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Sulaiman
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[*] posted on 30-3-2017 at 00:11
Solubility musings


What determines the solubility of salts ?

some salts are very soluble, >100 g/100ml
some salts are 'insoluble, p.p.m.

how does one molecule of a low solubility salt 'know' that somewhere in the surrounding few million molecules of water, there is another molecule like itself ?

the only idea that I have is that very large numbers (up to millions) of water molecules are somehow 'attached' to each salt ion,
but that would imply large scale water structures.
If so, why do 'insoluble' salts create such huge structures.

... point me to some useful info. ... please




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byko3y
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[*] posted on 30-3-2017 at 01:04


God determines. It may be illustrated with Rubik's Cube, where you can make one turn and the whole image becomes different, but has some similarities though.

freezingpt.JPG - 62kB
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Sulaiman
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[*] posted on 30-3-2017 at 01:22


+1 on the God thing, but that doesn't help my understanding very much,


Found it ! https://en.wikipedia.org/wiki/Solvation_shell
but still none the wiser as to why some ions/salts create such huge shells.

e.g.
Barium Chloride, 35.8 g/100 ml at 20 oC,
Barium Sulfate, 0.0002448 g/100ml @20 oC

(35.8/0.0002447)0.3333 = 52.7 : 1 solvation shell radius ratio.

Why ?



[Edited on 30-3-2017 by Sulaiman]




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[*] posted on 30-3-2017 at 06:06


Also striking are the perchlorates of the alkali metals.
At 20 deg in water:

HClO4 - infinity miscibility with water
LiClO4 - 56.1 g/100 mL
NaClO4 - 201 g/100 mL
KClO4 - 1.68 g/100 mL
CsClO4 - 1.6 g/100 mL
RbClO4 - 1.55 g/100 mL




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[*] posted on 30-3-2017 at 06:50


Dissolving / crystallisation is an equilibrium system. As such, when a solution is at its solubility limit the rate of dissolving is the same as the rate of crystallisation. Ions are leaving the solid and going into solution at the same rate as ions leave the solution and join the lattice. So, to answer your question, the low solubility salt does not "know" anything. It always behaves in the same way. And that behaviour is exactly the same as a soluble salt. (Although the rate might be different. However rate does not actually alter the position of the equilibrium and is mostly a distraction when discussing these things.)

So, what determines the position of the equilibrium? And what causes some salts to be more soluble than others? It comes down to a question of energy.

There are two processes going on in dissolving. There is the removal of ions from the crystal lattice. And there is the hydrolysing of these ions as they are surrounded by water molecules.

The first of these processes is an endothermic process. It requires energy (lattice energy) to remove ions from the crystal structure. Breaking of bonds is always endothermic.

The hydrolysing process is exothermic. Bonds are formed between the ions and the water.

Thus there is an activation energy associated with the process of dissolving. But more significantly the overall process will be either exothermic or endothermic depending on the magnitude of the two energies involved.

To a first approximation, a substance will be soluble if the energy released by hydrolysis exceeds the energy required to break the lattice. And a substance will be insoluble if the energy required to remove ions from the lattice exceeds the amount released by hydrolysis.


Now this all implies that a salt will only dissolve if the process is exothermic. Not actually true. There are plenty of salts that will lower the temperature of water when they are dissolved. So, what gives? There is a third factor to consider.

Chemical processes (and other processes) may be driven by either of two forces. The first of these is the energy given off. The second is an increase in entropy. If we define entropy as a measure of disorder (not the best definition, but it will do here) then it is easy to see that a crystal is highly ordered and that mobile ions in solution are very disordered. This means that there is an increase in entropy when a salt is dissolved. This entropy increase may be enough to cause a substance to dissolve even when otherwise energetically unfavourable.

So. An ionic substance will be soluble if the combined effect of entropy increase and hydrolysis is sufficient to match the energy required to remove ions from the crystal lattice. Similarly, a solution will crystallise if the energy released when ions join the lattice is sufficient to beat the combined effects of breaking the bonds with water and also decreasing the local entropy.

Now, all salts are soluble to a certain extent -- even if the amount is miniscule. Random quantum effects dictate that there will be at least some ions that have sufficient energy to break out of the lattice and join the solution. But for a poorly soluble salt, this is energetically unfavourable and in short time these ions will fall out of solution and join the crystal again.

