Acids Iteration Pattern

This tool uses an iteration pattern to compute the pH of acid solutions.

Other chemistry tools:

Cell Electrode Potentials

Chemical Reactions Writer

Electron Configurations

Janet Periodic Table

and many more »

Instructions

• Input Data
  Please keep in mind that this tool considers invalid any input that is not a positive number.
• pks value
  Enter solvent dissociation constant, pks. If the solvent is water pks = pkw. If in addition, activity effects are neglected and the temperature is 25^o Celsius, pks = pkw = 14. If working at other conditions, use the corresponding pks value.
• Ca and pka values
  Enter Ca and pka values in the textarea, in one line, and separated by commas (try example). For a strong acid, H_dX, enter the product of d*Ca, where for instance d = 1 for HCl, d = 2 for H₂SO₄, and so forth. For a weak acid, d is calculated by the tool. In general, d is the deprotonation degree of an acid.
• Submit or reset form as needed.

What is computed?

• This tool uses the following iteration pattern to find the pH of an acid solution regardless of its dissociation strength.

  [H⁺] = (ks + d*Ca*[H⁺])^1/2 (1)

  Defining x = [H⁺], we can see that (1) is of the form

  x = f(x) (2)

  Numerical Dynamics Theory (Devaney, 1989a, 1989b, 1992), states that (2) describes an iteration pattern that converges to attractive fixed points when |df(x)/dx| < 1.

  Thus, (1) should converge for any number of mixed acids, and positive input values of Ca, pks, pka's, and regardless of the initial guess value of [H⁺].

  In general for a combination of j = 1, 2, 3,...m acids

  [H⁺] = (ks + (Σd_j*Ca_j)*[H⁺])^1/2(3)

  where d_j is the deprotonation degree of acid j. For a strong monoprotic acid such as HCl, d_j = 1, whereas for a strong diprotic acid such as H₂SO₄, d_j = 2.

  By contrast, for a weak acid, d_j is a function of its alpha fractions

  d_j = α_1,j + 2*α_2,j + 3*α_3,j + ... n*α_n,j(4)

  where the α's are the dissociation fractions of acid j (Freiser, 1992).

  The proposed pattern (1) can be easily simplified: If only one acid is present, j = 1 so

  [H⁺] = (ks + d*Ca*[H⁺])^1/2(5)

  If this is a weak acid and monoprotic, d = α₁ so

  [H⁺] = (ks + α₁*Ca*[H⁺])^1/2(6)

  Finally, if the solvent is water, pks = pkw, hence ks = kw = 10^-pkw

  [H⁺] = (kw + α₁*Ca*[H⁺])^1/2(7)

• The guessed value is set to [H⁺] = 10^-pks/2, corresponding to the hydrogen ion concentration of the pure solvent. So if the solvent is water and pks = pkw = 14, the iterations start at [H⁺] = 1e-7 and stop when the relative error between iterates is less than 1 ppt (one part per thousand). To improve output readability, [H⁺] results are converted to pH values.

Who can use this tool?

• Data miners, computational chemists, chemical engineers, chemists, and chemistry teachers and their students.

Suggested Exercises

• What is the pH of a 0.01 M aqueous solution of
  • aspartic acid (pka₁ = 1.990, pka₂ = 3.900, pka₃ = 10.002)?
  • ethylenediamine diacetic acid (pka₁ = 1.66, pka₂ = 2.37, pka₃ = 6.53, pka₄ = 9.59)?
• In the previous exercise, sort the dissociated acid species by their α fractions. Which are the more and least abundant species and why?
• Compare the deprotonation degree between carbonic acid (pka₁ = 6.37, pka₂ = 10.32) and a hypothetical acid H₂A (pka₁ = 2.00, pka₂ = 3.00). Assume that both are 0.01 M. What is the chemical significance of the results?
• Show that the absolute value of the relative error in [H⁺] is Δ[H⁺]/[H⁺] = 2.303*ΔpH.

References

• Devaney, R. L. (1989a). Chaos, Fractals, and Dynamical Systems: Computer Experiments in Mathematics. Addison Wesley, New York.
• Devaney, R. L. (1989b). An Introduction to Dynamical Systems. Addison Wesley, New York.
• Devaney, R. L. (1992). A First Course in Chaotic Dyamical Systems. Addison Wesley, New York.
• Freiser, H. (1992). Concepts & Calculations in Analytical Chemistry: A Spreadsheet Approach. Chapter 4. CRC Press, Boca Raton.

Feedback

Contact us for any suggestion or question regarding this tool.