[Big-Daddy]

The label on a bottle containing a dilute aqueous solution of an acid became damaged. Only its concentration was readable. A pH meter was nearby, and a quick measurement showed that the hydrogen ion concentration is equal to the value on the label.

b) Could it be possible that the dilute solution contained sulfuric acid (pKa2=1.99)?

The answer says that because the first dissociation step can be regarded as complete the solution could not contain sulphuric acid, but I don't understand why this means it is impossible for [H+] to drop to 1/10th if the solution is diluted 10 times over?

c) Could it be possible that the solution contained acetic acid? If so, calculate the pH.

They start writing out mass balance and charge balance, which I might have done as well except that we don't have a starting concentration of acetic acid. And then all of a sudden they write:

C_HA=[HA]+[A-]=[H⁺]

Where does this equality come from? How does the question suggest it?

From there on, coupled with the equilibrium constant expression and charge balance, this is easy to solve.

d) Could it be possible that the solution contained EDTA (ethylene diamino tetraacetic acid)? If so, calculate the concentration.

Again, they write out mass balance and charge balance, but then equate the mass balance to [H⁺] - why? Following that the solution is relatively simple (you work out [H+], and then by this trick you automatically have the concentration) but how did they reach the conclusion that C_HA=[H+] from the proposition of the question?

[Sunil Simha]

The label on a bottle containing a dilute aqueous solution of an acid became damaged. Only its concentration was readable. A pH meter was nearby, and a quick measurement showed that the hydrogen ion concentration is equal to the value on the label.


c) Could it be possible that the solution contained acetic acid? If so, calculate the pH.

They start writing out mass balance and charge balance, which I might have done as well except that we don't have a starting concentration of acetic acid. And then all of a sudden they write:

C_HA=[HA]+[A-]=[H⁺]

Where does this equality come from? How does the question suggest it?

C_HA=[HA]+[A-] is the mass balance equation and C_HA=[H⁺] comes from the part of the question in red. So...

[Big-Daddy]

The label on a bottle containing a dilute aqueous solution of an acid became damaged. Only its concentration was readable. A pH meter was nearby, and a quick measurement showed that the hydrogen ion concentration is equal to the value on the label.


c) Could it be possible that the solution contained acetic acid? If so, calculate the pH.

They start writing out mass balance and charge balance, which I might have done as well except that we don't have a starting concentration of acetic acid. And then all of a sudden they write:

C_HA=[HA]+[A-]=[H⁺]

Where does this equality come from? How does the question suggest it?

C_HA=[HA]+[A-] is the mass balance equation and C_HA=[H⁺] comes from the part of the question in red. So...

Thanks. I must have misunderstood what that meant.

What's the issue with the sulphuric acid (part b)?

And then, in part d, there's another issue I don't understand. The solution says:

"We can suppose that this solution would be quite acidic, so the 3rd and 4th dissociation steps can be disregarded." It then goes on to neglect [OH^-] and the 3rd and 4th dissociations.

The more acidic the solution, the less far each dissociation goes (and the 3rd and 4th dissociatons are hindered even more than the 1st and 2nd, so they become more and more negligible as the solution is more acidic); the more alkaline the solution, the further each dissociation goes (and the 3rd and 4th dissociations also become more and more appreciable and comparable to the 1st and 2nd, so treating them negligible will work with less and less accuracy as the solution becomes more alkaline). Is that right?

But my question is: how we were meant to come to the conclusion that the solution of EDTA would be quite acidic in the first place?

[Sunil Simha]

Regarding the sulfuric acid part, assuming first dissociation is complete, I guess [H⁺] would be greater than the value on the label as there is also the second dissociation that is significant.

Regarding the H₄[EDTA], are the dissociation constants (1st and 2nd) given to you? If yes, then maybe you can judge the solution's acid strength.

[Big-Daddy]

Regarding the sulfuric acid part, assuming first dissociation is complete, I guess [H⁺] would be greater than the value on the label as there is also the second dissociation that is significant.

Oh I see - post dilution [H+]=C_H2A, according to the H+ ion concentration being the same as the concentration label on the bottle, which cannot be the case for sulphuric acid as its first dissociation will already provide [H⁺]=C_H2A and its second will then go over this value.

Question - if [H⁺]=C_HA+K_w/[H⁺] on the basis of 1 dissociation, then for strong monoprotic acids (e.g. HCl) do we say that they might have been possible because [H⁺]=C_HA (treating K_w/[H⁺] as negligible)?

Regarding the H₄[EDTA], are the dissociation constants (1st and 2nd) given to you? If yes, then maybe you can judge the solution's acid strength.

pKa1=1.70, pKa2=2.60 - still I can't understand where we come to the conclusion that the solution must be decently acidic.

[Sunil Simha]

Question - if [H⁺]=C_HA+K_w/[H⁺] on the basis of 1 dissociation, then for strong mono-protic acids (e.g. HCl) do we say that they might have been possible because [H⁺]=C_HA (treating K_w/[H⁺] as negligible)?

pKa1=1.70, pKa2=2.60 - still I can't understand where we come to the conclusion that the solution must be decently acidic.

I'm not sure but I guess strong mono-protic acid do satisfy the conditions.

