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Author: Subject: KCl solubility at high temp & pressure
RogueRose
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[*] posted on 6-3-2017 at 13:43
KCl solubility at high temp & pressure


As most know, KCl has increased solubility from 0C to 100C (280g/L to 563g/L), almost doubling between these two temperatures where as NaCl (356g/L vs 389g/L)has much less variation between the two temps.
Both of these have a near linear increase in solubility (KCl even more linear if not perfectly)

Deg C -- NaCl -- KCl - in g/L
0 -- 357 -- 280
10 -- 357 -- 312
20 -- 360 -- 342
30 -- 361 -- 372
40 -- 363 -- 401
50 -- 367 -- 426
60 -- 370 -- 458
70 -- 375 -- 486
80 -- 379 -- 513
90 -- 385 -- 539
100 -- 390 -- 563
*NOTE/question - is there a way to make tables and format them well in these forums?

Grams diff per 10 degree increments
degC dif = g of NaCl & KCl
0-10 = .7 -- 32
10-20 = 2.8 -- 30
20-30 = .09 -- 30
30-40 = 2.8 -- 29
40-50 = 3.2 -- 25
50-60 = 3.5 -- 32
60-70 = 4.2 -- 28
70-80 = 4.7 -- 27
80-90 = 5.4 -- 26
90-100 = 5.2 -- 24

As can be seen here, the differences aren't quite linear (though graphs usually show this) but it does seem to increase for NaCl and decrease with KCl.


Solubility of compounds

What I am wondering is whether I can get more KCl to dissolve in water at a higher temperature while under pressure of a minumum of 1ATM but more likely something close to 6-10atm (90-150 PSI)



Temp change vs pressure change of water (30 PSi is = to about standard pressure cooker rating of 15 psi due to 14.7 PSI standard pressure)
PSI -- deg F -- deg C
30 -- 250 -- 121
45 -- 267 -- 131
60 -- 293 -- 145
75 -- 308 -- 153
90 -- 320-- 160
105 -- 331-- 166
120-- 341 -- 172
135 -- 350-- 176.5
150 -- 359-- 181
165 -- 366 -- 185.5

Water temp at various pressures


Now if temp is the only thing that is the factor in dissolving the compound, then I would suspect the KCl to continue to slope upwards as the temp rises but I'm not sure if pressure has anything to do with helping a compound dissolve better into a solution or not. IDK if pressure effects anything else other than temperature in this case or any other case. I'm curious if the pressure would steepen the curve of solubility more than the standard linear incremental increase under normal pressure.

The goal is to be able to dissolve as much KCl in as little H2O as possible and then spray either the boiling solution onto/onto a cooler surface to allow the KCl to come out of solution. If the solution is pressurised then a good deal of the water should flash off as steam leaving more KCl behind

I am trying to find out the best method for this process to use the least amount of energy as related to the amount of KCl which can be recovered. I'm not sure how much more energy is needed to raise water temp from 50C to 100C vs 100C - 150C while in a pressurized vessel. Will it require the same amount of energy for each 50C rise in temperature? I'm just not sure if pressure effects the energy requirements in this application.

Also, if the water is raised to 320F degrees (about 5 bar or about 75 PSI over standard pressure) and then quickly released, would all of the water flash off as steam leaving all the KCl behind in the vessel?


Maximum solubility?
As far as the KCl, the average difference between each 10 degree interval is about 1g decrease for every 10 degree increase (in the 0-100C range), so if this pattern were to be followed, after 240 degree C increase above the 100C, there would be no increase in solubility as temp rises - as the difference between 90C and 100C was a 24g increase.

If this is true, then there is a diminishing return as the temperature increases. If it were a 1g decrease per 10deg increase the top end would be 340C for a 240 degree change (1g decrease per 10deg C) would give a 300g total increase over the 563g @ 100C. The 240 degree increase (for a 340C or 644F final temp) for a potential 963g/L. However my table only goes to 1000PSi = 545F or 285C. Rudimentary calculation show to reach the 340C would be about 1800 PSI - though don't quote me on that.

[Edited on 6-3-2017 by RogueRose]

[Edited on 6-3-2017 by RogueRose]

[Edited on 6-3-2017 by RogueRose]

[Edited on 6-3-2017 by RogueRose]

[Edited on 6-3-2017 by RogueRose]
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phlogiston
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[*] posted on 6-3-2017 at 13:58


On the effects of pressure on the solubility of solids in liquids

The abstract says:

Quote:
... it is concluded that only in somewhat exceptional cases is the solubility of a solid in a liquid raised by pressure ....