For a highly soluble salt a different situation arises: As you rightly point out with your mention of solvation shell, the hydrolysis process involves more than just a few water molecules. I recall reading more than a year ago that a single ion may have an affect on more than a million water molecules. (I don't have the link immediately at hand.) But if you consider that it is a charged particle and that its electric field acts over a distance, this indeed makes sense. So, as the concentration becomes higher, there are fewer water molecules available to interact with the newly released ion. Therefore the energy released by hydrolysis is lower. At a certain point of concentration this lowered energy of hydrolysis is sufficient to tip the equilibrium the other way -- it is more favourable to crystallise than it is to hydrolyse ions that leave the crystal. Thus you have a saturated solution. On the macro scale, no more will dissolve.




This is my understanding of the situation anyway. I am sure that if blogfast was around he would pick holes in it somewhere. (Probably my terminology.) And I lack the knowledge to tell you which combinations of ions have a high lattice energy and which release high amounts of energy when they hydrolyse. From a computational standpoint, these energies can be used to determine the solubility. This way beyond me.

Nevertheless, this should get you into the zone of appreciating why some salts are more soluble than others.

[Edited on 30-3-2017 by j_sum1]
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Sulaiman
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[*] posted on 30-3-2017 at 12:41


thanks for taking the time to explain,
... needs time to soak through the grey mush ...




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[*] posted on 30-3-2017 at 15:12


j_sum1: thanks for a wonderful summary, clearly written.

It seems that many (or all) chemical reactions happen for the same reason, a reduction in energy of the system, and/or an increase in entropy, ie, a net increase in the Gibbs' free energy, delta G. In organic chemistry one product may predominate as it is the most stable. Again, this is likely the same phenomenon.

[Edited on 30-3-2017 by Magpie]




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[*] posted on 30-3-2017 at 16:38


Quote: Originally posted by phlogiston  
Also striking are the perchlorates of the alkali metals.
At 20 deg in water:

HClO4 - infinity miscibility with water
LiClO4 - 56.1 g/100 mL
NaClO4 - 201 g/100 mL
KClO4 - 1.68 g/100 mL
CsClO4 - 1.6 g/100 mL
RbClO4 - 1.55 g/100 mL

Note that solubility decreases with increasing size of the cation. As the size of the cation increases, its positive charge is more shielded by its electron shells, and is therefore less able to bond with the relatively negative Oxygen atoms of water, and thus it is harder for the water to "pull it - the perchlorate salt- apart" (my terminology). The perchlorate ions can be ignored in this analysis because they are common to all the compounds in the list.
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[*] posted on 30-3-2017 at 20:05


It is all the increase in entropy of the universe, really. A decrease in energy of the system, really means that the surroundings increased by that same amount. And the surroundings have many different ways that the energy can be arranged, so adding energy to the surroundings adds entropy to the universe, by dS = Q / T, where Q is the amount of energy passed from the system to the surroundings as heat, and T the temperature. So you just look at ALL the entropy change: The energy change of the system is the entropy change of the surroundings, plus the entropy change of the system itself.

Also, when the solution becomes very concentrated, I would think that the solution is a lot more ordered than when dilute, since all the water molecules are interacting. So this is not as high entropy as when dilute, and this will also tip back the equilibrium.

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[*] posted on 30-3-2017 at 21:17


@CharleA
Yeah, but there is always something to buck the trend. Check Rb and Cs carefully. And no, I don't understand why. I note that phlogiston's inclusion of HClO4 is a bit of an anomaly since it is a covalently bonded molecule and not an ionic solid. However, it does form the same kinds of ions in solution. Comparing it with the alkali metals is always going to be an apples to oranges kind of thing.

@pantone159 Agreed on the steady increase of entropy in the universe. (This is a lovely description of time-dependent entropy increase.) I think I deliberately specified local entropy decrease during crystallisation -- just to cover my butt.
I nearly didn't mention anything about entropy since I think it is possible to get a grasp of solubility without it and with just the principles of equilibrium. However, I felt like there was a gaping hole in my explanation so it went in.
And yes, I think that there is less entropy per mole for a concentrated solution when compared with a dilute one. I pretty much glossed over that detail thinking I had already written enough.
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[*] posted on 5-4-2017 at 10:30


well the matrix knows whats up
i found it pretty disturbing back in time when i synthesized lithium carbonate to filter a hot solution, as lithium carbonate has a solubility curve thats reversed
an interesting thing.. some chemicals which are very soluble can once dissolved, move faster than a river flows, a strange between physics, this could become a sport




~25 drops = 1mL @dH2O viscocity - STP
Truth is ever growing - but without context theres barely any such.

https://en.wikipedia.org/wiki/Solubility_table
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[*] posted on 5-4-2017 at 13:08


Quote: Originally posted by Sulaiman  
some salts are 'insoluble, p.p.m.

how does one molecule of a low solubility salt 'know' that somewhere in the surrounding few million molecules of water, there is another molecule like itself ?

the only idea that I have is that very large numbers (up to millions) of water molecules are somehow 'attached' to each salt ion,
but that would imply large scale water structures.
If so, why do 'insoluble' salts create such huge structures.


