Acids Iteration Pattern
- 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 25o 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, HdX, 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.
- 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 + (Σdj*Caj)*[H+])1/2(3)
where dj is the deprotonation degree of acid j. For a strong monoprotic acid such as HCl, dj = 1, whereas for a strong diprotic acid such as H2SO4, dj = 2.
By contrast, for a weak acid, dj is a function of its alpha fractions
dj = α1,j + 2*α2,j + 3*α3,j + ... n*αn,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.
- Data miners, computational chemists, chemical engineers, chemists, and chemistry teachers and their students.
- 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.
- 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.
Contact us for any suggestion or question regarding this tool.