Also, you will probably need much higher pressures. hundreds to thousands of bars.



[Edited on 6-3-2017 by phlogiston]




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RogueRose
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[*] posted on 6-3-2017 at 14:38


Quote: Originally posted by phlogiston  
On the effects of pressure on the solubility of solids in liquids

The abstract says:

Quote:
... it is concluded that only in somewhat exceptional cases is the solubility of a solid in a liquid raised by pressure ....


Also, you will probably need much higher pressures. hundreds to thousands of bars.

Thank you for the link. I looked through and it is a little over my head ATM (not atmosphere, hehe) but I did see some interesting graphs in my skimming. Quite interesting when I saw the NaCl greatly increase in solubility with great pressures, especially vs the KCl. Thanks for quoting the abstract.
[Edited on 6-3-2017 by phlogiston]
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softbeard
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[*] posted on 6-3-2017 at 14:50


Quote: Originally posted by RogueRose  

Also, if the water is raised to 320 degrees (about 5 bar or about 75 PSI over standard pressure) and then quickly released, would all of the water flash off as steam leaving all the KCl behind in the vessel?


My thermodynamics is a little rusty, but what you're asking about there is called "throttling", a process where, theoretically, the enthalpy of the water before and after the pressure release is the same; ie. its delta H = 0.
So, now with the help of steam tables, which give the thermodynamic properties of water at different temperatures and pressures, you can find what happens to your water when you suddenly drop your pressure using the condition that the enthalpy is the same before and after your throttling process.
Of course you're dealing not with pure water here, but a saturated aqueous solution of KCl, but you should be able to estimate how much water flashes off by taking the heat of solution of KCl in water (which, I think, is quite endothermic).
The solubility of the KCl in water will affected only by water liquid temperature, not by any applied pressure since liquids are incompressible. Of course, at higher pressure you can keep water liquid far past its regular 100 deg. C boiling point, all the way up to it's critical temperature, so you can have it dissolve a lot more KCl by raising pressure and heat.
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RogueRose
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[*] posted on 6-3-2017 at 14:54



The goal of the exercise was to find the most efficient way to clean/filter KCl (into a solid final product) as opposed to NaCl due to its solubility curve. Whether working under standard ATM temps & pressures were better or if going to higher temps and pressures were more efficient and if so, how to figure out those temps and pressures. I choose water as I am not aware of a better solvent that is inexpensive, non toxic and available.

I was trying to see if increasing temp would allow more KCl to be dissolved, filtered then cooled (possibly quickly if under pressure to allow water/steam to escape) then cooling further to allow the KCl to totally fall out of solution. Finally vacuum filter/evap/dry the H2O.

I'm still uncertain as to the energy requirements to raise the water temp under pressure if it is the same, more or less, than water under normal atmospheric pressures. If it is less, there may be benefits to heating to higher temps (to a point where solubility increases aren't as drastic) and then allowing the water to flash of as steam (recaptured for next KCl dissolving process) leaving solids & hot brine behind - then starting over again with the condensed steam (that also heated next batch - or heated fresh solids to evap final water content).
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RogueRose
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[*] posted on 6-3-2017 at 15:06


Quote: Originally posted by softbeard  
Quote: Originally posted by RogueRose  

Also, if the water is raised to 320 degrees (about 5 bar or about 75 PSI over standard pressure) and then quickly released, would all of the water flash off as steam leaving all the KCl behind in the vessel?


My thermodynamics is a little rusty, but what you're asking about there is called "throttling", a process where, theoretically, the enthalpy of the water before and after the pressure release is the same; ie. its delta H = 0.
So, now with the help of steam tables, which give the thermodynamic properties of water at different temperatures and pressures, you can find what happens to your water when you suddenly drop your pressure using the condition that the enthalpy is the same before and after your throttling process.
Of course you're dealing not with pure water here, but a saturated aqueous solution of KCl, but you should be able to estimate how much water flashes off by taking the heat of solution of KCl in water (which, I think, is quite endothermic).
The solubility of the KCl in water will affected only by water liquid temperature, not by any applied pressure since liquids are incompressible. Of course, at higher pressure you can keep water liquid far past its regular 100 deg. C boiling point, all the way up to it's critical temperature, so you can have it dissolve a lot more KCl by raising pressure and heat.


