie, Chukwuebuka M., Cookey, Grace A., & Maduelosi, Jane N.. (2023). Volumetric and viscometric studies of binary mixtures of methanol and some alkyl acetates at varying temperatures. South African Journal of Chemistry, 77, 133-137. https://dx.doi.org/10.17159/0379-4350/2023/v77a16


The presentation of the demonstration can make clear the volume change, though only a few percent reduction.

For example, pour 50 ml of water, with a bit of food coloring added, into a 100 ml cylinder. Carefully add 50 ml of ethanol, with a different color dye, on top, without mixing (float a drop of olive oil on the water, if need be, to separate the layers).

Put a one-hole rubber stopper with a 50 cm or so long glass tube on top, pushing the stopper in so that the alcohol rises in the tube, and mark the top of that meniscus in the tube.

As soon as the cylinder is shaken, the level in the glass tube will drop greatly, because the apparent decrease in volume is magnified by the ratio of diameter of cylinder to glass tubing. Ah... a teachable moment -- have students prove, or disprove that statement!

  • $\begingroup$ Yes, this is a good way to demonstrate the effect. But are there liquids where the effect is larger? $\endgroup$
    – matt_black
    Commented Jan 10 at 11:38

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