# surface tension of an aqueous solution

I'm trying to determine the surface tension of an aqueous solution of glycerin (60 vol% h20, 40 vol% glycerin, @ 20°C) without having to
measure it with a test or expensive device. Is there something similar to the rule of mixtures for surface tensions of solutions?
pure water @ 20°C = 73 dynes/cm glycerin @ 20°C= 65 dynes/cm 60/40 vol% = 54/46 wt% for glycerin
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There is no simple way to calculate this that I know of. The reason is that it depends on the surface depletion or surface excess of solute, which is dependent on the geometry of the solvation of glycerol with water. The Gibbs adsorption equation is:
d(gamma) = -RT(Gamma_2) d(ln C2), where gamma is surface tension, Gamma_2 is surface excess of the solute, and C2 is concentration of the solute.
Not knowing Gamma_2, you can only make qualitative observations, eg it will probably be very slightly positive or very slightly negative, so I speculate glycerol has a very minute effect. It's not dependent on the surface tensions of the individual liquids. Take sucrose in water, sucrose by itself has a lower surface tension than water, but adding sucrose to water increases the surface tension higher than water's. This is because sucrose is surrounded by OH groups and prefers to be solvated by water than partitioned to the surface, and its Gamma_2 is negative (surface depletion).
It is not an expensive measurement. A surface tensiometer is an extremely simple and cheap instrument. However, this is such a common system that you should just look in the literature. I'd be willing to bet a large amount of money that this has been measured and published to death. There are also plenty of published empirical equations, but why bother with these and all the physical parameters involved when you can probably just find real data. If you know a few data points, you can fit it to the equation above to get Gamma_2, and then you can backcalculate surface tension for any concentration.
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