# Calculate Diprotic Acid Species Concentrations

• jonnyupton
In summary, the model developed in this work will allow for the calculation of [H2A]aq from known pH and Ca concentrations in the aqueous phase.
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?

Last edited:
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?

jonnyupton said:
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.

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?

jonnyupton said:
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]?

jonnyupton said:
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.

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!?

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.

[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.

## 1. How do you calculate the concentrations of diprotic acid species?

To calculate the concentrations of diprotic acid species, you will need the initial concentration of the diprotic acid and the acid dissociation constants (Ka) for each proton. You can use the Henderson-Hasselbalch equation or a systematic approach using the equilibrium constants to solve for the concentrations of each species.

## 2. What is a diprotic acid and how is it different from a monoprotic acid?

A diprotic acid is an acid that can donate two protons (hydrogen ions) in an aqueous solution. This means it has two dissociable hydrogen ions. In comparison, a monoprotic acid only has one dissociable hydrogen ion. This difference affects the calculations for determining the concentrations of acid species.

## 3. How do you determine the Ka values for a diprotic acid?

Ka values for a diprotic acid can be determined experimentally by measuring the equilibrium concentrations of the acid and its conjugate base at different pH levels. These values can also be found in reference tables or databases.

## 4. What is the significance of calculating diprotic acid species concentrations?

Calculating diprotic acid species concentrations is important in understanding the behavior and properties of a diprotic acid in a solution. It can also help in determining the pH of a solution and the extent of acid dissociation, which is useful in many scientific fields such as chemistry, biology, and environmental science.

## 5. Can diprotic acids have more than two dissociable hydrogen ions?

No, diprotic acids can only have two dissociable hydrogen ions. However, polyprotic acids, such as triprotic or tetraprotic acids, can have three or four dissociable hydrogen ions respectively. These types of acids require more complex calculations to determine the concentrations of their species.

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