[NotionCommotion]

I am trying to determine the volume (or density or specific volume) of a solution.  For instance, at standard atmospheric pressure and temperature, how would I determine the volume of the following?
3 Moles C6H12O6 (Glucose) plus 11 Moles CH3CH2OH (Ethanol Alcohol) plus 300 Moles H2O (water)

If my terminology is incorrect, please feel free to correct me.

Thank you very much!

[Mitch]

Can't you just measure it in a flask?

[mike]

First convert moles to mass....

[NotionCommotion]

Measure in a flask is unfortunately not an option.

In regards to converting to mass, I actually started with mass (around 90% water, 5% glucose, and 5% water) to come up with my moles.  I know the rule of thumb that a kg of sucrose increases the specific gravity by around 0.386 because the water-sugar hydrogen? bonds are stronger than the water-water bonds, but don't know how it was derived and would like to figure it out.  I also know that the volume of alcohol and water is less than additive because of the water-alcohol bonds are stronger than the water-water bonds, but don't know the change in specific gravity nor how it is effected by the presence of sugar.  Forgive me, but I am just an amateur brewer and lost my chemistry book many years ago!

Thank you

[Borek]

Your problem boils down to finding density of such solution - and the simple answer is "you are probably out of luck".

Such things can be only measured. You may use some approximations (I think our enginners may be able to tell more) but the only sure method is to use density tables. Problem is, there is only limited set of density tables available, and they cover mostly two compounds (like water/something) solutions. Tables exist only for some three-compounds mixtures, you may be able to find them in some reference books (I would start looking in CRC handbook or International Critical Tables).

If you can't measure volume, you may look for hydrometer to check the density of the solution.

[NotionCommotion]

"Out of Luck" was not the answer I wanted to hear!

Using a hydrometer just like measuring the volume is not an option because I wanted to use the solution density in an equation before actually creating the solution.

In reality, I will have even more than three compounds including water, ethanol alcohol, glucose, fructose, sucrose, maltose, maltotriose, and dextrins.  Good news is I don't need an exact density.

I've heard that a kg of sucrose plus water will result in 1 liter of with a specific gravity around 1.386.  Does this approach make any sense?  Can a similar approach be applied to other sugars or the alcohol? If using density tables, can they be applied individually by just multiplying the SG by several "factors" based on the quantity of each compound divided by the final volume?   What are the "approximation" approaches available should density tables not be used?

Thank you, thank you, thank you!

[Borek]

"Out of Luck" was not the answer I wanted to hear!

I value honesty higher then politeness

No idea about the approximations that you can use (ask in Chemical Engineering Forum, I suppose Eugene or Milt may know more, thay have hands-on industrial experience).

There is no systematical way of doing density calculations for a solution that I am aware off. SOlutions are never ideal and their volumes are almost never additive.

However, what precision do you need? As long as we are talking about 10% w/w solutions you may probably safely assume that your final solution will have density somewhere between 0.9 and 1.1 g/mL. 20% difference, which can be perfectly acceptable if all you need is information about number of buckets you have to buy

BTW: you may check my CASC for density tables (check link in signature), but only for 1-compound solutions.

[Mitch]

woops accidentally deleted his new topic, but I moved this here anyways.

[utramos]

volume of 1 mole of molecules at STP, 22.4 L . so just multiply out what u have.. this is right i think?

[NotionCommotion]

I believe you are thinking of the ideal gas law, and I have liquids.  I know that the volume for a given quanity of molecules change based on the bonds between them.  For instance, the hydrogen bonds between C6H12O6 (Glucose) and CH3CH2OH (Ethanol Alcohol) with H2O are stronger than these bonds between one another H2O molocules.

[Borek]

I know that the volume for a given quanity of molecules change based on the bonds between them.

That's only part of the story.

Imagine you are mixing marbles with sand. Sum of volumes is much lower then expected, just because sand fills holes between marbles. Similar thing happens when you mix two liquids with molecules of different sizes. Then it may happen then strong bonds between molecules force volume to GROW instead of getting smaller - if when some particular relative position of molecules is preferred, position in which combined molecules are more bulky.

And so on...

[Donaldson Tan]

the volume of a mixture (V) is given as the sum of its partial volumes (v_i), ie. V = sum {n_iv_i}. You need partial volume data. The partial volume can be obtained from differentiating the Equation of State: v_i = ?V/?n

I hope you can obtain the equation of state for your mixture.

Borek: I'm really not sure if this thread belongs to Chem Eng, P.Chem or here..

[Borek]

I hope you can obtain the equation of state for your mixture.

Just don't hold your breath... While Geo is right, that's just another perspective. In practical terms finding equation of state doesn't differ from finding density tables. Often none exist.

[NotionCommotion]

Thank you Borek and Geodome,

In advance, I apologize about not using the correct symbols.  It appears that there are many conflicts (i.e. molarity using G, c, m, and M).  Also, it is difficult to abbreviate solution, solute, and solvent as they all start with "sol".  If there is a single acknowledged standard, please direct me to it.

I reviewed the CRC Handbook (the International Critical Tables intimidated me with its antiquity!) and found a wealth of information for single solutes, but not multiple (wasn't surprised).  I noticed that the compounds I was interested in, both moles_solvent / volume and density were very linear with %m/m.  Even though density was listed in the tables, I also solved for density as (100 / %m/m) * MW_solvent * moles_solvent/volume and was off by a small amount (any ideas why?).  I am a little puzzled about them both appearing linear as my above equation for density has %m/m in the denominator and therefore they can't both be linear.  I am thinking of just picking one and using a single order extrapolation (any thoughts which?).  Since I have multiple compounds, I am thinking about equating total density equal to the (c1*mass_solute_1 +c2*mass_solute_2...) / mass_solution plus density of water where c1,c2, etc is the slope of the density - %m/m line (assuming I go with density and not moles/volume). This equation works if the solutes all have the same slope (i.e. are the some compound), and while I am sure it will not be exact, I am hoping it will be close (any comments?).  Am I doomed for disaster, or do you think it would be worthing giving this approach a try?

In regards to which forum this should be in, it started in general chemistry, but then I thought I was in the wrong forum, so I started a new post in chemical engineering, but then Mitch evidently accidentally deleted it and moved my original post moved here.  I don’t mind being moved to the right place, but the deleting was a little frustrating.

Thank you both again.  Michael

[Borek]

In advance, I apologize about not using the correct symbols.  It appears that there are many conflicts (i.e. molarity using G, c, m, and M).  Also, it is difficult to abbreviate solution, solute, and solvent as they all start with "sol".  If there is a single acknowledged standard, please direct me to it.

No standard, although c usually means just concentration (often molar, but not necesarilly), m stands for molality, M for molarity (check concentration lectures for details).

I reviewed the CRC Handbook (the International Critical Tables intimidated me with its antiquity!)

Many of CRC tables are just copied from ICT or some earlier source.

and found a wealth of information for single solutes, but not multiple (wasn't surprised).

Told you so.

Am I doomed for disaster, or do you think it would be worthing giving this approach a try?

I will repeat my earlier question - what precision do you need? My take is that you will waste your time because your results will be never really accuratee - and you may get good enough precision using some more practical rule of thumb. Don't let perfection hinder real task you want to solve (whatever it is - but sounds like it may be tasty saturated with CO₂. Note that CO₂ will change pH of the solution, modifying interactions between all molecules and possible changing density ).

then Mitch evidently accidentally deleted it and moved my original post moved here.  I don’t mind being moved to the right place, but the deleting was a little frustrating.

That's understandable, but be assured it was accidental