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Topic: How to calculate pH for a substances without known pka  (Read 390 times)

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Offline agBr

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How to calculate pH for a substances without known pka
« on: September 02, 2019, 03:59:46 PM »
Hello.

Sometime ago I started a thread asking for borax pka.
For some reason I don't know yet, it seems that there's no simple answer to that.

More generally, I wonder:
- how to calculate pH of a solution containing borax, or any other substance without a known pka (and, if possible, why aren't they known),
- how to calculate a buffer.

In photographic chemistry, borax is used as an alkali and sometimes as buffer also, along with boric acid.
Boric acid pka values are known, but what about borax? What's special about it?
All I know from practice is that a solution with borax tends to easily achive a pH close to 9.

Is there any way to work with this for home experimentation without relaing on trial and error?

Thanks for any advice or guide on this.

Offline chenbeier

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Re: How to calculate pH for a substances without known pka
« Reply #1 on: September 02, 2019, 04:18:16 PM »
Without any other information no way. Borax is sodium tetra borate. It is a salt of a strong base and a weak acid, so the result of pH will be alcaline. In combination with boric acid it works like buffer.

Offline AWK

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Re: How to calculate pH for a substances without known pka
« Reply #2 on: September 02, 2019, 05:05:23 PM »
Chemistry is experimental science. Someone once made the appropriate measurements and found that the pH of the borax decahydrate solution above 1% would show a fairly constant value between 9.2 and 9.3. Hydrolysis of borax simply creates a buffer solution formally containing equimolar amounts of hydrated NaBO2 and H3BO3. The pH value of a 1% solution (pH = 9.24) is quite a sufficient approximation to calculate the pH changes after adding small but known amounts of acid or base to this buffer solution provided that we know the initial molar concentration of borax.
AWK

Offline Borek

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Re: How to calculate pH for a substances without known pka
« Reply #3 on: September 02, 2019, 05:50:56 PM »
- how to calculate pH of a solution containing borax, or any other substance without a known pka (and, if possible, why aren't they known),

Without known Ka - impossible.

It is not like borax doesn't have known Ka values, more like it has several (stepwise dissociation) so in a general case calculations are rather difficult. But for some simple cases calculations are reasonably easy, as you can treat it as if had just one (in some pH ranges other dissociation steps can be ignored).
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Offline agBr

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Re: How to calculate pH for a substances without known pka
« Reply #4 on: September 03, 2019, 05:05:43 AM »
The pH value of a 1% solution (pH = 9.24) is quite a sufficient approximation to calculate the pH changes after adding small but known amounts of acid or base to this buffer solution provided that we know the initial molar concentration of borax.

Do you mean that adding small amounts of another acid or base (in moles, proportionally to borax) will not shift pH too much?

It is not like borax doesn't have known Ka values, more like it has several (stepwise dissociation)

That sounds like the case of multiprotic substances. But even in those cases, like citric acid, all the pka values are known... so I suppose borax is not just that, is it? If I understud correctly, it is because of hydrolysis products that it acts not as a "simple" substance that simply dissociates (right?).

But for some simple cases calculations are reasonably easy, as you can treat it as if had just one (in some pH ranges other dissociation steps can be ignored).

Do you mean that I could make approximation assuming pka=9.2?
Assuming we will be using borax in solutions with a target ph range close to 9 (let's say between 8 and 10).

Approximations are just fine for me.
I'm just interested in knowing and understanding the underlaying theory, and have some analytic tools to make estimations.
Thank you.

Offline Borek

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Re: How to calculate pH for a substances without known pka
« Reply #5 on: September 03, 2019, 06:40:52 AM »
The pH value of a 1% solution (pH = 9.24) is quite a sufficient approximation to calculate the pH changes after adding small but known amounts of acid or base to this buffer solution provided that we know the initial molar concentration of borax.

Do you mean that adding small amounts of another acid or base (in moles, proportionally to borax) will not shift pH too much?

Yes. That's almost a definition of the buffer solution.

Quote
It is not like borax doesn't have known Ka values, more like it has several (stepwise dissociation)

That sounds like the case of multiprotic substances. But even in those cases, like citric acid, all the pka values are known... so I suppose borax is not just that, is it? If I understud correctly, it is because of hydrolysis products that it acts not as a "simple" substance that simply dissociates (right?).

Many ways to skin that cat. You can think about it this way: boric acid easily loses water molecules and creates chains of (...)B-O-B(...) - some of the external -OH groups are left (I know it sound counterintuitive, but these are not equivalent to OH in hydroxides, they will dissociate H+ leaving (...)B-O-). Thus what you really deal with is a complicated mixture of multiprotic acids containing different numbers of B atoms. They are in constant equilibrium, and depending on what you need to do and what the concentration is they are reasonably well approximated by H3BO3 or B4O72- - or many others. This is not much different from what is happening in solutions of silicic acid or aluminates.

Quote
But for some simple cases calculations are reasonably easy, as you can treat it as if had just one (in some pH ranges other dissociation steps can be ignored).

Do you mean that I could make approximation assuming pka=9.2?

