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pH from Hydrogen Ion Concentration

Also known as pH formula · pH from concentration

pH=−log⁡10 [H+]\mathrm{pH} = -\log_{10}\,[\mathrm{H^+}]
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Worked example: [H+] = 1.0e-3 mol/L → pH = 3. Press Try an example to run it live, then adjust anything.

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Where pH from Hydrogen Ion Concentration fits

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Cooling Tower LSI at Cycles of ConcentrationLangelier Saturation Index (LSI)Langelier Saturation Index from a Full Water AnalysisRyznar Stability Index (RSI)
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See also

pOH from Hydroxide Ion Concentration: The same definition from the base end, for when the reagent bottle is caustic rather than acid.Fick's First Law of Diffusion: Both use hydrogen ion concentration.Ion Concentration from Dissociation: Both use hydrogen ion concentration.Percent Ionization of a Weak Acid: Both use hydrogen ion concentration.Henderson–Hasselbalch Equation (Weak Acid Buffer): Both use ph.pH and pOH Relation: Both use ph.
6 more relatedpH of a Weak Acid from Ka: Both use ph.pH of a Weak Base from Kb: Both use ph.Cooling Tower LSI at Cycles of Concentration: Both use ph.Langelier Saturation Index (LSI): Both use ph.Langelier Saturation Index from a Full Water Analysis: Both use ph.Ryznar Stability Index (RSI): Both use ph.
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pH from Hydrogen Ion Concentration explained

pH[H+]

Hydrogen ion concentrations in water span more than ten orders of magnitude, so in 1909 the Danish chemist Søren Sørensen, working at the Carlsberg brewery laboratory, compressed them onto a logarithmic scale. Each pH unit is a factor of ten: lemon juice at pH 2 carries a hundred times the hydrogen ion concentration of tomato juice at pH 4. Pure water at 25 °C sits at pH 7, where [H⁺] = 1.0 × 10⁻⁷ mol/L. The logarithm takes the concentration in mol/L, and the inverse direction is exact: [H⁺] = 10−pH10^{-\text{pH}}.

In water treatment pH is the master variable. Boiler water is typically held between 10.5 and 11.5 to suppress corrosion, cooling towers near 7–9 to balance scale against corrosion, and municipal drinking water around 7.0–8.5. A pH swing of a single unit, a tenfold chemistry change, is often the first sign that a chemical feed pump has failed.

pH from Hydrogen Ion Concentration formula

pH=−log⁡10 [H+]\mathrm{pH} = -\log_{10}\,[\mathrm{H^+}]
Where
  • pH\mathrm{pH}= pH
  • [H+][\mathrm{H^+}]= Hydrogen ion concentration (M)
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Acid–base relations

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

Revised 31 October 2026
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formula.expert. (2026, October 31). pH from Hydrogen Ion Concentration Formula & Calculator. https://formula.expert/solvers/ph-hydrogen-ion

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