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Author: Subject: Mathematical relationship between concentration and density
Amy Winehouse
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Mathematical relationship between concentration and density

Does any mathematical relationship exist between the concentration of a solute and the change in density of the solvent?

For example, wikipedia has a table of aqueous ethanol properties at varying concentrations. But if I didn't have that table, could I know the concentration of ethanol just by measuring the density? Obviously the lower the density, the higher the concentration of ethanol, but it's definitely not linear. Is it different for a gas dissolved in a liquid?

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sargent1015
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I know there is a relationship, but I think tables are necessary. I know my grandpa would measure the concentrations of his acids this way.

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IanCaio
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I would use something like this:

i.e., we have a solution of ethanol and water:

Assuming 'X' is the percentage of ethanol, and 'Y' is the percentage of water in a solution.

a) X*(Ethanol Density) + Y*(Water Density) = Measured Density

b) X + Y = 100%

Solving the system should work.

Example:
Measured Density = 0.86593 g/cm3
Ethanol Density = 0.78522 g/cm3
Water Density = 1 g/cm3

a) X*0.78522 + Y = 0.86593
b) X+Y=1 (or 100%)

from b):
0.78522X + 1 - X = 0.86593
0,21478X = 0.13407
X=0.62
Y=0.38

I took this data from a 70% ethanol. Since the error is quite big, I'm not sure if this method is accurate, if I dont have the right data here, or even if there is some kind of interaction between the ethanol and water that might make this sort of calculation misleading..
Amy Winehouse
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^That system assumes that the ethanol addition is volumetric to the density. All the tables I've looked at aren't linear =\

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tetrahedron
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everyone knows that ethanol and water shrink when mixed
IanCaio
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My bad guys, this explains the big difference on the values.
There is no way to deduce the final volume of a mixture of ethanol and water?
Nicodem
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Yes, for some systems you can find empirical mathematical models of density vs. concentration in the literature. These are commonly polynomial equations using at least two empirical factors. But a mathematical model is generally no more exact than a data rich table can be. Due to lack of proper advantage, and due to practical reasons, most people will still prefer to use tabular data.

The "EniG Chemistry Assistant" chemical calculator has some mathematical models of a few most common compositions with water already integrated (e.g., acetic acid, acetone, HCl, H2SO4, etc.).

…there is a human touch of the cultist “believer” in every theorist that he must struggle against as being unworthy of the scientist. Some of the greatest men of science have publicly repudiated a theory which earlier they hotly defended. In this lies their scientific temper, not in the scientific defense of the theory. - Weston La Barre (Ghost Dance, 1972)

Amy Winehouse
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Thanks Nicodem that was a really helpful answer. I gassed some methylamine into some methanol and my dumbass didn't weigh it. I had to spend two days neutralizing it and vaccuum distilling. Also, thanks for the info on the chemistry assistant. I had a feeling there was too much randomness in volumetric additions to be modeled simply by mathematics. Data tables and excel linear least square approximations are the best we can get.

Maybe I'll start collecting data on various solvent/concentration relationships and save them as excel files and collect a database of least square approximation equations for various systems. Most of the chemistry I do I use methanol as a solvent. If I made tables, where would an appropriate place to post my data on SM be/would people even be interested? If anyone has any methanolic equations please PM them to me.

Thanks again guys.

"I'm too drunk to taste this chicken"
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