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Concentrations of conjugate bases at specific pH levels

  1. Sep 6, 2009 #1
    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. jcsd
  3. Sep 6, 2009 #2
    The problem isn't very clear, unless they mean they initially started with [tex]PO_{4}^{3-}[/tex] 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 [tex]H^{+}[/tex] may not be the same as the [tex]H_{2}PO_{4}^{-}[/tex] concentration if the pH was adjusted to 3.21.

    I would try "initial phosphate concentration" [tex]=[H_{3}PO_{4}]+[H_{2}PO_{4}^{-}] [/tex] and see what the quadratic equation gives.
    Last edited: Sep 6, 2009
  4. Sep 7, 2009 #3


    User Avatar

    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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