Measuring Solubility: "A Riddle Wrapped In A Mystery Inside An Enigma"

[escape_velocity]

In the chapter on solutions of Sienko & Plane's Chemistry the authors say that the amount of grams per liter of solution is not a reliable indicator of solubility, but the molarity --moles per liter of solution-- is, without explaining why. The following example is given.

 

"At room temperature the solubility of saccharose [sugar] in water is 1311 g. per liter of solution, more than four times that of sodium chloride [table salt]. These figures are, however, misleading, and it is necessary to compare the molar solubilities if one wants to infer some consequence relating to the number of [dissolved] particles. The saturated solution of sodium chloride is 5.3 M, whereas that of saccharose is 3.8 M, that is to say, in that sense the solubility of the former compound is greater than that of the latter, which is logical, since between the ions Na+ and Cl- and the dipolar water molecules there is a greater attraction than between these and the nonpolar saccharose molecules."

 

So, the question is why "grams per liter of solution" and "moles per liter of solution" can indicate opposite circumstances. This is puzzling since grams and moles (meaning "gram-molecules", of course, as usual) are akin (a gram-molecule being the amount in grams of a substance numerically equal to its molecular weight) and one would expect them to show the same situation.

 

I suspect the explanation is elementary, which is a disturbing idea, so I'm in urgent need of it so I can get on with the task of going back to my high-school knowledge base.

 

 

 

 

[CaptainPanic]

[...] it is necessary to compare the molar solubilities if one wants to infer some consequence relating to the number of [dissolved] particles. [...]

 

Your book seems to suggest that it is somehow really important to know how many particles you have in solution (or not).

 

I'm a chemical engineer - and all I care about it grams (or preferably: tons) of material.

 

I would suggest that the whole point is an opinion that moles/liter are the relevant parameter instead of grams/liter nothing more.

 

I think I can argue that the solubility of glucose is greater for 2 reasons (it's a subjective argument, just like the book):

1. The dissolved mass per liter of water is greater

2. The glucose has multiple hydrogen bonds per molecule with water molecules. This interaction explains its solubility.

 

And I think I can argue with the writer of that book for quite a long time, and nobody would be any the wiser.

 

 

Let me finish by saying that there is one thing in the book that I STRONGLY disagree with, to a point where I would say it's just plain wrong: saccharose molecules are not non-polar. Every molecule has 8 -OH groups, and 3 C-O-C groups, which are all (locally) quite polar. It's not ionized, but it's certainly polar, which explains its high solubility in water!

Edited June 28, 2011 by CaptainPanic

[John Cuthber]

The question is roughly equivalent of asking about a bowl full of sand and a bowl full of steel ball bearings.

Which bowl has stuff more in?

 

Well, the steel is much denser so (for a given size of bowl) a bowl full will weigh more.

On the other hand the sand grains are smaller so a bowl full will have a much larger number of "particles".

Which one is "better" depends on what you want to measure, mass or number.

 

 

In the case of the salt and sugar solutions, if you want to guess which one will have a lower freezing point then you have to look at the number of particles present. But, if that's what you are talking about you need to consider that a mole of NaCl dissolves in water to form 2 moles of ions ( equal numbers of Na+ and Cl-).

 

However, by that argument you would expect a saturated salt solution to have a higher boiling point. It doesn't because the solubility of sugar rises much faster with a rise in temperature than the solubility of salt.

 

Confused yet?

I don't blame you; that book isn't helping.

[escape_velocity]

Sorry about the delay, and thank you for the prompt and juicy replies. I have not remained idle. It's that they had me thinking hard all these days, and maybe I finally reached a loftier level of understanding.

 

So, the answer was NOT "simple and straightforward". There might be a "subjective" element involved, and controversies over basic matters, and "second opinions", just as with medical diagnoses. This is completely unexpected since we're dealing with one of the "exact sciences".

 

Moreover, it's unquestionably the simplest: both advanced math and advanced physics are out of bounds for most people, including most scholars. Chemistry is reassuringly down-to-earth. I'm one third of the way through the textbook and by now it seems like most problems are to be solved by applying a "rule of three", or two or three (a matter of elementary proportionality).

 

"(…) the whole point is an opinion that moles/liter are the relevant parameter instead of grams/liter, nothing more.

 

"(…) I can argue that the solubility of glucose is greater [since the] dissolved mass per liter of water is greater (…)." --Capt. Panic

 

The confusion seems to be caused by failing to make a distinction between dissolved and dissociated particles. The dissolved mass of sugar per liter of water is greater, but four out of the five ways of expressing concentration in a solution relate to the number of moles, and thus the number of particles, not to the mass, like the fifth way (normality) does. Also, the dissolved mass is greater but not the number of dissociated ions. Strong electrolytes such as table salt dissociate nearly 100 per centum. The solute in a 5.3 M salt solution weighs less (about four times less) than the solute in a 3.8 M sugar solution because the molecules are much, much lighter (6.5 times lighter), but the degree of dissociation is greater.

 

Thus, molarity is the adequate measure for solubility, at least as regards four out of the five ditto, because one mole, of whatever substance, always has the same number of particles (the Avogadro number), so that a greater number of moles indicates a greater number of particles, and it's even greater in this case since salt dissociates almost entirely, which means that the initial number of particles (NaCl) is multiplied by two (Na+ and Cl-). Maybe the argument is fueled by not realizing that four of the methods are related to the number of particles and only one is mass-related?

 

A question remains: does molarity always reveal the greater number of particles of a solute? In this case the number of grams does not because the sugar molecules are 6.5 times heavier than table salt molecules, so that less particles of the former can weigh much more than more particles of the latter.

