pH from hydrogen-ion concentration
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pH = −log₁₀([H⁺])
In the dilute concentration model, use the numerical hydrogen-ion concentration in mol dm⁻³ inside the logarithm. A tenfold increase lowers pH by one. For the inverse, raise 10 to the power (−pH) to obtain the numerical hydrogen-ion concentration in mol dm⁻³. pH has no concentration unit.
Strong monoprotic acid
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[H⁺] ≈ c(acid)
For a fully dissociated monoprotic acid, hydrogen-ion concentration is approximately the analytical acid concentration when water autoionisation is negligible. Strong describes dissociation, while concentrated describes amount per volume. Dilution can make the water contribution important.
- c(acid)
- analytical monoprotic-acid concentration (mol dm⁻³)
Water equilibrium and neutrality
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Kw = [H⁺][OH⁻]; pKw = −log₁₀ Kw
At a fixed temperature, the water ionic product relates hydrogen- and hydroxide-ion concentrations in the stated dilute model. Neutrality means equal concentrations, so neutral pH is half pKw. pH 7 is the usual neutral value at 298 K, not at every temperature. Use the numerical Kw value in the stated concentration convention.
OCR A: The common data sheet p2 prints Kw = 1.00 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K. The concentration-product relationship on this card is Learn this.
- Kw
- water ionic product in the concentration convention (mol² dm⁻⁶)
Strong-base pH
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[H⁺] = Kw / [OH⁻]; pH = −log₁₀([H⁺])
Find hydroxide-ion concentration from dissociation and stoichiometry, then use the water ionic product at the stated temperature. For ordinary dilute NaOH with negligible water contribution, [OH⁻] ≈ c(NaOH). A base supplying two hydroxide ions per formula unit needs that factor.
Weak monoprotic-acid equilibrium
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Ka = [H⁺][A⁻] / [HA]
For HA ⇌ H⁺ + A⁻, use equilibrium concentrations in the stated dilute aqueous convention. Undissociated HA belongs in the denominator. If the equilibrium is instead written using H₂O and H₃O⁺, omit [H₂O] from Ka because water is the solvent in large excess.
- Ka
- acid dissociation constant in this concentration convention (mol dm⁻³)
Weak-acid square-root approximation
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[H⁺] ≈ √(Ka c)
For a pure monoprotic weak acid with negligible water contribution and small fractional dissociation, take [A⁻] ≈ [H⁺] and [HA] ≈ c. Then hydrogen-ion concentration is approximately the square root of Ka times c. Check that the resulting dissociation is small.
- c
- analytical acid concentration (mol dm⁻³)
pKa and acid strength
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pKa = −log₁₀ Ka
Within the stated dilute concentration convention at a fixed temperature, a larger Ka means greater dissociation and a smaller pKa. Acid strength differs from the concentration of a prepared solution. Use the numerical Ka value in this convention. For the inverse, raise 10 to the power (−pKa) to recover that numerical Ka in mol dm⁻³.
- Ka
- acid dissociation constant in this concentration convention (mol dm⁻³)
- pKa
- negative base-10 logarithm of the specified numerical Ka
Acid-buffer pH
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[H⁺] ≈ Ka × n(HA) / n(A⁻)
For the stated weak-acid / conjugate-base buffer model, obtain the acid and conjugate-base amounts after any neutralisation first. With both present in the same solution volume, their concentration ratio equals their amount ratio. The approximation needs appreciable amounts of both partners.
- n(HA), n(A⁻)
- amounts remaining after reaction (mol)
How an acid buffer responds
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The conjugate base consumes small added amounts of H⁺, while the weak acid consumes small added amounts of OH⁻. This limits the change in their ratio and hence in pH. Buffer capacity is finite; a buffer does not hold one exact pH after unlimited additions.
Half-neutralisation of a weak acid
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at half-neutralisation: pH ≈ pKa
In a monoprotic weak-acid / strong-base titration, the usual buffer approximation gives equal remaining acid and formed conjugate-base amounts at half the stoichiometric equivalence volume. Their ratio is one, so pH ≈ pKa. This requires the stated valid buffer model.
Choosing an indicator
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Choose a stated indicator whose transition interval lies within the steep pH change around the titration’s equivalence region. Use the colour change expected for the actual titration direction (which solution is in the burette). The end point is the observed colour change and should fall within the equivalence region. Equivalence need not be pH 7, and a shallow weak-acid / weak-base curve lacks a suitable sharp colour endpoint in the usual model.