Weak Acid Equilibrium and Ka

Introduction

A weak acid does not release all of its transferable protons into water. Its molecular acid, hydronium and conjugate base coexist at equilibrium. Ka quantifies their activity ratio at a stated temperature; initial concentration and mass balance are also needed to find actual pH or fraction ionized.

Core explanation

Write HA + H₂O ⇌ H₃O⁺ + A⁻. The thermodynamic acid-dissociation constant uses activities, with pure water's activity absorbed into Ka. In a dilute concentration approximation, Ka ≈ [H₃O⁺][A⁻]/[HA]. A larger Ka generally indicates stronger dissociation for comparable acid reactions and standard states. A small Ka indicates reactant acid is favored in the standard comparison, but not zero ionization.

For a monoprotic weak acid initially C₀ M with negligible initial A⁻, let x dissociate. The ICE table gives [HA] = C₀ − x, [A⁻] = x and acid-derived [H₃O⁺] ≈ x when water contribution is negligible. Therefore Ka ≈ x²/(C₀ − x). Solve for x, then pH ≈ −log₁₀x under the dilute activity approximation. The acid's analytical starting concentration is not itself the hydronium concentration.

Ka is not percent ionization. The fraction ionized is α = x/C₀, which changes with C₀. For the same weak acid, dilution often increases the percentage ionized even while the absolute hydronium concentration can fall. This subtle result follows from the Ka equation and should not be confused with the statement that dilution “makes the acid stronger” by changing Ka; Ka stays fixed at the same temperature.

The conjugate base A⁻ can accept a proton. Adding a soluble salt containing A⁻ introduces a common ion, shifting acid dissociation and requiring a different ICE setup. For mixtures with significant background acid or base, the simple x²/(C₀ − x) form may also need modification.

Weak acid is a thermodynamic category, not a measure of how much acid is present. A concentrated weak acid can still have substantial hydronium, and a very dilute strong acid may have less. The term also does not by itself settle safety or corrosiveness.

Step-by-step reasoning

1. Write HA's proton transfer to water and identify conjugate base. 2. Construct Ka from equilibrium activities or dilute concentrations. 3. Use an ICE table and mass balance to solve dissociation x. 4. Convert hydronium to pH and verify any approximation.

Visual explanation

Draw many HA molecules alongside smaller numbers of H₃O⁺ and A⁻ in water. Put their activity product over remaining HA in a Ka fraction.

Real-world analogy

Only some members of a group leave one room for another at a given time. The fraction that moved depends on starting crowd size and the balance conditions, not just a label saying the transfer is “weak.”

Real-world example

Acetic acid in water is a weak acid. A vinegar solution's hydronium concentration cannot be equated directly with its total acetic-acid analytical concentration without equilibrium reasoning.

Why?

Why is [HA] retained in the denominator? Undissociated acid remains at equilibrium and its activity affects the balance between proton donation and reverse proton uptake.

Common misconception

“Weak acid means no dissociation.” Weak acids dissociate partly and may still produce measurable hydronium and substantial chemical effects in aqueous solutions.

Worked example

A 0.100 M weak HA has Ka = 1.0 × 10⁻⁵ under the classroom concentration convention. Approximate x ≈ √(KaC₀) = √(1.0 × 10⁻⁶) = 0.0010 M. The fraction ionized is 0.0010/0.100 = 0.010, or 1.0%, validating the small-x approximation. Approximate pH is 3.00. The starting acid concentration was 0.100 M, not 0.0010 M.

Quick check

1. Write the simple concentration expression for Ka of HA. Answer: [H₃O⁺][A⁻]/[HA] at equilibrium under dilute assumptions.

Exam focus

Use equilibrium concentrations, not initial values, in Ka. Check the fractional ionization after any small-x approximation.

Advanced insight

At very low acid concentration, water autoionization may contribute significantly to hydronium. Then setting [H₃O⁺] = x without a water term can be inaccurate, and charge balance is needed.

Summary

Ka relates hydronium, conjugate base and undissociated weak acid at equilibrium. pH requires both Ka and composition information, while percent ionization additionally depends on initial concentration.

Practice questions

1. Is 0.10 M weak HA necessarily [H₃O⁺] = 0.10 M? Answer: No. Only a fraction dissociates, so hydronium is usually lower. 2. What happens to Ka when the same weak acid solution is diluted at fixed T? Answer: Ka stays the same; the fraction ionized can change. 3. What species is HA's conjugate base? Answer: A⁻, formed after HA transfers a proton to water.