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Author: Subject: Relation between solubility and temperature
r0749547
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Relation between solubility and temperature

Is there a real mathematical relation between solubility and temperature?
Exmp. molality ~ epx(temperature),
molarity ~ exp(temperature),
...
I've seen a few documents where they say the relation is exponentially.

But some solubility curves look like they have no relation at all (CaCl2).
Sulaiman
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Most things approximately double for every 10oC change,
https://en.wikipedia.org/wiki/Arrhenius_equation
but solubility has to be looked up.
Attachment: AlphabeticalSolubilityOfSalts.ods (55kB)
This file has been downloaded 388 times

[Edited on 11-1-2019 by Sulaiman]

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Metacelsus
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The relationship between temperature and solubility will vary depending on the solute and solvent in question. Generally, it can be described by the van't Hoff equation. See: https://en.wikipedia.org/wiki/Van_%27t_Hoff_equation

This equation uses the changes in enthalpy and entropy to describe changes in equilibrium with temperature. Therefore, in order to use it, the changes in enthalpy and entropy must be known beforehand. Practically speaking, it's often easier to just use a solubility table for the particular substance.

[Edited on 2019-1-10 by Metacelsus]

As below, so above.

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DraconicAcid
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 Quote: Originally posted by Metacelsus This equation uses the changes in enthalpy and entropy to describe changes in equilibrium with temperature. Therefore, in order to use it, the changes in enthalpy and entropy must be known beforehand.

You don't need to know the entropy change; just the enthalpy of solution. If you've got that and a solubility at one temp, you can calculate the solubilities at other ones.

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r0749547
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Quote: Originally posted by DraconicAcid
 Quote: Originally posted by Metacelsus This equation uses the changes in enthalpy and entropy to describe changes in equilibrium with temperature. Therefore, in order to use it, the changes in enthalpy and entropy must be known beforehand.

You don't need to know the entropy change; just the enthalpy of solution. If you've got that and a solubility at one temp, you can calculate the solubilities at other ones.

Don't you need the Gibbs free energy? to get the ln(K) = -G0/RT
(I can't write the delta of the Gibbs free energy)

[Edited on 10-1-2019 by r0749547]
DraconicAcid
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ln(K1/K2)= (-(delta)H/R)*(1/T1-1/T2) The delta H, and the solubility at one temp, is all you need.

This doesn't apply to something like calcium chloride, because you have calcium chloride hexahydrate dissolving at lower temperatures, and then calcium chloride tetrahydrate dissolving at higher temperatures (and the two hydrates have different enthalpies of solution).

[Edited on 10-1-2019 by DraconicAcid]

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i don't think there is a general formula since every solute and solvent would have different solubility.

edit: changed equation to formula

[Edited on 10-1-2019 by lordcookies24]

r0749547
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 Quote: Originally posted by DraconicAcid The delta H, and the solubility at one temp, is all you need.

Can't you use the solubility at two different temps to calculate the change in enthalpy?

[Edited on 11-1-2019 by r0749547]
DraconicAcid
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Quote: Originally posted by r0749547
 Quote: Originally posted by DraconicAcid The delta H, and the solubility at one temp, is all you need.

Can't you use the solubility at two different temps to calculate the change in enthalpy?

[Edited on 11-1-2019 by r0749547]

Yes, that works, too.

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r0749547
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Last question.
since solubility tables are always in molality,
to go from the molality to molarity I would need the density of the solution.
But that's hard to find. Do you just assume that the volume stays constant at 100ml?
at first I tought to calculate the mole fraction equilibrium constant and to convert that to the concentration equilibrium constant,
using Kc = Kx(P/RT)^delta(v) (but that only applies to gasses right?)

[Edited on 11-1-2019 by r0749547]
DraconicAcid
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Mole fraction equilibrium constant? I've never heard of that- equilibrium constants are always in molarity for solutes (with gases, you can use Kc or Kp, but that's not relevant here).

If you ignore the difference between molarity and molality, it really won't make much difference for the van't Hoff eq'n.

For example, let's look at what chemister.ru says about the solubility of benzoic acid in ethanol:

ethanol: 47.1 (15°C) [Ref.]
ethanol: 52.4 (19.2°C) [Ref.]
ethanol: 55.9 (23°C) [Ref.]

Because benzoic acid doesn't dissociate in ethanol, we can just use the solubility as the equilbrium constant (unlike an ionic compound in water, where we'd have to convert solubility to Ksp). The van't Hoff eq'n gives us 15.2 kJ/mol for the enthalpy of solution (based on the 15 and 23 oC values).

Using this enthalpy, we can find the solubility at 19.2 oC as 51.6 g/ 100 g solvent, which is pretty close.

