Ksp calculation for certain temps

[andy-hipkiss]

Randy et al,


arrrghhh, help please!

I'm trying to do a calculator of solubility of Ca(OH)2 vs temp based on thermodynamic data.

Sadly it's turning in a spectacular failure ??

At 25C I've calculated the Ksp is 4.36*10^-9 however all the reference to the Ksp of Ca(OH)2 have values in the 10^-6 range



Anyway I'm using the following equation ... rather than trying to type it out and abuse all the delta and degree stuff, have a looksee at http://bilbo.chm.uri.edu/CHM112/lectures/lecture31.htm

And using the values at http://bilbo.chm.uri.edu/CHM112/tables/thermtable.htm


I derived the attached spreadsheet

Any ideas what I am doing wrong?

Finally the dumb question ... how do I go from Ksp to g/l solubility at a specific temp?


Thanks muchly

[Habib]

Andy:

[Habib]

Andy:

I obtained the values by using the coefficients they give for the following graph:





The coefficients they give are:

slope = 1970

intercept = –19.1


From these the lnKsp can be calculated for any temperature within the range or close to the temperature range they used.


From the ln Ksp the Ksp can be calculated. from that the moles/L can be calculated and using the molar mass of ca(OH)2 the solubility in g/L can be calculated.

Be prepared that using such coefficients can introduce significant errors.

Much better, IMO, is by using a very good fit obtained by using non logarithmic and non inverse values.

[skearse]

Check your units-entropy is being reported in Joule/mole-Kelvin; enthalpy & Gibbs are in kJ/mol-K.

To convert to g/L, the Ksp is the product of teh concentration of the Ca and OH in solution. Since there are 2 OH for each Ca, the solubilty eqution is reduced to [Ca][OH]², or [Ca][2Ca]², or, finally, [4Ca³]. Set this equal to the Ksp at the desired temperature, and you get the molarity of Ca in solution. Convert this to g/L by use of the molecular weight of the species.

[Randy Holmes-Farley]

Unfortunately, Ksp won't give you the solubility of calcium hydroxide as there is a substantial amount of CaOH+ that is soluble and present at 25 deg C near saturation of Ca(OH)2.

[andy-hipkiss]

Habib,

As ever - you're a star. I hate to think how much beer I owe you


Randy,

Are you saying the modifications Habib did are incorrect or has he built in the correct variance?

[Randy Holmes-Farley]

I'm saying it isn't possible to use Ksp to get total solubility in this fashion. You also need to know the constant for the formation of CaOH+.

Likewise, it isn't possible to use Ksp to get the total amount of soluble iron from the KSp of Fe(OH)3 because the solubility is dominated by forms other than Fe+++, such as Fe(OH)3, Fe(OH)2+, Fe(OH)++. The same for other metals.


This article, for example, discusses these concerns:

The Self Purification of Limewater (Kalkwasser)
http://www.advancedaquarist.com/issues/may2003/chem.htm


See, for example, figure 4, where copper is more soluble at pH 13 than at pH 9, because Cu(OH)3- becomes the most soluble species, but wouldn't even be noticed by a Ksp calculation of Cu(OH)2.

[Habib]

Originally posted by andy-hipkiss
Habib,

As ever - you're a star. I hate to think how much beer I owe you


Randy,

Are you saying the modifications Habib did are incorrect or has he built in the correct variance?

Wait with the beer because ther might be an error in of the last colums. Somehow the one I posted does not load and gives me the sheet I made with some other modifications.


Randy is correct in saying about the Ca(OH)+ because the Ca(OH)2 is not a strong base and will not be dissociated completely. The first step will be but not the second step : CaOH+ <--> Ca++ + OH-

[andy-hipkiss]

Randy,

Ah I see now what you are saying.

(sorry dieing of a cold, oops no I mean a manly sized bout of flu only women have colds of course , and the brain is roughly 33cm distant from my skull at the moment).

This is probably a stupid question but couldn't knowing the delta Gf deg of CaOH+ be used to modify the equation or would we get into the realms of some perverse modification involving pH?

[skearse]

If the system is treated as a buffer and the pH/net ionic equation used along with the Ksp, would this then 'close the gap' in the data?

[skearse]

Never mind-different problem.

