[Donaldson Tan]

i used the wrong value of Kb1 in my first attempt and i got pH = 3.75

after i rectified the value of kb1, i got pH = 13

what is wrong with the nature of my working, that i can discount the other equilibrium based on which equilibrium is much more dominant?

[Borek]

(1) H₂PO₄^- + H₂O <-> HPO₄^2- + H₃O⁺
(2) H₂PO₄^- + H₂O <-> H₃PO₄ + OH^-

the first step is govened by Ka2 and the second step is governed by Kb1.

No - the second equilibrium is governed by Kb3 (related to Ka1).

[Donaldson Tan]

Funny thing is, adding acid or base you will effectively increase the buffer capacity, as you will get closer with pH to pKa1 or pKa2.Not exactly if I recall correctly - it rather states that if differences between pKa values are large enough you can use HH equation for calculation independently for both buffers. If the Ka values are too close, HH equation is no longer valid. However, such substances (TRIS, citric acid) are very good for buffer creation. They can be used in much wider pH range, cause the buffering effects of different dissociation steps overlap.

yeah. the titration curve for H3PO4 suggested so. There are two points of inflexion where it allows the solution to act as effective buffer. We all learn something new everyday. I saw this mention in AWK's pdf. (Cheers, AWK)

No - the second equilibrium is governed by Kb3 (related to Ka1).

I just realise the order of Ka begins with H3PO4 and the ordering of Kb begins with PO4 3-. I never knew Kb was arranged in such an order. I always thought the conjugate base from Ka1 will be responsible for Kb1. I learned something new today.

No - the second equilibrium is governed by Kb3 (related to Ka1).

I just realise the order of Ka begins with H3PO4 and the ordering of Kb begins with PO4 3-. I never knew Kb was arranged in such an order. I always thought the conjugate base from Ka1 will be responsible for Kb1. I learned something new today.

kb1 = Kw/Ka3 = 0.0222
Since Kb1/Ka2 = 352733, then Kb1 is primarily responisble for the pH, and not Ka2.

This should be:
Kb3 = Kw/Ka1 = 1.408E-12 (similar to my first workings). The pH I get in the end is still 3.75. I still don't know why my assumption to neglect the basic hydrolysis of H2PO4 2- is wrong. sigh..

[Donaldson Tan]

with reference to the attached table,

Since Ka2/Ka3 = 140000, then pH contribution by the Ka3 is negligible, ie. D = 0

mole balance of all phosphate ions,
[H2PO4 -]o = [H2PO4 -] + [H3PO4] + [HPO4 2-]
0.5 = (0.5 - A) = B + C => A = B + C

Ka1 = [H+](0.5-A)/B
[H+] = Ka1 * B/(0.5-A)

Ka2 = [H+]C/(0.5-A)
[H+] = Ka2 * (0.5-A)/C

[H+] = C - B = (A-B) - B = A - 2B
[H+]² = Ka1Ka2*B/C = Ka1Ka2*B/(A-B)
(A-2B)² = Ka1Ka2*B/C = Ka1Ka2*B/(A-B)

assume A >> B, the above equation is simplified to:
A² = Ka1Ka2*B/A
A³ = Ka1Ka2*B

[H+] = Ka1 * B/(0.5-A)
(A-2B) = Ka1 * B/(0.5-A)
A = Ka1 * B/(0.5-A) (assume A >> B)
B = A(0.5-A)/Ka1

A³ = Ka1Ka2*B
A³ = Ka1Ka2*A(0.5-A)/Ka1 = Ka2*A(0.5 - A)
A² = Ka2*(0.5 - A) = -0.5A + 0.5Ka2
A² + 0.5A - 0.5Ka2 = 0

solving quadratically,
A = 6.3E-8
B = A(0.5-A)/Ka1 = 4.44E-6 <-- this is wrong because B must be less than A

[Borek]

assume A >> B

A, B and C are all comparable.

[GCT]

Geodome, don't you have the answer to this question?  I've been reading upon the link AWK provided, and it seems that the hydrolysis of iron needs to be taken into account, it is actually the reason why the solution qualifies as a buffer (dihydrogen phosphate does have buffer properties as indicated by AWK, however we do not have dihydrogen phosphate alone, but also a concentration of the iron).  Remember that with buffer solutions, the reaction of either the conjugate acid/base can be neglected due to the common ion effect.  Thus treating this as a buffer problem would probably suffice.  Try observing the link for references (AWK's link)  

[Borek]

it seems that the hydrolysis of iron needs to be taken into account

No. It has to be ignored. Fe concentration is 15200 times smaller than phosphate concentration.

[Donaldson Tan]

GCT: The solution to this buffering problem is enclosed in AWK's PDF. It's just that I don't understand why my workings is wrong. I begin to see more light in understanding why my workings is wrong, as our discussion carries on. I am not interested in the answer, but to learn the concept required to solve all buffer problems.

Cheers to all of you