 

" (…) saccharose molecules are not non-polar [because they bear polar bonds]." --Capt. Panic

 

…but the presence of polar bonds doesn't necessarily imply a polar molecule. It depends on the molecular structure. The book explains this with the following example (from the chapter on the chemical bond).

 

"It is possible to predict the polar or nonpolar nature of a diatomic molecule: if both atoms are equal, their bond must be nonpolar, and so will the molecule; if they are different, both the bond and the molecule will be polar. (…) It is not that easy to predict the polar nature of a molecule having more than two atoms, since it can be nonpolar even if all of its bonds are individually polar. An example of this is carbon dioxide (CO2), in whose molecule the two oxygen atoms are linked to the carbon atom (Fig. 4-6).

 

O.…C….O

 

-..+…..+..-

 

Fig. 4-6. Nonpolar molecule with polar bonds

 

"Since the latter attracts the shared electrons with less strength than the oxygen atoms do, it is understandable that each one of the carbon-oxygen bonds must be polar. (…) Now, the molecule as a whole is linear, and the effect of one dipole is annulled by that of the other one. Thus, when the CO2 molecules are placed in an electric field, they do not align, because the momentum of each one of the dipoles is counteracted by the momentum (in the opposite sense) of the other one. This is why carbon dioxide has a very low dielectric constant."

 

Then they point out that if the water molecule were linear, too…

 

H….O….H

 

…then it, too, would be nonpolar, but that a high dielectric constant argues in favor of a structure where the bonds are at an angle.

 

"Confused yet?" --John Cuthber

 

Maybe less so. I think the sand and steel ball simile finally managed to shake me out of my daze, because it reminded me of the tricky question meant for schoolchildren. Which weighs more: a pound of feathers or a pound of lead?

 

Why this led to what seemed like a sudden insight is not clear. Anyway, what I then realized was the simple fact that fewer moles of sugar can weigh much more than more moles of salt, which is why the first pair of figures (number of grams) is misleading, apart from the fact that salt dissociates almost completely.

 

This is all so intricate that it's starting to look like a complete chapter in a book or a paper sent to a journal, and I'm wondering whether or not I'm still unaware of something.

 

To make a long story even longer, it might be helpful to say that the book is an old one, from the 60's, but the publishers are reliable (McGraw-Hill) and both coauthors were professors of chemistry at Cornell U. It's one of the books of my youth. I dropped out during my third semester of Biology in 1970 and never went back. You all will have to help me catch up at the virtual college here.

 

One who did go back was the 99-year-old man who finally got his college degree just two weeks ago. In 1932 he, too, had to drop out, because he was offered a job as a professor during his very last semester, then he was offered twice as much at a lumber yard (not sawing logs, I guess). That was after the Crash of '29, when everyone was in a panic and no job opportunity was turned down, even barely months away from graduation, which shows how desperate people were, back in those days…just like right now once again! This piece of TV news on June 16 was quite encouraging for a (relatively youthful) nearly 60-year-old.

 

…and going now somewhat off the topic, I recently came across another old textbook in the inexhaustible used-book market, Chemical Engineering Plant Design (Vilbrandt & Dryden, McGraw-Hill, too, 1959), which was exciting, like finding an Egyptian papyrus. Questions will come up while thumbing through it, and maybe our resident expert, the Captain, will have the patience to answer them?

 

The very first phrase in the preface is just like the opening words of The Gallic Wars (Julius Caesar): "Chemical engineering design is divided into equipment design and plant design (…)." The Roman general starts out by saying: "The whole of Gaul is divided into four parts."

 

 

 

 

 

[CaptainPanic]

Thus, molarity is the adequate measure for solubility [...]

It is indeed adequate, but not always the most practical.

The most important lesson here should be that you must always write down the units (mol/l or g/l or any other unit of your choice).

 

" (…) saccharose molecules are not non-polar [because they bear polar bonds]." --Capt. Panic

 

…but the presence of polar bonds doesn't necessarily imply a polar molecule. It depends on the molecular structure. The book explains this with the following example (from the chapter on the chemical bond).

A glucose molecule is so large that locally it is actually polar. A very polar water molecule that is near a sugar molecule only "sees" (if it had eyes) the nearest couple of C-OH groups or C-O-C groups. It does not "see" all the other ones because they are quite far away.

 

Also, glucose is in a 3D structure (as shown here), and the C-O and O-H bonds do not cancel out completely in the middle. To make it even more fun (chemistry can be fun), glucose can actually also open and close. So, it can be a ring of 5 carbons and 1 oxygen, but it can also become linear. And it can go back too. This happens already at room temperature.

[escape_velocity]

"(…) it can be a ring (…) but it can also become linear. And it can go back too."

 

... a surprising supplement to the subject of the denaturation of proteins and the recent findings about partially or completely unstructured or unfolded proteins. Disarray can be catastrophic and irreversible in proteins, as in the classical example of the heated egg white, yet now it's known that many proteins are not rigidly folded and that this doesn't imply a loss of function, so one wonders whether or not they, too, can go back and forth between different shapes the way simpler molecules like glucose do.

 

It also brings to mind the difference between normal chemical reactions, which eventually reach a state of equilibrium between reactives and products, and wildly oscillating reactions, which are exceptional. The latter seem to be similar to shape-shifting glucose, but since only 0.02 % of glucose molecules in solution are chained, according to the Virtual Chembook, stability would seem to be the usual thing. Otherwise, wouldn't one see far more chain molecules?

 

"This happens already at room temperature."

 

...which seems to be saying that shape-shifting increases as temperature increases, and maybe at high temperatures no glucose molecules are ring-shaped….