How to Determine pH From pKa

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The strength of an acid is measured by both its pH and its pKa, and the two are related by the Henderson-Hasslebalch equation. This equation is: pH = pKa + log[A-]/[AH], where [AH] is the concentration of the acid and [A-] is the concentration of its conjugate base after dissociation. pH is a variable that depends on concentration, so if you want to derive its value from this relationship, you need to know the concentrations of the acid and its conjugate base.

What Are pH and pKa?

The acronym pH stands for "power of hydrogen," and it's a measure of the concentration of hydrogen ions in an aqueous solution. The following equation expresses this relationship:

pH = -log [H+]

The value of pKa, on the other hand, depends on the concentrations of acid and conjugate base in solution after the acid dissociation has achieved equilibrium. The ratio of the concentrations of conjugate base and conjugate acid to the acid in question, in an aqueous solution, is called the dissociation constant, Ka. The value for pKa is given by:

pKa = -log (Ka)

Although pH varies by solution, pKa is a constant for each acid.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch formula comes directly from the definition of the dissociation constant Ka. For an acid HA that dissociates into H+ and A- in water, the dissociation constant is given by:

Ka = [H+][A-]/[HA]

We can take the logarithm of both sides:

log (Ka) = log ([H+][A-]/[HA]), or log Ka = log (H+) + log [A-]/[HA]

Referring to the definitions of pH and pKa, this becomes:

-pKa = -pH + log [A-]/[HA]

Finally, after adding pH and pKa to both sides:

pH = pKa + log [A-]/[HA].

This equation allows you to calculate pH if the dissociation constant, pKa, and the concentrations of the acid and conjugate base are known.

References

About the Author

Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. He began writing online in 2010, offering information in scientific, cultural and practical topics. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts.

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