The Henderson–Hasselbalch equation works in reverse too: given the pH of a solution, it tells you which form of an acid dominates. This is how chemists and biologists predict the charge of a molecule in a given solution.
Key idea
When $\text{pH} < \text{p}K_a$, the protonated form (HA) dominates. When $\text{pH} > \text{p}K_a$, the deprotonated form ($\mathrm{A^-}$) dominates. At $\text{pH} = \text{p}K_a$ they are equal, and each pH unit away from the $\text{p}K_a$ is another factor of 10 in the ratio.
Why it works
From the equation, $\dfrac{[\mathrm{A^-}]}{[\mathrm{HA}]} = 10^{\text{pH} - \text{p}K_a}$. A high pH means few protons around, so the acid has given its proton up; a low pH means plenty of protons, so the acid keeps it. The fraction in the base form is $\dfrac{1}{1 + 10^{\text{p}K_a - \text{pH}}}$.
Worked examples
Worked example: Two units above the pKa
Acetic acid ($\text{p}K_a = 4.74$) is in a solution buffered at pH 6.74. What is $[\mathrm{CH_3COO^-}]/[\mathrm{CH_3COOH}]$, and what fraction is acetate?
- $\text{pH} - \text{p}K_a = 2.00$, so the ratio is $10^{2.00} = 100$.
- Fraction as acetate $= \dfrac{100}{101} = 0.99$, about 99%.
Answer: 100 to 1; about 99% acetate.
Worked example: Below the pKa
A weak acid with $\text{p}K_a = 10.0$ is in blood at pH 7.4. Which form dominates, and by how much?
- $\text{pH} - \text{p}K_a = 7.4 - 10.0 = -2.6$, so $\dfrac{[\mathrm{A^-}]}{[\mathrm{HA}]} = 10^{-2.6} = 2.5 \times 10^{-3}$.
- The protonated form wins by about 400 to 1.
Answer: HA, by about 400 to 1.
| pH − pKa | $[\mathrm{A^-}]/[\mathrm{HA}]$ | Percent as A⁻ |
|---|---|---|
| −2 | 1/100 | 1% |
| −1 | 1/10 | 9% |
| 0 | 1 | 50% |
| +1 | 10 | 91% |
| +2 | 100 | 99% |
Common mistake
Saying the protonated form dominates when the pH is above the $\text{p}K_a$. It is the reverse: high pH means the proton has gone. Check: at very high pH (very basic), every acid ends up as its conjugate base.
The same rule explains indicators: an indicator is a weak acid whose two forms have different colors, so the color switches as the pH passes its $\text{p}K_a$. It also explains why many drugs are absorbed in one part of the body and not another: the uncharged form crosses cell membranes more easily, and which form dominates depends on the local pH.
Amino acids carry several groups with different $\text{p}K_a$ values, so their overall charge changes with pH. That is how proteins are separated by charge in a gel.