Thank you for your reply as this has helped a lot in what I am looking at. I wasn't sure what enthalpy was before and now that helps a lot! Thanks!

I edited my OP (again I know) and headlined a section towards the bottom called "Maximum solubility" which I'm curious to have you read if you would be so kind. I looked at the diminishing solubility as the temp rises, factored it by each 10 degree and went to where increases = 0 and found that temp. IDK if that is necessary or even accurate, but it was an exercise non the less. There has to be a point at which putting more energy into the vessel to increase temp is not worth it as less and less KCl is dissolving as the temp increases (IF the solubility remains near linear as it is from 0-100C).

Also, the energy released as steam should leave more KCl behind than allowing to cool slowly as H2O has exited. My plan is to use the steam to heat the next batch or a continual process possibly - & probably re-use the condensed water, as it will be hot, to dissolve more KCl.

This will be interesting to find if it is even worth going above the 100C BP at standard pressure.

Thanks again for your post!
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[*] posted on 6-3-2017 at 15:12


I'd say you could probably extrapolate the KCl/water solubility table vs. temperature quite a bit to higher temperatures past 100 deg. C with little loss in accuracy, since the relationship appears quite linear. At some point the linearity of the relationship will break, but it's a good 1st estimate.
You could also do curve fitting to the solubility data for more accuracy.

I wouldn't carry this much beyond ~150 deg C, where you're at ~3.74 bar pressure (probably somewhat less pressure for your sat. KCl solution). You really don't want accidents with high temperature/high pressure steam.

As for energy requirements; that's given by heat capacity of your KCl solution vs. temperature. It may vary a bit with temperature, but probably not much across any reasonable range (up to say ~200 deg C). Pure water's heat capacity is pretty constant with temperature across the usual liquid water temperature ranges.

Simple steam table calculators are available on-line, eg.
http://www.spiraxsarco.com/Resources/Pages/Steam-Tables/satu...

edit: added more info


[Edited on 6-3-2017 by softbeard]
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DraconicAcid
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[*] posted on 6-3-2017 at 15:46


The solubility of a solute as a function of temperature will vary as a function of ln(K) = -deltaH/R*(1/T) + deltaS/R, where deltaH is the enthalpy of solution, deltaS is the entropy of solution, and K is the eq'm constant for the solid going to solute.

With the data you give, and some quick least squares analysis, the solubility of KCl in g/L will be e to the power of (-707.4*T + 8.244), with T in Kelvin.

Extrapolating gives:
570 g at 100 C (it's not a perfect linear fit)
585 g at 105 C
600 g at 110 C
614 g at 115 C
629 g at 120 C
643 g at 125 C
658 g at 130 C




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RogueRose
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[*] posted on 6-3-2017 at 19:28


Quote: Originally posted by DraconicAcid  
The solubility of a solute as a function of temperature will vary as a function of ln(K) = -deltaH/R*(1/T) + deltaS/R, where deltaH is the enthalpy of solution, deltaS is the entropy of solution, and K is the eq'm constant for the solid going to solute.

With the data you give, and some quick least squares analysis, the solubility of KCl in g/L will be e to the power of (-707.4*T + 8.244), with T in Kelvin.

Extrapolating gives:
570 g at 100 C (it's not a perfect linear fit)
585 g at 105 C
600 g at 110 C
614 g at 115 C
629 g at 120 C
643 g at 125 C
658 g at 130 C


Thaks for the reply. I see what you extrapolate and think that is similar to what I have come up with but I did notice a diminishing solubility as temp increases of an average of 1g per 10 deg C - cumulative.

deg range in C (10 deg increments) = g of KCl
0-10 = 32
10-20 = 30
20-30 = 30
30-40 = 29
40-50 = 25
50-60 = 32
60-70 = 28
70-80 = 27
80-90 = 26
90-100 = 24
Total g increase - 283g
avg 28.3g per 10 deg C change - or -
avg 14.15g per 5 deg C change
I think the above is where you got your numbers.

