Acid Dissociation Constants

Introduction

A pKa table ranks acid strength only when entries refer to comparable proton-transfer reactions and conditions. A molecule with several acidic hydrogens has several stepwise constants; solvent, temperature and ionic strength change the reported values. Reading “pKa = 5” without a species, medium or convention is an invitation to misuse the number.

Core explanation

For HA + H₂O ⇌ H₃O⁺ + A⁻, an activity-based equilibrium expression is Ka = a(H₃O⁺)a(A⁻)/a(HA), with solvent activity incorporated in the standard treatment. The constant is dimensionless when activities use defined standard states. Introductory calculations often approximate it by concentration ratios, which can be reasonable in sufficiently dilute solutions. IUPAC's acid-dissociation entry notes that concentration constants neglect activity coefficients and are valid at specified ionic strength.

pKa = −log₁₀Ka, so smaller pKa generally means stronger acid for the same solvent and comparable definitions. A difference of one pKa unit represents a factor of ten in Ka. For polyprotic acids, label each step Ka1, Ka2 and so on; the species losing the proton changes after each step. A table value measured in water should not be compared mechanically with one in a nonaqueous solvent, because solvation and reference conventions differ.

Temperature affects acid equilibria through reaction thermodynamics. A pKa measured at 25 °C may not describe a hot process. Ionic strength affects concentration-based apparent constants because ion activities differ from concentrations. An IUPAC study of pKa measurements explicitly distinguishes activity-based thermodynamic constants from concentration constants at particular ionic strength and temperature. Check whether the source reports a thermodynamic, apparent or conditional value before inserting it into a buffer calculation.

At pH = pKa under a matching convention and conditions, conjugate acid and base activities are comparable; in simple dilute concentration treatment, [A⁻] ≈ [HA]. The Henderson–Hasselbalch equation is a rearranged equilibrium relation, not a guarantee that any chosen total concentration gives a useful buffer. Very dilute systems, strong ionic media and competing equilibria require more careful treatment.

Step-by-step reasoning

1. Write the exact acid dissociation step and identify conjugate species. 2. Confirm solvent, temperature, ionic strength and constant convention. 3. Convert between Ka and pKa with the negative logarithm. 4. Use activities or a justified concentration approximation consistently. 5. Check whether other protonation or complexation equilibria matter.

Visual explanation

Draw a pKa scale with stronger acids to the lower-number side. Place one hypothetical acid with pKa 4 and another with pKa 6; the first has Ka one hundred times larger under comparable conditions. On a second graph, show the fraction of HA and A⁻ crossing near pH = pKa, with a note that the curves depend on the chosen medium.

Real-world analogy

A price quoted in one currency cannot be directly ranked against another without exchange information. pKa values from different solvents or ionic conditions similarly lack a clean common basis. The comparison is meaningful only after confirming the reference context.

Real-world example

A buffer is designed for an analytical assay at high salt concentration. A dilute-water pKa gives a starting estimate, but the assay medium shifts the apparent acid-base ratio. The chemist calibrates the buffer at the working ionic strength and temperature instead of assuming a table value transfers exactly.

Why?

Why can a large ionic strength change a concentration-based pKa without changing the acid's identity? Ions interact electrostatically, changing activity coefficients. The activity ratio governing equilibrium is then not equal to the concentration ratio. A conditional constant absorbs those medium effects for a specified solution.

Common misconception

“pKa is universal for a molecule” ignores solvent and temperature. “A larger pKa means stronger acid” reverses the scale. “A polyprotic acid has one pKa” ignores successive dissociations. “A table's concentration constant always equals a thermodynamic activity constant” ignores ionic strength.

Worked example

Suppose two monoprotic acids in the same solvent at the same temperature have pKa values 4.0 and 6.0. Their Ka values are 10⁻⁴ and 10⁻⁶, so the first acid's dissociation constant is 100 times larger. At pH 5.0 under a simple dilute approximation, for the pKa 4 acid [A⁻]/[HA] ≈ 10^(5−4) = 10; for the pKa 6 acid the ratio is 10^(5−6) = 0.1. These ratios illustrate equilibrium tendencies, not total amounts, and would need activity corrections in a concentrated salt medium.

Quick check

1. Which is stronger under comparable conditions: an acid with pKa 4 or pKa 6? Answer: The pKa 4 acid, whose Ka is 100 times larger.

Exam focus

Write Ka for a specified step, compute pKa differences and state their factor-of-ten meaning. Label successive pKa values for polyprotic acids. Check temperature, solvent and ionic strength before using a tabulated constant in a quantitative problem.

Advanced insight

In mixed solvents and highly concentrated electrolytes, defining and measuring pH itself becomes more complex. Published apparent pKa values may include a particular pH scale or electrode calibration. A careful data user carries that convention into calculations and avoids merging values from incompatible scales.

Summary

Acid dissociation constants describe named proton-transfer equilibria under specified conditions. pKa compresses Ka logarithmically, but medium and temperature matter. Activity-based and conditional concentration values should not be mixed without justification.

Practice questions

1. What factor in Ka corresponds to two pKa units? Answer: A factor of 100 under comparable definitions. 2. Why does H₂A have two stepwise pKa values? Answer: H₂A → HA⁻ and HA⁻ → A²⁻ are distinct equilibria involving different acid species. 3. What ratio is expected near pH = pKa in a dilute matching convention? Answer: Conjugate base and acid concentrations are approximately equal. 4. Why should a 25 °C pKa not be inserted uncritically at 80 °C? Answer: The equilibrium constant and solution activities can change with temperature.