Chemistry

Conjugate Acid–Base Constants

Relate the strengths of a conjugate acid and base in water.

K_{a} K_{b} = K_{w}

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Difficulty

Beginner

Read time

3 min

Prerequisites

Basic algebra and molar quantities

Review statusNeeds review

Source

OpenStax, Chemistry 2e, §14.3

Adapted from Teng-Jui Lin’s CHEM 155 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Definition

Understanding the core concept

A conjugate acid’s K_a and its conjugate base’s K_b multiply to the water ion-product constant at the same temperature. A larger K_a therefore corresponds to a smaller conjugate-base K_b.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$K_{a}$	Dimensionless dissociation constant of the conjugate acid	$1$
$K_{b}$	Dimensionless dissociation constant of its conjugate base	$1$
$K_{w}$	Dimensionless water ion-product constant at the same temperature	$1$

Real-World Applications

Where this formula is used in practice

Conjugate strength

Calculate a base constant from its conjugate acid constant.

Acid–base comparison

Compare linked acid and base equilibria.

Worked Example

Step-by-step calculation with real numbers

Problem

At 25 °C, an acid has K_a = 1.80 × 10⁻⁵. Using K_w = 1.00 × 10⁻¹⁴, find its conjugate base’s K_b.

Given

K_{a} = 1.80 \times 1 0^{- 5}

K_{w} = 1.00 \times 1 0^{- 14} (25^{\circ} C)

Solution

K_{a} K_{b} = K_{w}

K_{b} = \frac{K _{w}}{K _{a}}

K_{b} = \frac{1.00 \times 1 0 ^{- 14}}{1.80 \times 1 0 ^{- 5}}

K_{b} \approx 5.556 \times 1 0^{- 10}

Final Answer

K_{b} \approx 5.556 \times 1 0^{- 10}

Formula Guide

Info

DifficultyBeginner

Read Time3 min

PrerequisitesBasic algebra and molar quantities

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, Chemistry 2e, §14.3

Adapted from Teng-Jui Lin’s CHEM 155 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.

Assumptions

• The acid and base must be a conjugate pair in water at the same temperature.
• Use consistent standard states; K_w is approximately 1.00 × 10⁻¹⁴ at 25 °C.

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