What I looked at is the deviation from the linearity of the average (plotted curve) and stated them in the table below.
(last number is difference of previous line solubility increase minus current line increase) ex line 1 = 32g line 2 = 30g so 32 - 30 = 2. Which is indicated with the :: 2 This shows how the line isn't linear and how it moves up or down (from linearity) from each 10deg increment. The average difference between each 10 degree increment is .889 deviation from linearity
range = g increase :: difference between previous 10 deg increment
0-10 = 32
10-20 = 30 :: 2
20-30 = 30 :: 0
30-40 = 29 :: 1
40-50 = 25 :: 4
50-60 = 32 :: -7
60-70 = 28 :: 4
70-80 = 27 :: 1
80-90 = 26 :: 1
90-100 = 24 :: 2
sum of increment increases = 8
Avg increment difference = .889

As you can see as the temp rises, it seems the "grams per 10 degree" decreases as temp rises. That is why I said as temp rises it may not increase solubility at the same rate - IF - the numbers I have written show an actual pattern (I didn't make them up..) So, it looks like it may decrease about 1g per 10 degree increase so after 50 degree increase, that is 5, 10 degree increments at ~ 1 gram less per 10 deg so 1 + 2 + 3 + 4 + 5 = 15 grams less than what would be linear. This effect is greater the higher it goes, as the change is cumulative with each 10 degree interval increasing (well actually decreasing total solubility).

As I said before, if looking at the 90 to 100deg range (increase of 24g from the 80-90 range) this means that at a 1 degree decrease per 10 degree range, then in 240 degrees that is when there will no longer be any increase with only an increase of temp. IDK if there is a point where heating past a point would cause the salt to start crashing out, is something that might be possible if the statistics are accurate.

To me, looking at how statistics works this makes total sense to me, but I'm not sure if this is reflective to how compounds work relative to heat in the "real world"
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DraconicAcid
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[*] posted on 6-3-2017 at 21:05


I'm not basing my extrapolation on statistics, but on thermodynamics.



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[*] posted on 8-3-2017 at 04:55
Water properties


For more water properties see:
http://www.engineeringtoolbox.com/water-thermal-properties-d...
4 C - 0,009 bar - 1000 kg/m3
100 - 1 - 958
150 - 4,77 - 918
180 - 10 - 887
200 - 15,5 - 864
250 - 39,9 - 799
300 - 86 - 714
350 - 165,4 - 575
360 - 186,8 - 528
374 - 217 - 322

As water is heated and expands, water gets less polar. Eventually, water becomes a poor solvent for polar salts.
That's "eventually". Water at 300 Celsius, 86 bar and 714 kg/m3 is still fairly good solvent for polar salts. It is somewhere between 300 and 374 Celsius that salts precipitate - because water at 374 Celsius, 217 bar and 322 kg/m3 is a poor solvent for polar salts.
Also: water at 374 Celsius and 217 bar has infinite compressibility. It follows that water at slightly below 374 Celsius would be liquid - with a large (and nonlinear!) compressibility.
When water is a poor solvent because of low density, does increase of pressure cause a large increase of solubility? For example, what could be density of water at 374 Celsius but 400 bar?
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[*] posted on 8-3-2017 at 07:33


Quote: Originally posted by chornedsnorkack  
For more water properties see:
http://www.engineeringtoolbox.com/water-thermal-properties-d...
4 C - 0,009 bar - 1000 kg/m3
100 - 1 - 958
150 - 4,77 - 918
180 - 10 - 887
200 - 15,5 - 864
250 - 39,9 - 799
300 - 86 - 714
350 - 165,4 - 575
360 - 186,8 - 528
374 - 217 - 322

As water is heated and expands, water gets less polar. Eventually, water becomes a poor solvent for polar salts.
That's "eventually". Water at 300 Celsius, 86 bar and 714 kg/m3 is still fairly good solvent for polar salts. It is somewhere between 300 and 374 Celsius that salts precipitate - because water at 374 Celsius, 217 bar and 322 kg/m3 is a poor solvent for polar salts.
Also: water at 374 Celsius and 217 bar has infinite compressibility. It follows that water at slightly below 374 Celsius would be liquid - with a large (and nonlinear!) compressibility.
When water is a poor solvent because of low density, does increase of pressure cause a large increase of solubility? For example, what could be density of water at 374 Celsius but 400 bar?


At 374 C and 217 bar, you don't have liquid water- you have a supercritical fluid. I'm not sure how the solvent properties of supercritical fluids change with pressure.




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