pH, pOH and Hydrogen Ion Converter

pH ⇄ pOH ⇄ [H⁺] ⇄ [OH⁻] with temperature as a real input, because pH + pOH is 13.99 at 25 °C and 12.25 at 100 °C — so pure water boils at pH 6.13 and is still neutral. Computed from IAPWS R11-24, not from a hard-coded 14.

Two logarithms and one temperature-dependent constant

Where neutral actually is, degree by degree

The pH of some familiar things, as published

pH is not confined to 0–14, and above 1 M it is not −log[H⁺] either

Neutral is not pH 7, and that is the whole point

Almost every pH page on the web says that pH plus pOH is 14, and that pH 7 is neutral. Both are true at one temperature and false everywhere else. pH is defined as minus the base-ten logarithm of hydrogen ion activity, pOH the same for hydroxide, and the two are linked by the ion product of water: [H⁺] × [OH⁻] = K_w, so pH + pOH = pK_w. The point is that K_w is strongly temperature dependent. At 25 °C pK_w is 13.9944 — which is where the famous 14 comes from, and it is not 14.00. At 0 °C it is 14.9466 and at 100 °C it is 12.2537. Divide each by two and you get the neutral point: pH 7.473 in ice water, pH 6.997 at room temperature, pH 6.127 in a kettle. That is a swing of 1.346 pH units, and the whole of it is invisible on a page that hard-codes 14.

Boiling water at pH 6.13 is not acidic. It is neutral. This is the sentence worth taking away. Neutral means [H⁺] = [OH⁻], not pH 7. In a kettle both ion concentrations have risen by a factor of 7.42 because water dissociates more readily when it is hot, and they have risen together, so the water is exactly as neutral as it was cold. Only the number has changed. This is also why a pH meter has to be temperature compensated and why a “pH 7.00” buffer is only pH 7.00 at the temperature printed on the bottle.

Where the 6.14 you may have seen comes from. The figure usually quoted for boiling water is pH 6.14, and it is a slightly old number. It corresponds to K_w = 51.3 × 10⁻¹⁴, that is pK_w = 12.2899, which halves to 6.145. IAPWS’s current release gives pK_w = 12.2537 at 100 °C and therefore pH 6.127. The difference is 0.018 of a pH unit — it changes nothing about the argument, and this page prints the newer figure and says where the older one came from rather than quietly disagreeing with every textbook.

pH is not confined to 0 to 14. One molar strong acid is pH 0 and two molar is pH −0.30; concentrated hydrochloric acid at about 12 molar computes to pH -1.08. The page will print those. What it will also tell you is that the simple treatment has broken down long before you get there, because pH is a logarithm of ACTIVITY and activity parts company with concentration above roughly 0.1 mol/L. McCarty and Vitz report 7.6 M hydrochloric acid at about pH −1.85 where the concentration formula gives −0.88 — a full unit, because the mean ionic activity coefficient has climbed past nine. The answer is still negative; it is just more negative than the arithmetic suggests.

What the strong-acid and strong-base modes actually do. Not −log c. They solve the charge balance [H⁺] = c + K_w/[H⁺] exactly, which matters at the dilute end: 10⁻⁸ molar hydrochloric acid is pH 6.976, not pH 8 — an acid cannot make water alkaline, and the naive formula says it can. Both figures are printed side by side so you can see the size of the error. Strong means fully dissociated: hydrochloric, nitric, perchloric, sodium and potassium hydroxide. Sulfuric acid is strong in its first proton only and is not covered.

Weak acids need a pKa, and this page asks for one rather than guessing. Given a concentration and a pKa it solves the quadratic for a monoprotic weak acid, K_a = [H⁺]²/(c − [H⁺]), which is exact for that model. The model’s own assumptions are the interesting part and the page reports the term it drops: water’s own contribution, K_w/[H⁺]², is shown in the results, and when it exceeds one per cent the page says the answer is no longer trustworthy. The buffer mode uses Henderson–Hasselbalch, pH = pKa + log([A⁻]/[HA]), which assumes the ratio you type is the ratio of the species actually present — true when both are well above 10⁻³ molar and the ionic strength is low, and progressively untrue otherwise. The pKa values in the dropdown are at 25 °C and zero ionic strength, as the CRC handbook publishes them, and they are NOT temperature corrected, so the temperature box moves pK_w and the neutral point but does not move the pKa. That is a limitation, and stating it is better than pretending to a correction this page does not have.

Where this page stops. It does not do dilutions or molarity from a mass — the laboratory utilities section owns C1V1 = C2V2, serial dilution and molarity, and duplicating them here would just be a second answer to maintain. For parts per million in a gas see the gas concentration converter, which makes the same kind of point about reference conditions; for calcium and magnesium in water see the water hardness converter. For the percentage-strength side of a solution — % w/w against % w/v, and the density that separates them — see the percent concentration converter. And for another quantity whose published value moves with temperature in a way people forget, the density and specific gravity converter makes the same argument about water itself.

Frequently asked questions

Related calculators

References

1. International Association for the Properties of Water and Steam. IAPWS R11-24, Revised Release on the Ionization Constant of H₂O (iapws.org). Fetched and implemented in full. Gives pK_w as a function of temperature and of the density of water, its seven parameters, and six test values in Table 2. Those test values are reproduced by this page’s implementation to better than 5×10^-7 in pK_w, which is how the parameters’ signs were established: the fetched table prints magnitudes, and the one sign pattern of sixty-four that reproduces all six test values was the one used.
2. Kell, G.S. