Concentrations of conjugate bases at specific pH levels

1. Sep 6, 2009

Shafty

The pKa for the dissociation of H3PO4 is 2.15. What is the concentration of H2PO4-1 (in M) at pH 3.21 if the original concentration of the phosphate was 2.37 M?

My Attempt:

Key Information:

pH final: 3.21
Initial Molarity of phosphate: 2.37 M
pKa: 2.15

I started with the first dissociation of the weak acid into its proton and conjugate base.
The stoicheometry is as follows:

H3PO4 <-----> H3O+ + H2PO4-

I am only looking at the first dissociation constant K1.

pKa = -log Ka

2.15 = -log Ka = 10^-2.15 = 7.08e-3

-----This is where I am stuck------

When the question refers to the "original concentration of the phosphate", is it referring to the conjugate base or the original acid? When I try to set up an "ICE table" plugging the given molarity into the "Initial" conjugate base column, I end up with too many unknowns and can not solve quadratically. Yet when I plug the Molarity into the [HA] column I get values that do not make sense. I understand that:

Ka= [H+][A-]/[HA]

If I gloss over this middle step I can continue to find the concentration of H2PO4- ions in the final solution. Since the first dissociation is 1:1, the concentration of H+ ions will be the same as the concentration of H2PO4- ions. Therefore:

pH = 3.21 = 10^-3.21 = 6.17e-4 M

I feel like I am missing a crucial part of this problem (obviously, since my attempts have yielded wrong answers). I have solved for the original pH of the solution at 2.37 M (0.89), I just dont know how to pull all the pieces together to solve the problem. Any help would be greatly appreciated. Thank you in advance.

2. Sep 6, 2009

PhaseShifter

The problem isn't very clear, unless they mean they initially started with $$PO_{4}^{3-}$$ in solution. If that's the case you need a few more constants. (and it seems a little early in the semester to be working with competing equilibria, so I suspect it's not that.)

The concentration of $$H^{+}$$ may not be the same as the $$H_{2}PO_{4}^{-}$$ concentration if the pH was adjusted to 3.21.

I would try "initial phosphate concentration" $$=[H_{3}PO_{4}]+[H_{2}PO_{4}^{-}]$$ and see what the quadratic equation gives.

Last edited: Sep 6, 2009
3. Sep 7, 2009

Staff: Mentor

As PhaseShifter suggests, treat 1M as a total concentration of all forms of pohosphoric acid.

No need for quadratic though. Take a look here:

acid base titration indicators

Don't pay attention to the fact it describes indicator, formula derived works for ANY acid.

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