CHEMISTRY · ACID–BASE MASTER GUIDE

pH, pOH, Ka, Kb & Kw: The Complete Student Guide

A concept-first map of acid–base quantities: what each one measures, how logarithms connect them, how acid/base strength relates to Ka and Kb, and where the common shortcuts stop being valid.

Study Tools / Informational / pH, pOH, Ka, Kb & Kw: The Complete Student Guide
Research edition · Updated 19 September 2026 · Built for MDCAT study and reference
Research note: This page combines PM&DC curriculum context with standard scientific references. It is designed as a study aid; the current official syllabus and examination notices remain the source of truth for exam-specific requirements.
pH
−log₁₀[H⁺]
pKa
−log₁₀Ka
25 °C
pKw ≈ 14 in dilute water
Official-context note: IUPAC defines the acid dissociation constant Ka as an equilibrium constant for acid dissociation. The familiar pH/pOH and pKw shortcuts used in introductory chemistry are condition-dependent; the common 14 value is associated with water at about 25 °C, not a universal temperature-independent constant.

Quick Reference

Quick take

Strength ≠ concentration

A dilute strong acid can have a lower pH than a concentrated weak acid; strength and amount are different concepts.

Quick take

Logs invert intuition

A tenfold increase in [H⁺] changes pH by one unit.

Quick take

Ka and pKa move opposite

Larger Ka means smaller pKa.

Quick take

Equilibrium matters

Ka and Kb describe equilibrium behavior, not simply how many particles you started with.

1. The Five Quantities

QuantityMeaningCore relation
[H⁺]Hydrogen-ion concentration (with the usual introductory concentration approximation).pH = −log₁₀[H⁺]
[OH⁻]Hydroxide-ion concentration.pOH = −log₁₀[OH⁻]
KaAcid dissociation equilibrium constant.pKa = −log₁₀Ka
KbBase dissociation equilibrium constant.pKb = −log₁₀Kb
KwIonization product of water.Kw = [H⁺][OH⁻]

2. Why the pH Scale Is Logarithmic

A logarithmic scale compresses very large concentration ranges into manageable numbers. If [H⁺] changes from 1×10⁻³ M to 1×10⁻⁴ M, the pH changes from 3 to 4. A one-unit pH difference therefore corresponds to a tenfold change in the hydrogen-ion concentration under the same concentration-based convention.

Worked example: If [H⁺] = 2.0 × 10⁻⁴ M, then pH = −log₁₀(2.0 × 10⁻⁴) ≈ 3.70. The “4” in the exponent gives the scale, while the coefficient 2.0 shifts the final value below 4.

3. Ka and pKa: Strength of an Acid

General acid dissociation
HA ⇌ H⁺ + A⁻ ; Kₐ ∝ [H⁺][A⁻]/[HA]

The exact thermodynamic expression uses activities and standard-state conventions; at the introductory level, concentration expressions are commonly used. IUPAC notes that Ka can span many orders of magnitude, which is why pKa is convenient.

At the same general conditions, larger Ka → stronger acid → smaller pKa. Do not read a larger pKa as “more acidic”; the logarithm reverses the numerical direction.

4. Kb and pKb: The Base Side

General base reaction
B + H₂O ⇌ BH⁺ + OH⁻ ; K_b ∝ [BH⁺][OH⁻]/[B]

The same logic applies: larger Kb corresponds to greater base dissociation tendency under the same general conditions, while pKb is the negative base-10 logarithm of Kb.

5. Kw, pKw, pH and pOH

Water self-ionizes to a tiny extent, producing hydronium/hydrogen-ion and hydroxide species. In the common dilute-aqueous approximation, the product of the concentrations is represented by Kw. At 25 °C, the numerical value is approximately 1.0 × 10⁻¹⁴, leading to pKw ≈ 14 and therefore pH + pOH ≈ 14.

Temperature warning: the ion-product of water changes with temperature. The number 14 is a useful 25 °C classroom value, not a permanent feature of water at every temperature.

6. Strong vs Weak Does Not Mean Concentrated vs Dilute

Strong/weak describes the extent to which an acid or base dissociates in the stated medium. Concentrated/dilute describes how much solute is present per volume. A strong acid can be dilute. A weak acid can be concentrated. Those two axes must be kept separate in both conceptual and numerical questions.

7. Buffers: Why pH Can Resist Change

A buffer typically contains a weak acid and its conjugate base, or a weak base and its conjugate acid. When small amounts of acid or base are added, the buffer components consume much of the added material, reducing the resulting pH change compared with unbuffered water.

Henderson–Hasselbalch
pH = pKₐ + log₁₀([A⁻]/[HA])
Use under the usual approximations; it is not a universal substitute for equilibrium analysis.

Frequently Asked Questions

Does a lower pH always mean a stronger acid?
No. A lower pH means a higher hydrogen-ion concentration in the solution. Acid strength is a property of dissociation tendency; concentration also affects the resulting pH.
Is pKa the same thing as pH?
No. pKa characterizes an acid’s dissociation equilibrium constant. pH describes the hydrogen-ion concentration of a solution.
Why does larger Ka mean smaller pKa?
Because pKa is defined as −log₁₀Ka. Taking the negative logarithm reverses the numerical ordering.
Can I always use pH + pOH = 14?
Use it as the common 25 °C dilute-water shortcut. Outside that context, use the temperature-appropriate Kw relationship.
Research & reference sources:
PM&DC — Uniform Curriculum MDCAT-2025 (official PDF) · IUPAC Gold Book — acid dissociation constant · OpenStax — College Physics 2e: Physical Quantities, Units, Accuracy & Significant Figures

Scope: scientific explanations are written for student use and simplified where appropriate. Exact exam wording, syllabus scope and current administrative rules should be checked against PM&DC documents.