Acid-Base Equilibria, Ka Kb Kw, pH Calculations Cheat Sheet

A printable reference covering $K_a$, $K_b$, $K_w$, pH, pOH, conjugate pairs, and acid-base equilibrium calculations for grades 11-12.

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Acid-base equilibria explain how acids and bases partially or completely ionize in water and how their concentrations are related at equilibrium. This cheat sheet helps students organize the key constants, formulas, and calculation steps used in Grade 11-12 chemistry. It is especially useful for solving pH, pOH, weak acid, weak base, and conjugate acid-base problems. The goal is to connect equilibrium ideas with fast, accurate calculations. The most important relationships are $K_a$ for weak acids, $K_b$ for weak bases, and $K_w = [H_3O^+][OH^-]$ for water. At $25^\circ\text{C}$ , $K_w = 1.0 \times 10^{-14}$ , so $\text{pH} + \text{pOH} = 14.00$ . Strong acids and bases are treated as fully dissociated, while weak acids and bases require equilibrium expressions. Conjugate pairs are linked by $K_aK_b = K_w$ , which helps compare acid and base strength.

Key Facts

For water at $25^\circ\text{C}$ , $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$ .
The pH of a solution is calculated with $\text{pH} = -\log[H_3O^+]$ , where $[H_3O^+]$ is measured in $\text{mol}\,\text{L}^{-1}$ .
The pOH of a solution is calculated with $\text{pOH} = -\log[OH^-]$ , where $[OH^-]$ is measured in $\text{mol}\,\text{L}^{-1}$ .
At $25^\circ\text{C}$ , pH and pOH are related by $\text{pH} + \text{pOH} = 14.00$ .
For a weak acid $HA$ , the acid dissociation constant is $K_a = \frac{[H_3O^+][A^-]}{[HA]}$ .
For a weak base $B$ , the base dissociation constant is $K_b = \frac{[BH^+][OH^-]}{[B]}$ .
For a conjugate acid-base pair at $25^\circ\text{C}$ , $K_aK_b = K_w = 1.0 \times 10^{-14}$ .
A small $K_a$ or $K_b$ means the acid or base ionizes only slightly, while a larger value means stronger ionization.

Vocabulary

Acid: An acid is a substance that donates $H^+$ or increases $[H_3O^+]$ in water.
Base: A base is a substance that accepts $H^+$ or increases $[OH^-]$ in water.
Conjugate acid-base pair: A conjugate acid-base pair consists of two species that differ by exactly one $H^+$ .
Dissociation constant: A dissociation constant such as $K_a$ or $K_b$ measures the extent to which an acid or base ionizes at equilibrium.
pH: pH is a logarithmic measure of acidity defined by $\text{pH} = -\log[H_3O^+]$ .
Equilibrium expression: An equilibrium expression relates product and reactant concentrations at equilibrium using coefficients as exponents.

Common Mistakes to Avoid

Using initial concentrations directly in $K_a$ or $K_b$ expressions for weak acids or bases is wrong because the expression must use equilibrium concentrations.
Forgetting that strong acids and strong bases fully dissociate leads to unnecessary ICE tables and incorrect pH values.
Mixing up pH and pOH gives the wrong acidity because $\text{pH} = -\log[H_3O^+]$ and $\text{pOH} = -\log[OH^-]$ measure different ions.
Applying $\text{pH} + \text{pOH} = 14.00$ at temperatures other than $25^\circ\text{C}$ without checking $K_w$ is wrong because $K_w$ changes with temperature.
Assuming a larger $K_a$ means a stronger base is wrong because a larger $K_a$ means a stronger acid and a weaker conjugate base.

Practice Questions

1 Calculate the pH of a solution with $[H_3O^+] = 2.5 \times 10^{-4}\,\text{M}$ .
2 Calculate $[OH^-]$ and pH for a solution with $\text{pOH} = 3.20$ at $25^\circ\text{C}$ .
3 A weak acid $HA$ has $K_a = 1.8 \times 10^{-5}$ . Find $K_b$ for its conjugate base $A^-$ at $25^\circ\text{C}$ .
4 Explain why a weak acid can have a low pH even though it does not fully dissociate.

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