[Habib]

IIRC Craig had solubilty data (as g/L) at various temps. It had been posted here as well but I must confess my brain is working at a very low speed right now.

[andy-hipkiss]

Habib,

Hmm the search button doesn't seem to be my friend at the moment.

I've collected the following (I've derived the Ca levels ... hopefully correctly)


Temp g/l ppm Ca
0 1.85 1001
10 1.76 952
20 1.07 579
25 0.97 525
100 0.77 417


Does that help at all?

[Habib]

Searching for "table" and posted by Habib gave the thread.

FWIW the table is not in that post, I'll have to look up the magazine to see if besides the pH also the concentrations are given.

http://archive.reefcentral.com/forum...ighlight=table

[andy-hipkiss]

curse, I can't find my AFQ mags.

[Randy Holmes-Farley]

Andy:

Those values are substantially too low, I believe. At 25 deg C, the solubility is about 0.0204 M according to an old article of Craig's. That is just over 800 ppm Ca++.

[andy-hipkiss]

Randy,

The g/l figures for 20 and 25C came from MSDSs. I wonder how much variabilities of manufacturer impact here.

Either way, I suspect I need to go back to the spreadsheet and factor in CaOH+ in some fashion to at least come up with "ideal" figures.

Habib,

Is the error in your additions to the spreadsheet only down to CaOH+ or should I not take them as a baseline?

[andy-hipkiss]

Habib,

I found part of the error in your additions. You hadn't divided the Ksp by 4 before raising it to the 1/3. Also found part of the error in my original sheet, I'd missed a conversion between J and kJ hence the 10-9 vs 10-6 error.

Still don't get the Ksp figures given in the table on the website hmmm wonder if the table includes the CaOH+ correction since it talks about the values being measured rather than calculated???

Attached is the latest version of the sheet

[skearse]

FWIW, CRC & Perry's Chem Eng Handbooks both report the same 0ºC and 100ºC solubility for calcium hydroxide as Andy does above. I think the original reference for both of these are from Lange's.

[Habib]

Andy,

If for the eqaution of the solubility product the following reaction was used:

Ca(OH)2 <---> x Ca++ + (1-x) CaOH+ + [2x + (1-x)] OH-

then obtaining the solubility in moles or gram/L will not be straightforward.

[andy-hipkiss]

I suspect you're right!

Interestingly perhaps, the figures given in GEM-Selektor appear quite different to those from the previously given web page. I'm just trying to find the G and S for Ca(OH)2 (I already have Ca and OH-) and see if we get anything like more sensible results.

[Boomer]

Andy, nice to see you around, missed you here.

This post is a little deep for me but have you see this. Maybe it will help.

http://michele.usc.edu/java/solubility/solubility.html

From http://michele.usc.edu/105a/solutions/crimeanswer.html

[Randy Holmes-Farley]

This is the article where Craig claimed that the solubility was 1.5 grams/L:

Precipitation of phosphate in limewater and in the aquarium by Craig Bingman, Aquarium Frontiers, 2(4) 6-9. 1995

[Habib]

Originally posted by Randy Holmes-Farley
This is the article where Craig llaimed that the solubility was 1.5 grams/L:

Precipitation of phosphate in limewater and in the aquarium by Craig Bingman, Aquarium Frontiers, Fall 1995

Randy, you are getting reaaly slow. I did beat you by almost 29 hours.

[andy-hipkiss]

Having spent hours yesterday night trawling the internet looking for Gibbs data and Ksp values the one firm conclusion I've come to it that nobody seems to know! The 1.85 g/l at 0C and 0.77 at 100C is oft repeated. 0.97 g/l at 25C is also occasionally repeated although at odds with Craig's claimed value. The Ksp is reported as 5.5x10-6 or 8.8x10-6 or well any number really.

I played around with the spreadsheet yesterday search for Hod and Sod values for Ca(OH)2 and although I can get a good match for 0 and 100C , nothing gave me the 25C value claimed by Craig (I suspect the CaOH+ effect is releveant here yet why I could get matches at either end of the scale yet not a quarter of the way in I don't understand).


Therefore I'm wondering if I can attack this problem in a different manner. Since limewater is a secondary pH standard and thus we do have agreement on pH values, is it possible to calculate the solubility? Or does our best new friend CaOH+ muddy the water?