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Calculate Diprotic Acid Species Concentrations

  1. Nov 2, 2011 #1
    I would like to relate the pH of an aqueous phase diprotic acid solution to a value of the undissociated acid species concentration in the aqueous phase, and vice versa.

    I have Ka1 and Ka2 values for the acid.

    The overall dissociation equilibrium can be written:

    Ka1*Ka2 = ([A2-]*([H+]^2))/[H2A]

    The pH can be used to give a direct value for [H+], so my question is: from this how do I find the value of [H2A]?

    Additionally, for a given value of [H2A], how do I calculate the value of [H+]?

    This work is for the purpose of creating a mathematical model in Excel for the dissociation process. The pKa1 and pKa2 values of the acid are close together and I would like to try and avoid as many assumptions as possible, no matter how hard the maths becomes.

    Is anyone able to help?
    Last edited: Nov 2, 2011
  2. jcsd
  3. Nov 2, 2011 #2


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    Staff: Mentor

  4. Nov 2, 2011 #3
    I have previously found and read that webpage but cannot figure out how that helps in this case.

    As far as I can work out I need to work out the stoichiometric relationship between the A2- and H+ ions.

    Is is accurate simply to say that [A2-] is equal to [H+]/2 from the dissociation stoichiometry?
  5. Nov 2, 2011 #4


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    I am afraid that means you will be not able to solve your problem.

    There is no stoichiometric relationship of this type. One of the equations on the page I linked to describes the relationship you are looking for - but it is far from simple stoichiometry.

    No, it is not that simple.
  6. Nov 2, 2011 #5
    Could you please then explain which relationship I can use to solve the problem?
    I am a final year Chemical Engineering student with only my basic A-Level Chemistry to rely on here and I'm not finding that it's helping much in this case.

    All the relationships described involve at least 2 unknowns and therefore require at least 2 equations to solve them.

    Which of the equations listed will I have to substitute into which?
  7. Nov 2, 2011 #6


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    After reading your first post I was under impression you are looking for equation that will let you find concentration of any form of the acid as a function of pH ([H+])- and there are three such equations on the page. But now I am no longer sure I know what you are looking for. Please elaborate.
  8. Nov 2, 2011 #7
    I have an initial aqueous phase concentration of diprotic acid H2A of 0.2 M.

    pKa1 4.418
    pKa2 5.412
    pKa 9.830
    Ka1 3.82E-05
    Ka2 3.87E-06
    Ka 1.48E-10

    [ACID]aq = [H2A]aq + [HA-]aq + [A2-]

    I have calculated the equilibrium concentrations of all species in the aqueous phase as:

    [ACID]aq [H2A]aq [HA-]aq [A2-]aq [H+]aq
    0.200 0.197 2.74E-03 3.86E-06 2.75E-03

    However, these equilibrium concentrations are taken to be initial concentrations in a liquid-liquid extraction process.
    Over time an equilibrium is established between a 2nd phase which then leaves overall equilibrium species concentrations in the aqueous phase: [H2A]aq, [HA-]aq, [A2-]aq and [H+]aq

    In the model I am developing I am setting different [H2A]aq values at the overall equilbrium and need to relate these to a corresponding [H+] such that an equilibrium curve can be plotted between each phase.

    In addition, experimentally, the only data I have available is pH (hence [H+]) of the aqueous phase at the overall equilibrium. I would therefore like to know how to use this data to calculate [H2A]aq such that [ACID]aq can then be calculated.

    Does this clarify... or makes things worse!?
  9. Nov 2, 2011 #8


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    Staff: Mentor

    Why do you concentrate on H2A?

    You can start estimating total acid concentration from the known pH - solve equation 9.14 for Ca. Then use equations 9.11 to 9.13 to calculate concentrations of different forms. But I doubt in accuracy of this approach - measuring pH is one of the least accurate methods of acid concentration determination.
  10. Nov 3, 2011 #9
    [H2A]aq is the species concentration used to relate the total acid concentrations in both phases of the liquid-liquid equilibrium mixture which is what I am interested in. Only undissociated acid is transferred between the two phases in this case.

    I will try as you suggest and see how well the model then predicts the system.
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