They don´t.
And neither do involatile solids.
What happens is that if there are just a few molecules of low solubility salt among millions of water molecules, or of low volatility substance in a volume of air, they are wandering around by Brownian motion.
In air, a molecule undergoes 1011 collisions per second. Even if some of them are the same molecules, due to Brownian moment a molecule of low volatility vapour or of low solubility solute would be apt to meet another molecule of the same compound - and then stick firmly.
And the pair would remain stuck till the third joins them. And so forth.
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[*] posted on 5-4-2017 at 13:48


A compound will be soluble if the Gibbs free energy change associated with its solvation is exothermic. The exact balance of enthalpy and entropy terms is delicate and complex to assess (because of the effect of the ordering of the solvent molecules on system entropy), but you can make broad conclusions by considering enthalpy terms only.

For a compound to be soluble, we want its lattice energy to be small but the sum of the hydration enthalpies of its ions to be large.

Suppose we let (r+) denote the radius of the cation of an ionic solid, and let (r-) denote the radius of the anion.

Since the lattice enthalpy is inversely proportional to the sum of the radii, i.e.
ΔHlatt ∝ 1/((r+)+(r- )) (Kapustinskii equation)
whereas the hydration enthalpy is composed of each ion being hydrated individually, i.e.
ΔHhyd∝ 1/(r+) + 1/(r-)
the lattice enthalpy will be minimised while the hydration enthalpy will be maximised if r+ is small and r- is large (or vice versa).

In general, therefore, an ionic compound will be soluble if there is a reasonable difference between the ionic radii of its cation and its anion. If both ions are small, then both the lattice enthalpy and total hydration enthalpy may be large and so dissolution might not be very exothermic. If both ions are large, although the lattice enthalpy will be low, the hydration enthalpy may also be low and so the dissolution might not be very exothermic.

This is shown in that the most soluble halides of group 1 are LiI and CsF. Similarly, the most soluble group 2 sulfate is MgSO4 (largest difference in ionic radius - beryllium is anomalous) whereas the least soluble is BaSO4.

Edit: I have used the terms "lattice energy" and "lattice enthalpy" interchangeably. They are fundamentally different quantities, but generally only vary by a few kJ/mol in perhaps 10^3 kJ/mol and so can be treated as being identical. The lattice enthalpy is in fact the sum of the lattice energy and the integral, between zero and a defined temperature, of the heat capacities of each of the ions minus the heat capacity of the ionic solid.

[Edited on 5-4-2017 by Hexavalent]

[Edited on 5-4-2017 by Hexavalent]




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Sulaiman
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[*] posted on 5-4-2017 at 22:47


I was thinking more of the solution rather then the solvation,

. as there are salts that are endothermic on solvation, and some exothermic on crystallization, I'm a little confused ... I'll catch up ..

but I consider all salts to be soluble, just a matter of degree and duration, (random thermally driven bond breaking/making)
so the process of getting ions into solution is not what I'm considering,
it is what determines the maximum density of various ions that water can support
....................................
the source of my musings is related to what is going on in the solution

for example, barium carbonate, 197.34 g/mol, solubility in water 0.0002448 g/100ml = 1.24.10-6 moles/100ml (@20oC)
and 100ml water = 100/18.015 = 5.55 moles H2O
so concentration of barium carbonate in water = 1.24.10-6/(100/18)/5.55 = 2.23.10-7 moles/mole

i.e. one molecule of barium carbonate per 4,475,806 molecules of water
equivalent to a cubic grid of 164 x 164 x 164 water molecules.
or if just ions are considered, approx 100 water molecules distance between each barium and/or carbonate ion.

why can't more barium carbonate ions 'fit in' to the solution ?
there seems to be plenty of space ... unless it is somehow organised ?

So what determines solubility, or more specifically, insolubility/saturation ?
how does a solution become saturated at such low ion density ?

