Calculate Diprotic Acid Species Concentrations

[jonnyupton]

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?

 

[Borek]

Browse this derivation of pH of polyprotic acid.

 

[jonnyupton]

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?

 

[Borek]

I have previously found and read that webpage but cannot figure out how that helps in this case.

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

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

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.

Is is accurate simply to say that [A2-] is equal to [H+]/2 from the dissociation stoichiometry?

No, it is not that simple.

 

[jonnyupton]

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?

 

[Borek]

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]?

All the relationships described involve at least 2 unknowns

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.

 

[jonnyupton]

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!?

 

[Borek]

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.

 

[jonnyupton]

[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.