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Acid–base relations

pH formulaspH and pOHKa Kb Kwweak acid pHpercent ionizationhow to calculate pH

pH, pOH, Kw, Ka and Kb and the weak-acid shortcut — the chain that turns a concentration into a pH and back again.

pH from Hydrogen Ion Concentration

pH=−log⁡10 [H+]\mathrm{pH} = -\log_{10}\,[\mathrm{H^+}]

Expresses acidity as the negative base-10 logarithm of the hydrogen ion concentration in mol/L.

pH and pOH Relation

pH+pOH=14\mathrm{pH} + \mathrm{pOH} = 14

Links the acidity and basicity scales of any aqueous solution at 25 °C, where pKw = 14.

Ka and Kb Relation through Kw

Ka Kb=KwK_a \, K_b = K_w

Links a weak acid's dissociation constant to that of its conjugate base through the ion product of water, Kw = 1.0 × 10⁻¹⁴ at 25 °C.

pKa from Acid Dissociation Constant

pKa=−log⁡10Ka\mathrm{p}K_a = -\log_{10} K_a

Converts an acid dissociation constant into its logarithmic pKa form and back, compressing a huge range of acid strengths onto one readable scale.

pKb from Base Dissociation Constant

pKb=−log⁡10Kb\mathrm{p}K_b = -\log_{10} K_b

Converts a base dissociation constant into its logarithmic pKb form and back, the basic-side counterpart of the pKa scale.

pH of a Weak Acid from Ka

pH=−log⁡10Ka C\mathrm{pH} = -\log_{10}\sqrt{K_a\,C}

Estimates the pH of a weak monoprotic acid solution from its dissociation constant and formal concentration using the standard x-is-small approximation.

Percent Ionization of a Weak Acid

% ion=[H+]C×100%\%\,\text{ion} = \frac{[\mathrm{H^+}]}{C} \times 100\%

Expresses what fraction of a weak acid has actually donated its proton, comparing the equilibrium hydrogen ion concentration to the formal concentration.

How they fit together

All of these hang off one fact: water autoionises, and at 25 °C the product [H⁺][OH⁻] is fixed at 1.0 × 10⁻¹⁴. That single constant is what ties pH to pOH (they sum to 14), what ties Ka to Kb for a conjugate pair (Ka × Kb = Kw), and what makes the p-scale useful at all — a logarithm turns a range spanning fourteen orders of magnitude into a number between 0 and 14.

Choose by the strength of the acid. For a strong acid the concentration is [H⁺], so go straight to pH = −log[H⁺]. For a weak acid it is not, and you need Ka: the weak-acid shortcut pH = −½log(Ka·C) assumes the dissociated fraction is under about 5%, which fails for a fairly strong weak acid at low concentration and forces you back to the quadratic. Percent ionisation is the check on that assumption — compute it, and if it comes out above 5% the shortcut you just used was not valid. Two more traps: the 14 in pH + pOH = 14 is only true at 25 °C because Kw itself changes with temperature, and a negative pH is not an error, it is what a concentrated strong acid genuinely reads.