Weak Acid Calculators

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A weak acid is an acid that only partially dissociates in water — establishing a dynamic equilibrium between the undissociated acid (HA) and its conjugate base (A⁻) and hydrogen ions (H⁺). Unlike strong acids, which dissociate completely, weak acids are characterized by a small acid dissociation constant (Ka) and relatively high pKa. Weak acids are ubiquitous in biology — acetic acid, carbonic acid, lactic acid, amino acid side chains, and the phosphate and bicarbonate buffer systems all involve weak acid equilibria that are critical for maintaining cellular and physiological pH.

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Weak vs. Strong Acids

  • Strong acids (HCl, HNO₃, H₂SO₄, HBr, HI, HClO₄): dissociate ~100% in water. Ka → ∞ (very large).
  • Weak acids (acetic acid, carbonic acid, lactic acid, H₂PO₄⁻, ammonium NH₄⁺): only partially dissociate. Ka is small (typically 10⁻² to 10⁻¹⁰).

Weak Acid Equilibrium

HA ⇌ H⁺ + A⁻

Ka = [H⁺][A⁻] / [HA]

pKa = −log₁₀(Ka). Lower pKa = stronger acid. At pH = pKa, exactly 50% of the acid is dissociated ([HA] = [A⁻]).

Calculating pH of a Weak Acid Solution

For a weak acid HA with initial concentration C and Ka:

[H⁺] ≈ √(Ka × C) (valid when Ka ≪ C, i.e., <5% dissociation)

pH = −log[H⁺] = ½(pKa − log C)

Example: 0.1 M acetic acid (Ka = 1.8 × 10⁻⁵, pKa = 4.74):
[H⁺] = √(1.8 × 10⁻⁵ × 0.1) = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³ M → pH = 2.87

Henderson-Hasselbalch Equation

For a buffer (mixture of weak acid and conjugate base):

pH = pKa + log([A⁻]/[HA])

At pH = pKa: [A⁻]/[HA] = 1 → equal concentrations of acid and conjugate base. Buffer capacity is maximal within ±1 pH unit of pKa.

Biological Weak Acids

  • Carbonic acid (H₂CO₃/HCO₃⁻): pKa = 6.1. Major blood buffer system
  • Phosphate (H₂PO₄⁻/HPO₄²⁻): pKa = 7.2. Intracellular buffer
  • Acetic acid: pKa = 4.76. Lab buffer at pH 3.6–5.6
  • Lactic acid: pKa = 3.86. Produced in anaerobic exercise

Glossary

Weak Acid
An acid that partially dissociates in water: HA ⇌ H⁺ + A⁻. Characterized by small Ka and high pKa. Establishes an equilibrium rather than complete dissociation. Examples: acetic acid (pKa 4.76), carbonic acid (pKa 6.1).
Ka (Acid Dissociation Constant)
The equilibrium constant for weak acid dissociation: Ka = [H⁺][A⁻]/[HA]. Larger Ka = stronger acid (more dissociation). pKa = −log Ka. At pH = pKa, [HA] = [A⁻] — equal concentrations of acid and conjugate base.
Henderson-Hasselbalch Equation
pH = pKa + log([A⁻]/[HA]). Calculates pH of a buffer from the ratio of conjugate base to weak acid concentrations. Buffer capacity is maximum within ±1 pH unit of pKa.

Frequently Asked Questions

A strong acid dissociates completely in water — essentially no HA remains; all molecules donate their proton. Ka is very large (»1). A weak acid only partially dissociates, establishing an equilibrium between HA, H⁺, and A⁻. Ka is small (typically 10⁻²–10⁻¹⁰). Examples of weak acids: acetic acid (Ka = 1.8×10⁻⁵), carbonic acid (Ka₁ = 4.3×10⁻⁷), ammonium (Ka = 5.6×10⁻¹⁰). Examples of strong acids: HCl, H₂SO₄, HNO₃.

Ka (acid dissociation constant) is the equilibrium constant for the ionization of a weak acid: Ka = [H⁺][A⁻]/[HA]. A large Ka = stronger acid (more dissociation). pKa = −log₁₀(Ka) — lower pKa = stronger acid. At pH = pKa, the acid and conjugate base are present in equal concentrations. pKa values are used in the Henderson-Hasselbalch equation to predict the ratio of protonated/deprotonated species at any pH.

For weak acid HA at concentration C: set up the equilibrium Ka = x²/(C−x) where x = [H⁺]. If x ≪ C (Ka ≪ C): [H⁺] ≈ √(Ka × C) → pH = ½(pKa − log C). Example: 0.05 M acetic acid (pKa 4.74): pH = ½(4.74 − log 0.05) = ½(4.74 + 1.30) = ½(6.04) = 3.02. If the 5% approximation fails (Ka/C > 0.01), solve the quadratic exactly.

Weak acid equilibria underlie all biological pH buffering. The carbonate/bicarbonate system (pKa 6.1) maintains blood pH at 7.4 through CO₂ exchange in the lungs. The phosphate system (pKa 7.2) buffers intracellular pH. Amino acid side chains with ionizable groups (His pKa ~6, Cys pKa ~8, Asp pKa ~3.9) act as weak acids/bases in enzyme active sites, mediating proton transfer in catalysis. The Henderson-Hasselbalch equation governs all these equilibria.