[Big-Daddy]

Calculate the volume of 0.80 M NaOH solution that should be added to a 250 mL aqueous solution containing 3.48 mL of concentrated phosphoric acid in order to prepare a pH 7.4 buffer. Answer with three significant figures. (H3PO4 (aq), purity = 85 % wt/wt, density = 1.69 g/mL, FW = 98.00)
(pK1 = 2.15, pK2 = 7.20, pK3 = 12.44).

How do I set up equilibrium expressions for this problem which express the fact that adding more NaOH changes the total volume of the solution? Is it possible to write a charge balance expression for this (given that the solution is a buffer)?

[Borek]

If you use Henderson-Hasselbalch equation volume cancels out and it doesn't matter.

Yes, it is perfectly possible to write charge balance, you have full control over all substances present - there are no unknown counterions in undefined quantities.

[Big-Daddy]

If you use Henderson-Hasselbalch equation volume cancels out and it doesn't matter.

Yes, it is perfectly possible to write charge balance, you have full control over all substances present - there are no unknown counterions in undefined quantities.

OK so this is one case where it is pretty difficult to solve exactly but easier with the Henderson-Hasselbalch equation? I'll take the approximate route first then go back and try and do it exactly.

This is a simple combination of NaOH and H3PO4 to form Na⁺ ions, and each of the forms of H3PO4 (from H3PO4 itself to PO4^3-).

How should I apply the Henderson-Hasselbalch to a triprotic acid?

[Borek]

How should I apply the Henderson-Hasselbalch to a triprotic acid?

When Ka values are distinct enough (at least 3 pKa units apart) you can ignore other protons. Just use pK_a2 (but don't forget about them when dealing with the neutralization stoichiometry!).

[Big-Daddy]

How should I apply the Henderson-Hasselbalch to a triprotic acid?

When Ka values are distinct enough (at least 3 pKa units apart) you can ignore other protons. Just use pK_a2 (but don't forget about them when dealing with the neutralization stoichiometry!).

I've never seen the Henderson Hasselbalch applied to problems like these. This will be covered in most undergrad analytical chemistry books I buy, right? I will need to study it in more detail there.

With regards to this problem, let's say I can calculate the final analytical concentration in solution of NaOH and H3PO4. Can I write

C[H3PO4]=n[H3PO4]/V_total=(C₁[H3PO4]*V₁[H3PO4])/V_total

And then solve for V_total (n[H3PO4] can be worked out from the quantities given, as 0.05101 mol, and this does not change ever in this problem; C₁[H3PO4]=n[H3PO4]/V₁[H3PO4]=0.05101/0.250 if you really want but it isn't necessary) so V_total=n[H3PO4]/C[H3PO4] (C[H3PO4] is analytical conc in new solution) =(C₁[H3PO4]*V₁[H3PO4])/C[H3PO4] and this value of V_total can be used, with the analytical concentration of NaOH in the final solution (C[NaOH]) known, to calculate the original volume of NaOH used:

C[NaOH]=n[NaOH]/V_total=(C₁[NaOH]*V₁[NaOH])/V_total

And solve for V₁[NaOH]: V₁[NaOH]=C[NaOH]*V_total/C₁[NaOH], V_total worked out as before, C[NaOH] known, and C₁[NaOH] given as 0.80 M, so you get the volume of NaOH required.

Is this correct? Sorry for the maths/strange notation :p

[Borek]

I've never seen the Henderson Hasselbalch applied to problems like these. This will be covered in most undergrad analytical chemistry books I buy, right?

No.

You are believing every type of the problem, with every twist, will be covered by books, which is why you are asking thousands of questions whether this or that is covered by this or that book. That's not how it works. There are general ways of solving problems, and general theories/ideas that are covered in most books that were mentioned before. Once you understand the idea and theory you have to start to think how to apply it. Not because you have seen this particular problem in one of the books, but because you understand the theory and its implications.

Back to the buffer problem.

I have no idea what you are doing.

You should start calculating ratio of HPO₄^2-/H₂PO₄^- in the buffer solution.

[Big-Daddy]

I've never seen the Henderson Hasselbalch applied to problems like these. This will be covered in most undergrad analytical chemistry books I buy, right?

No.

You are believing every type of the problem, with every twist, will be covered by books, which is why you are asking thousands of questions whether this or that is covered by this or that book. That's not how it works. There are general ways of solving problems, and general theories/ideas that are covered in most books that were mentioned before. Once you understand the idea and theory you have to start to think how to apply it. Not because you have seen this particular problem in one of the books, but because you understand the theory and its implications.

Back to the buffer problem.

I have no idea what you are doing.

You should start calculating ratio of HPO₄^2-/H₂PO₄^- in the buffer solution.

OK.

First things first: why are HPO4^2- and H₂PO₄^- the only species in solution worth mentioning for H3PO4, analytical concentration = 0.20404 moldm^-3, [H+]=10^(-7.40) (all 3 pKa values given)? Any method to find, using the pH, which 2 species will be most prevalent - and under which circumstances this method is a safe approximation to take?

[Borek]

It is easy to show that

[tex]\frac {[HA]}{[A^-]} = 10^{pK_a-pH}[/tex]

(this is just a rearranged dissociation constant)

When pH is three units from pKa, concentration ratio of protonated and non-protonated form is 1000:1 (or 1:1000). That means one of them can be safely ignored.

[Big-Daddy]

It is easy to show that

[tex]\frac {[HA]}{[A^-]} = 10^{pK_a-pH}[/tex]

(this is just a rearranged dissociation constant)

When pH is three units from pKa, concentration ratio of protonated and non-protonated form is 1000:1 (or 1:1000). That means one of them can be safely ignored.

From this I observe that:

For a general n-protic acid,
If [H+]>Ka1, [HnA] is most prevalent.
If Ka1>[H+]>Ka2, [H_n-1A^-] is most prevalent.
If Ka2>[H+]>Ka3, [H_n-2A^2-] is most prevalent.
And so on and so forth.

To work out the ratio between two forms, [H_n-jA^(j)-] and [H_n-j+1A^(j-1)-], [H_n-j+1A^(j-1)-]/[H_n-jA^(j)-]=[H+]/K_a(j). Is this all correct?

In this case, because pK_a2 is the only pK_a value within 3 units either way of the pH, the two forms of the acid to which the pKa₂ refers are the only two we need to consider present in the solution. The other 2 forms are negligible, so we can use the Henderson-Hasselbalch equation.

The [H₂PO₄^-]/[HPO₄^2-] ratio for [H⁺]=10^(-7.40) and Ka1=10^(-7.20) is 0.630957. Now what?

[Big-Daddy]

I have worked out it is fairly easy to go from the analytical concentrations of NaOH and H3PO4 (in the pH 7.40 buffer solution, final) to the volume of NaOH required to reach, but I still don't understand how it helps to know the [H₂PO₄^-]/[HPO₄^2-] ratio to find the original volume of NaOH required to reach this?

[Big-Daddy]

Where do I go from here?