Sciencemadness Discussion Board

Calculating solution composition from density?

Elrik - 28-10-2018 at 21:07

I have a question about density. I did UTSE but the number of web pages about grade school density calculation outnumber pages about this topic by a seemingly infinite degree without the exactly correct search parameters, it seems. I'm missing a keyword or two ;)
If the densities of the components of a solution of two known compounds in unknown relative proportion to eachother are known, and the density of the solution is known, how can one accurately calculate the composition of the solution?
For example, the density of 2-butoxyethanol is 0.90 and the density of limonene is 0.8411. If a solution known to contain only those components was placed in a pycnometer and determined to have a density of 0.853 is there some book or website that would explain to me how to use that to calculate the exact composition of the solution?
I know that 0.90X + 0.8411(1-X) = 0.873 would be incorrect. Possibly quite close depending on the compounds, but incorrect because of how different molecules pile together. For instance, if the numbers are plugged in to predict the density of 50% ethanol the answer actually corresponds to the density of 59% ethanol.
So what complicated math that will make me regret not properly learning calculus is used to get the exact answer?
Thanks :)

[Edited on 2018-10-29 by Elrik]

DraconicAcid - 28-10-2018 at 21:29

That would depend on exactly how ideal or non-ideal the solution is. If you were mixing 2-butoxyethanol with 2-butoxypropanol, we'd declare it to be probably ideal, and just use the kind of calculation that you'd expect to be incorrect. With 2-butoxyethanol and limonene....I have no idea. I strongly suspect you'd have to experimentally determine the density of various mixtures, and draw a graph.

Elrik - 29-10-2018 at 08:56

I was afraid that might be the answer.
I initially learned chemistry from my grandfathers books and I expect that's how they'd do it in his college days. I just thought that by now we'd have a method that used greek letters and large amounts of aspirin to get it done purely theoretically ;)

unionised - 29-10-2018 at 12:11

Quote: Originally posted by Elrik  
how can one accurately calculate the composition of the solution?

[Edited on 2018-10-29 by Elrik]

You can't.

But the approach you use is probably not bad for hydrocarbons, halocarbons, ketones, ethers, esters etc.
It's not going to be perfect, but it might be "good enough".

That calculation's going to fail badly for amines, alcohols + acids.

It's also going to fail for solutions of solids.

Fulmen - 29-10-2018 at 12:18

Quote: Originally posted by unionised  

You can't

Are you absolutely sure about that? It is possible to model quite complex molecular interactions, so I suspect it's doable. But yes, it would likely require both greek letters and aspirin.

[Edited on 29-10-18 by Fulmen]

unionised - 29-10-2018 at 13:22

Quote: Originally posted by Fulmen  
Quote: Originally posted by unionised  

You can't

Are you absolutely sure about that? It is possible to model quite complex molecular interactions, so I suspect it's doable. But yes, it would likely require both greek letters and aspirin.

[Edited on 29-10-18 by Fulmen]

Yes I'm sure.
One might; he can't.

AJKOER - 6-11-2018 at 08:00

My advice, perform experiments in known measures of two known compounds of interest recording relative proportions and the resulting density of the mixed solution.

Develop the best fitting parsimonious modelings producing good fits and note the statistical errors.

Knowledge and related modelling studies in physical chemistry could improve model development efforts.
-----------------------------------------------

An alternate method than using density in special case of an ionic salt than dissolves in one component of the solution and not in the other. Then, the electrical resistance of the mix could be used to estimate the concentration of one of the components (see https://www.mt.com/us/en/home/library/guides/process-analyti... ) and total statistics could indicate conc of second component.

[Edited on 6-11-2018 by AJKOER]

Texium - 6-11-2018 at 08:53

I had to do a lab in my physical chemistry class that involved using a pycnometer and measuring the densities of different sodium chloride solutions, and calculating partial molar volumes and crap... it was convoluted, over complicated, and very frustrating. Even my professor admitted he didn't see much practical use for the technique, but it's part of what the ACS wants chemistry majors to learn, so we learn it. Honestly I've already forgotten the finer details of that experiment just a semester later. I don't think it's much of a loss though.

Tsjerk - 6-11-2018 at 09:29

For more known mixtures there are graphs available, I would stick with those, you can't find them... Too bad.

For example "density dmso water mixtures" in Google gives some nice results.

Edit: the freezing point graph for that mixture is also real nice I think




[Edited on 6-11-2018 by Tsjerk]