Amy Winehouse - 14-10-2012 at 18:52
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?
sargent1015 - 14-10-2012 at 18:58
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.
IanCaio - 14-10-2012 at 20:24
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 - 14-10-2012 at 20:46
^That system assumes that the ethanol addition is volumetric to the density. All the tables I've looked at aren't linear =\
tetrahedron - 15-10-2012 at 02:08
everyone knows that ethanol and water shrink when mixed
IanCaio - 15-10-2012 at 19:11
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 - 16-10-2012 at 07:57
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.).
Amy Winehouse - 23-10-2012 at 14:29
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.