[Edited on 11-1-2019 by DraconicAcid]

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r0749547
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 Quote: Originally posted by DraconicAcid Mole fraction equilibrium constant? I've never heard of that- equilibrium constants are always in molarity for solutes (with gases, you can use Kc or Kp, but that's not relevant here). If you ignore the difference between molarity and molality, it really won't make much difference for the van't Hoff eq'n. For example, let's look at what chemister.ru says about the solubility of benzoic acid in ethanol: ethanol: 47.1 (15°C) [Ref.] ethanol: 52.4 (19.2°C) [Ref.] ethanol: 55.9 (23°C) [Ref.] Because benzoic acid doesn't dissociate in ethanol, we can just use the solubility as the equilbrium constant (unlike an ionic compound in water, where we'd have to convert solubility to Ksp). The van't Hoff eq'n gives us 15.2 kJ/mol for the enthalpy of solution (based on the 15 and 23 oC values). Using this enthalpy, we can find the solubility at 19.2 oC as 51.6 g/ 100 g solvent, which is pretty close. [Edited on 11-1-2019 by DraconicAcid]

But what do you do if it does dissociate and you do need the molarity for the Kst?
Do you simply assume the 100g of water to be 100ml and neglect the volume change of mixing? (ex. NaCl in water)

And about the mole fraction equilibrium constant...
It stands in one of my books I need to know for my exams

[Edited on 11-1-2019 by r0749547]
DraconicAcid
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If you need the molarity for a dilute solution, then just assume that the 100 g of water makes 100 mL of solution. If it's a concentrated solution (such as saturated sodium chloride in water), then it's not going to work anyway because the ionic strength mucks things up, and you have to use activities instead of concentrations. Even without considering ions, if you have a solution that is 10% non-ionizing solute (such as 2-butanone), the solution doesn't act as a pure aqueous solution (it's only 90% water). That will change K for anything dissolving in it- ionic compounds will be less soluble, and organic compounds will be more soluble.

Even then, the van't Hoff eq'n isn't exact, because the enthalpy of solution will vary slightly with temperature.

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Morgan
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Is there a solid substance that is more soluble at a lower temperature than at a higher temperature?

[Edited on 12-1-2019 by Morgan]
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Many lantjanide series salts do this. Ce2(SO4)3 is one if I am not mistaken.

For something a bit less exotic, calcium carbonate. Tdep did a nice video on this on his extractions and ire channel.
Sulaiman
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the van 't Hoff equation seems to be applicable only over a range of temperature that needs to be chosen by refering to a solubility table or chart.
No doubt useful for optimising/fine-tuning an industrial application but not much use to me.

Praseodymium sulfate* has a third-order behaviour (see file I posted above)
- fit that with a van 't Hoff equation

* the first one I spotted, many other salts have anomalies

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fusso
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@Sulaiman I can't open the ods file with excel, something unreadable

Sulaiman
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The file is just a version of the Wikipedia page https://en.wikipedia.org/wiki/Solubility_table

Attachment: AlphabeticalSolubilityOfSalts.xls (401kB)
This file has been downloaded 392 times

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fusso
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 Quote: Originally posted by j_sum1 For something a bit less exotic, calcium carbonate. Tdep did a nice video on this on his extractions and ire channel.
Really? Did he? I can't find that.

Metacelsus
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Quote: Originally posted by DraconicAcid
 Quote: Originally posted by Metacelsus This equation uses the changes in enthalpy and entropy to describe changes in equilibrium with temperature. Therefore, in order to use it, the changes in enthalpy and entropy must be known beforehand.

You don't need to know the entropy change; just the enthalpy of solution. If you've got that and a solubility at one temp, you can calculate the solubilities at other ones.

Yes. Knowing the enthalpy and the solubility at one temperature is equivalent to knowing both the enthalpy and entropy.

As below, so above.

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nezza
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Some reagents do follow a simple solubility curve if you plot solubility agaist temperature. There is always a caveat. Reagents which react with the solvent do not, even if it is only hydrate formation. The curve is usually linear or exponential and can be used as a guide for recrystallising reagents. I have attached 2 curves BaNO3 which is just about linear and CuSO4 which approximates to exponential.

If you're not part of the solution, you're part of the precipitate.
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If you assume that the solute is forming an "ideal solution" then the mole fraction of solute (x) at temperature T is related to the fusion enthalpy (effectively going into solution is similar in energy to melting)

ln(x)=(/\H(fusion)/R)*(1/T(fusion)-1/T)

 Sciencemadness Discussion Board » Fundamentals » Beginnings » Relation between solubility and temperature Select A Forum Fundamentals   » Chemistry in General   » Organic Chemistry   » Beginnings   » Responsible Practices   » Miscellaneous Engineering and Equipment   » Reagents and Apparatus Acquisition   » Electronics   » Process Engineering   » Materials and Metallurgy Special Topics   » Analytical Chemistry   » Electrochemistry   » Energetic Materials   » Biochemistry   » Radiochemistry   » Computational Models and Techniques Literature and Documentation   » Sciencemadness Wiki   » Prepublication Non-science   » Forum Matters   » Legal and Societal Issues