AP Chemistry · Unit 8 · Topic 8.7
pH and pK_a
pH describes the solution; pKa describes a particular acid equilibrium at a specified temperature. Comparing them tells you which protonation state is more abundant.
Keep the two quantities distinct
The pKa value is \(-\log K_a\). A lower pKa means a larger acid ionization constant. The pH can change when the same acid is diluted or mixed with a conjugate-base salt without changing its Ka at fixed temperature in the chosen model. Therefore, an acid does not have one universal solution pH.
Rearrange the equilibrium ratio
For \(HA\rightleftharpoons H^++A^-\), the acid equilibrium gives \([A^-]/[HA]=K_a/[H^+]\) under the concentration approximation. Converting both constants to logarithmic form gives
This is an equilibrium speciation relation. Using preparation concentrations in place of equilibrium values adds a separate buffer approximation.
Read the ratio at a glance
| pH − pKa | A⁻ : HA | Fraction deprotonated |
|---|---|---|
| −2 | 1 : 100 | 0.99% |
| −1 | 1 : 10 | 9.1% |
| 0 | 1 : 1 | 50% |
| +1 | 10 : 1 | 90.9% |
| +2 | 100 : 1 | 99.0% |
Protonation is a continuous equilibrium distribution, not an all-or-nothing switch at pKa.
Work a fraction calculation
An original weak-acid dye has pKa = 6.40 and is measured at pH 7.00. The ratio is \(r=10^{0.60}=3.98\). The A⁻ fraction is \(r/(1+r)=0.799\), so about 79.9% is deprotonated and 20.1% protonated. If the total dye concentration is 10.0 μM, the approximate concentrations are 7.99 μM A⁻ and 2.01 μM HA.
Explain an indicator's transition
If the two forms have different colors, the observed color depends on their relative contributions to absorption. A visible transition often spans a range around pKa rather than one exact pH. Color intensity also depends on total dye concentration and optical path length, so “darker” alone does not uniquely determine the acid–base ratio.
Estimate pKa from evidence
In a weak-monoprotic-acid titration by a strong base, the half-equivalence point approximately has equal acid and conjugate-base amounts. Its pH estimates pKa when the buffer model applies. Locate equivalence from the curve first; taking half of an arbitrary last recorded titrant volume is not a valid substitute.
Use the right species pair
A polyprotic acid has different pKa values for successive proton losses. Compare the pH with the pKa connecting the two specific forms of interest. A basic solution does not guarantee that every available proton has been removed, and a negatively charged form can still retain an acidic proton.
Practice with answers
- If pH = pKa − 1, which form dominates? HA, by a factor of ten.
- At pH = pKa + 0.30, estimate A⁻/HA. About 2.0.
- Does changing an acid solution's pH necessarily change its pKa? No; pH changes composition, while pKa is tied to the equilibrium under specified conditions.
Factual references: OpenStax Chemistry 2e, 14.3 and 14.6. The dye, quantities, table, and questions are original teaching models.
Official curriculum reference: College Board AP Chemistry course page. The explanation and worked example are independently written for this study site.