[Merrels]

Hi,

I wonder how to calculate the ionic strength of the following buffer:

0.1M boric acid + 0.1M borax -> mix to pH 8.5

I don't exactly know what ions are formed in this solution. My guess is

H₃BO₃ H₂BO₃^-+H⁺
Na₂B₄O₇.10H₂O 2Na⁺+B₄O₅(OH)₄^2-+8H₂O

so that the ionic strength becomes

I_c=1/2 ([H₂BO₃^-]+[H⁺]+2[Na⁺]+4[B₄O₅(OH)₄^2-])

But then I should know all these concentration. For [H₂BO₃^-] I can use the Henderson-Hasselbalch equation because pKa=9.23, and the H⁺ concentration can be obtained via pH (?). For the other two ions I have no clue. So first of all have i got all the ions, or are others? And second, is my method for ionic strength calculation correct.

[Borek]

Why 2[Na⁺]?

You will need pKa (or Ka) values for B₄O₇^2- (or whatever form it takes in the solution) protonation.

Concentration of Na⁺ will be known once you calculate amount of borax that has to be added - but that requires Ka values mentioned. I have at hand only overall one and that's not enough.

IMHO simplest approach is to use my Buffer Maker, as it will calculate everything automatically.

[Merrels]

Hi, thanks for the quick reply.

I thought the 2[Na⁺] was needed because of stoichiometry...

Any idea where I can find this pKa value? Also I'm looking at this Buffer Maker program, but borax is not in the database, so can't use that I guess.

btw, do I need to include chemical activity? I saw it in a few topics on this forum.

[Borek]

No, it should be just [Na⁺]. Because of stoichiometry [Na⁺] = 2[B₄O₇^2-]

Without activity you will be not able to calculate real concentrations of ions. Note, that if IS is too high, you won't be able to calculate them no matter how you try - limitations of theory.

As for pKa values - no idea, I have checked my sources and I found only

Na₂(B₄O₅(OH)₄)^.8H₂O + 2H⁺ -> 2Na⁺ + 4B(OH)₃ + 5H₂O

with log K=12 and

B₄O₅(OH)₄^2- + 2H⁺ -> H₂B₄O₅(OH)₄

with log K=16.3

Unfortunately these won't be easy to use for calculations, as they are overall constants. No idea where else to look

[Merrels]

Your first equation looks quit useful. Can't I determine [Na⁺] using

K=[Na⁺]²[4B(OH)₃] / [H⁺]²[Na₂(B₄O₅(OH)₄).8H₂O]

where I know [Na₂(B₄O₅(OH)₄).8H₂O]=[4B(OH)₃]=0.1M and [H⁺]=10^-pH? Or isn't this correct (maybe a should include [H₂O] as well, I'm not sure)? But then, if it is correct, [Na⁺] and [B₄O₅(OH)₄^2-] become negligible compared to the ions from the boric acid with its pKa=9.23 (about 100 times less at first sight).

What do you mean by "overall constants"? And where did you get this K value?

[AWK]

In fact, this is a quite complex problem.
Borate buffer should contain additionally HB(OH)₄ and NaB(OH)₄ from borax hydrolysis (both concentration will be 2 times the borax concentration when assumption concerning complete hydrolysis of borax was made). Assuming this mixture has pH 8.5 you can calculate concentration of NaB(OH)₄. You can safely neglect the ionic strenght coming from boric acid and in this case ionic strenght of solution will be equal to twice the borax concentration

[Merrels]

But how can HB(OH)₄ and NaB(OH)₄ contribute to the ionic strength as they are not ions? And if you are right (which I assume you are), is there some kind of proof for this? Or is it a more intuitive argumentation? 

Maybe I should also say why I want to know all this. I, as a physicist, did some experiments and made a theoretical model for these experiments. But in this model the ionic strength should be know (has to do with Debye length). I can make this model fit if I choose the ionic strength to be about 1/5 of the buffer molarity (I=~M/5). So I hope that by doing these calculations, I can come up with this factor 1/5 somehow. Otherwise, my model might be wrong 

And unfortunately, I was already aware of the (huge) complexity of this system...but thanks for the reminder AWK

[Borek]

But how can HB(OH)₄ and NaB(OH)₄ contribute to the ionic strength as they are not ions?

They are dissociated, so they are in ionic forms, AWK just wrote formulas of undissociated reagents involed.

[Merrels]

Okay, sorry for that question.

Coming back on AWK's story: I know that I need to mix the 0.1M BA and 0.1M borax in a ratio of 3.5:1 to get pH 8.5. Then this means my ionic strength is about 2/4.5 times the molarity of the solution?
And, because the mentioned ions are "dominant", would this mean I'm dealing with a 1:1 electrolyte ?

[AWK]

Assuming reaction is proceed according my previous post the ionic strength is approximately just 2 x concentration of borax in the final solution.

[AWK]

Assuming the complete hydrolysis of borax to 2HB(OH)4 + 2NaB(OH)4 you can obtain concentration of HB(OH)4 = 0.1 + 0.2 = 0.3 and concentration of NaB(OH)4 = 0.2 with ionic strentgh close to 0.2.