I guess what I'm asking is,
can solvation shells extend to 100's water molecules radius ?
i.e. the limit of solubility is related to solvation shell size ?
i.e. the water is highly/completely structured ?
(allowing for thermal 'jiggling')

[Edited on 6-4-2017 by Sulaiman]




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[*] posted on 6-4-2017 at 00:14


Quote: Originally posted by Sulaiman  

. as there are salts that are endothermic on solvation, and some exothermic on crystallization, I'm a little confused ... I'll catch up ..

but I consider all salts to be soluble, just a matter of degree and duration, (random thermally driven bond breaking/making)
so the process of getting ions into solution is not what I'm considering,
it is what determines the maximum density of various ions that water can support
....................................
the source of my musings is related to what is going on in the solution

i.e. one molecule of barium carbonate per 4,475,806 molecules of water
equivalent to a cubic grid of 164 x 164 x 164 water molecules.
or if just ions are considered, approx 100 water molecules distance between each barium and/or carbonate ion.

why can't more barium carbonate ions 'fit in' to the solution ?
there seems to be plenty of space ... unless it is somehow organised ?

So what determines solubility, or more specifically, insolubility/saturation ?
how does a solution become saturated at such low ion density ?

I guess what I'm asking is,
can solvation shells extend to 100's water molecules radius ?
i.e. the limit of solubility is related to solvation shell size ?
i.e. the water is highly/completely structured ?


No.
Try to look at the analogy between solution and vapour.
All substances are endothermic on evaporation. Yet they evaporate. And do not organize vacuum by their vapour.
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Sulaiman
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[*] posted on 6-4-2017 at 04:41


do gasses have solubility limits ?
I thought gasses are miscible in any proportions.




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[*] posted on 6-4-2017 at 04:49


@ Sulaiman - It's not about "fitting" into the solution but more about whether the solvent can support additional ions.

Ions enter solutions because of weak attractive interactions with polar solvents. You can imagine that the "sphere of hydration" around an ion is supporting it like a bunch of balloons supporting a weight. Imagine gravity as the electrostatic force trying to reattach the ion (the weight) back to a crystal lattice (the earth). If you have a fixed amount of solvent (balloons), you can easily support a small amount of weight. However, when you add more weights, you will have to start borrowing balloons from other weights. Eventually, there will be so many weights (ions) suspended, that there aren't enough balloons to keep any more off the ground, and for every new weight you release, another will fall back to earth (rejoin the lattice) since you have borrowed its balloons. This represents a saturated solution.

Of course, this is only a simplified, macroscopic example. Gravity has a negligible effect on such a small scale when compared to electrostatic force and brownian motion, and each ion is suspended in solution via a sphere of millions of solvent molecules with which it weakly interacts. In the real world, many factors come into play, like lattice energy, enthalpy of solvation, ambient temperature, and a few complex entropic effects.




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[*] posted on 6-4-2017 at 05:09


Quote: Originally posted by Praxichys  

You can imagine that the "sphere of hydration" around an ion is supporting it like a bunch of balloons supporting a weight. Imagine gravity as the electrostatic force trying to reattach the ion (the weight) back to a crystal lattice (the earth). If you have a fixed amount of solvent (balloons), you can easily support a small amount of weight. However, when you add more weights, you will have to start borrowing balloons from other weights. Eventually, there will be so many weights (ions) suspended, that there aren't enough balloons to keep any more off the ground, and for every new weight you release, another will fall back to earth (rejoin the lattice) since you have borrowed its balloons. This represents a saturated solution.
.. snip ..
Of course, this is only a simplified, macroscopic example. Gravity has a negligible effect on such a small scale when compared to electrostatic force and brownian motion, and each ion is suspended in solution via a sphere of millions of solvent molecules with which it weakly interacts.


i.e. a saturated solution occurs when there are no 'spare' balloons
... when the water molecules all become associated with the spheres of hydration,
q.e.d. water is weakly but completely structured in a saturated solution. :D




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[*] posted on 6-4-2017 at 07:25


Quote: Originally posted by Sulaiman  
do gasses have solubility limits ?
I thought gasses are miscible in any proportions.


Precisely.
Gases have vapour pressures. Steam condenses at a specific density of water molecules - a density which gets very low as temperature is lowered.

And it´s not because the water molecules somehow "structure" the air. Actually, the density of saturated vapour at a given temperature is the same regardless of whether the vapour is a small admixture in air or whether it is in vacuum.
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