As for the EDTA part,pka3=6.16 and pKa 4=10.26. This means, due to common ion effect from [H⁺] the 1st and 2nd dissociation, that the solution is acidic enough to ignore the contribution of 3rd and 4th dissociation.(It need not be strongly acidic but sufficiently)

[Big-Daddy]

As for the EDTA part,pka3=6.16 and pKa 4=10.26. This means, due to common ion effect from [H⁺] the 1st and 2nd dissociation, that the solution is acidic enough to ignore the contribution of 3rd and 4th dissociation.(It need not be strongly acidic but sufficiently)

Yes but [OH^-] is also being ignored in the charge balance. For this the solution must be strongly acidic (not pH 1 or 2 necessarily but at least pH 4 or maybe 5 tops). This leads to the rather strange approximation [H₄[EDTA]]=[H₂[EDTA]^2-] to be made after which the solution is pretty doable. Without that approximation, ignoring the 3rd and 4th dissociations is not enough to avoid lengthy maths.

[Sunil Simha]

I'm not sure but maybe it's like this:

Consider a 1M solution of EDTA. Then assuming only first dissociation takes place, the concentration of [H⁺] would be around 0.01M (given the pK₁). This would be very much large compared to [OH^-] which would be around 10^-12 at 25⁰C.

This is just an example, and I guess an expert's view on this topic would be much appreciated.

[Big-Daddy]

I'm not sure but maybe it's like this:

Consider a 1M solution of EDTA. Then assuming only first dissociation takes place, the concentration of [H⁺] would be around 0.01M (given the pK₁). This would be very much large compared to [OH^-] which would be around 10^-12 at 25⁰C.

This is just an example, and I guess an expert's view on this topic would be much appreciated.

I actually got 0.132 moldm^-3 for [H+] with Ka=10^-1.70 and Ca=1 M (neglected K_w). In general this only strengthens your case as now [OH-] is around 10^-13 moldm^-3. Unfortunately you are assuming a certain concentration for our EDTA which we don't know. In fact, we have to work it out!

[Sunil Simha]

This is simply an assumption but it may be valid up to a certain extent. In a lab, the most dilute acid solutions rarely have concentrations less than 0.001 M (at least I haven't seen even more dilute solutions). So EDTA dissociates up to ~10% which would still mean 0.0001M hydronium ion concentration. The concentration of [OH^-] would still be negligible.

Theoretically, this assumption is not logical of course. Like, I said earlier, it would really help if an expert would sort out stuff a bit.

But have they mentioned elsewhere in your source about validity of their assumptions?

[Big-Daddy]

This is simply an assumption but it may be valid up to a certain extent. In a lab, the most dilute acid solutions rarely have concentrations less than 0.001 M (at least I haven't seen even more dilute solutions). So EDTA dissociates up to ~10% which would still mean 0.0001M hydronium ion concentration. The concentration of [OH^-] would still be negligible.

Theoretically, this assumption is not logical of course. Like, I said earlier, it would really help if an expert would sort out stuff a bit.

But have they mentioned elsewhere in your source about validity of their assumptions?

I'm not sure if an expert is reading this - you are the expert!

This is all the information they gave in the question. In the solutions, they wrote for the acetic acid question:

"Yes, but only in quite dilute solutions can this happen." Followed by calculations, but this bit of info is irrelevant anyway - if I had read the question properly I'd have written [H+]=C_HA=[HA]+[A^-]=[A^-]+[OH^-], spotted [HA]=[OH-]=Kw/[H+] then substituted in Kw/[H+] for [HA] in the equilibrium expression and C_HA-[HA]=C_HA-Kw/[H+] for [A-]. This boils out to a cubic and I don't think the calculators they give in the exam can solve cubics but I'd just have used iteration. So they realized that "only in quite dilute solutions" can it be acetic acid (pKa=4.76, monoprotic) - again I don't know how they arrived at this but it didn't matter.

In the EDTA case:
"Yes. We can suppose that this solution would be quite acidic, so the 3rd and 4th dissociation steps can be disregarded." They also disregard [OH^-] from the charge balance, without explanation, presumably because it is negligible in "quite acidic" solutions. This then leads to the strange equivalence [H₄A]=[H₂A^2-] which makes a solution possible and indeed quite neat ([H+]=Ka1*Ka2 and we know [H+]=C_HA so we get both pH and concentration in one bargain). But the solution has to be decently acidic right, and how did they work out that it would be?

[Sunil Simha]

This then leads to the strange equivalence [H₄A]=[H₂A^2-]

This implies that both first and second dissociation are complete ( or else there would be a mention of[H₃A^-]) right? Maybe that's what they mean by "quite acidic". Though I cannot guess what gave them the insight to that matter.

[Big-Daddy]

This then leads to the strange equivalence [H₄A]=[H₂A^2-]

This implies that both first and second dissociation are complete ( or else there would be a mention of[H₃A^-]) right? Maybe that's what they mean by "quite acidic". Though I cannot guess what gave them the insight to that matter.

Well they have made a few strange insights but this is a natural result of them: if we know that the solution is highly acidic and treat [OH-] as negligible and neglect the 3rd and 4th dissociations, our mass balance and charge balance become:

Mass Balance (A): [H+]=C_HA=[H₄A]+[H₃A^-]+[H₂A^2-]
Charge Balance: [H+]=[OH-]+[H₃A^-]+2·[H₂A^2-]=[H₃A^-]+2·[H₂A^2-]

So [H₃A^-]+2·[H₂A^2-]=H₄A]+[H₃A^-]+[H₂A^2-], [H₃A^-] cancels and the equivalence from before falls out. Then using the Ka1 and Ka2 expressions we can reach [H+]=C_HA=(Ka1*Ka2)^1/2.

[Big-Daddy]

Can someone help? How is it obvious that the EDTA solution will be "quite acidic"?

[Borek]

Have you tried to estimate pH using just first step of EDTA dissociation? For a weak acid it is relatively strong.