No idea how precisely they would work, but in general - yes. As I tried to explain above this is a rather complex mixture so exact predictions are not trivial, and to be sure approximations should be based on experimental data.
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Offline AWK

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Re: How to calculate pH for a substances without known pka
« Reply #6 on: September 03, 2019, 01:25:07 PM »
If you take a look at the technical documentation of a vendor, e.g. http://www.andreagallo.it/images/schedepdf/TDS/SODIO_BORATO_TETRA_DECAIDRATO_EP_821756_tds.pdf.
The documentation contains data on the pH of the borax solution for several concentrations. Understanding borax hydrolysis, from these data, you can read (you don't even need no calculation)
the value of the first dissociation constant of boric acid (the others can be safely ignored). From these data, it can also be seen that the borax solution itself is a buffer solution.
AWK

Offline agBr

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Re: How to calculate pH for a substances without known pka
« Reply #7 on: September 04, 2019, 04:50:49 AM »
Many ways to skin that cat.

Thank you for the explanation. More complicated than I thought, indeed.

If you take a look at the technical documentation of a vendor, e.g. http://www.andreagallo.it/images/schedepdf/TDS/SODIO_BORATO_TETRA_DECAIDRATO_EP_821756_tds.pdf.
The documentation contains data on the pH of the borax solution for several concentrations. Understanding borax hydrolysis, from these data, you can read (you don't even need no calculation)
the value of the first dissociation constant of boric acid (the others can be safely ignored). From these data, it can also be seen that the borax solution itself is a buffer solution.

Thanks for the document link. The pH graph is very illustrative.
I found over the Internet this reaction:
Na2B4O7 + 7 H2O -> 2 NaOH + 4 H3BO3
So borax dissociates as boric acid and sodium hydroxide. You said hydrated NaBO2. I'm not able to tell which one is right or wrong, but,
if we work out the pH of 0.5 M of NaOH and 1 M of H3BO3 we get the pKa value of H3BO3 (boric acid), 9.2.
Is it a coincidence?
I know that pH = pka when a substance and its conjugate are present in same proportion. But it is harder for me to understand why it is so with NaOH and H3BO3 in 1:2 ratio.

Offline AWK

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Re: How to calculate pH for a substances without known pka
« Reply #8 on: September 04, 2019, 05:48:21 AM »
Quote
But it is harder for me to understand why it is so with NaOH and H3BO3 in 1:2 ratio.
2H[B(OH)4] + NaOH = H[B(OH)4] + Na[B(OH)4] + H2O

What are the salt and excess acid concentrations after the reaction?
AWK

Offline Borek

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Re: How to calculate pH for a substances without known pka
« Reply #9 on: September 04, 2019, 06:10:14 AM »
I found over the Internet this reaction:
Na2B4O7 + 7 H2O -> 2 NaOH + 4 H3BO3
So borax dissociates as boric acid and sodium hydroxide. You said hydrated NaBO2. I'm not able to tell which one is right or wrong

Note: this is more or less what I wrote about earlier, not only there is a problem with creation of (...)B-O-B(...) chains, also, the structure of the anion is actually a series of forms differing by the level of hydration:

BO2- + H2O ::equil:: H2BO3-

and so on, actually when you look at their structure you can also think about H3BO3 as B(OH)3, and what one might write as NaBO2 in the presence of water will take a form of Na+ and B(OH)4- that AWK listed (check, that these formulas differ just by the number of water molecules involved - and number of these molecules depends on the solution concentration). The idea behind is not that complicated, there are several reasonably simple processes involved, it is just that they produce a huge variety of possible formulas, none of them really dominating. Some substances are quite simple and easy to understand (think NaCl), some are a real PITA when one tries to describe them in simple terms. Borates are definitely in the latter group.
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Offline agBr

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Re: How to calculate pH for a substances without known pka
« Reply #10 on: September 05, 2019, 03:05:13 PM »
2H[B(OH)4] + NaOH = H[B(OH)4] + Na[B(OH)4] + H2O

BO2- + H2O ::equil:: H2BO3-

and so on, actually when you look at their structure you can also think about H3BO3 as B(OH)3, and what one might write as NaBO2 in the presence of water will take a form of Na+ and B(OH)4- that AWK listed (check, that these formulas differ just by the number of water molecules involved

Even though I tried for quite long, that seems beyond my understanding.
I do understand the reaction: Na2B4O7 + 7 H2O -> 2 NaOH + 4 H3BO3
But I don't really see how to get from this to yours. I think I almost get it, but there're some voids... I'd need some more clues.
Maybe I'm asking for such a simple trivial thing, I wouldn't like to bother you. If you know of some reference I can study, I'll try to get time for it.

Offline AWK

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Re: How to calculate pH for a substances without known pka
« Reply #11 on: September 05, 2019, 04:29:56 PM »
Strong base immediately neutralizes boric acid
2NaOH + 4H3BO3 = 2NaH2BO3  + 2H3BO3 + 2H2O

but hydrolysis of borax is in fact
Na2[B4O5(OH)4]·8H2O = 2H[B(OH)4] + 2Na[B(OH)4] + H2O
AWK

Offline agBr

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Re: How to calculate pH for a substances without known pka
« Reply #12 on: September 07, 2019, 03:55:33 AM »
Strong base immediately neutralizes boric acid
2NaOH + 4H3BO3 = 2NaH2BO3  + 2H3BO3 + 2H2O

Got it. Acid and salt are in equal concentrations, so according to Henderson-Hasselbalch equation, pH = pka.

but hydrolysis of borax is in fact
Na2[B4O5(OH)4]·8H2O = 2H[B(OH)4] + 2Na[B(OH)4] + H2O

Na[B(OH)4 seems like sodium metaborate plus 2 water molecules. Na[B(OH)4 - 2H2O = NaBO2.
The hydrolysis reaction I posted for anhydrous borax is incorrect? It creates NaOH instead of NaBO2, which seems a big difference to me.
The reaction is given in these sources:
Source 1
Source 2
Source 3

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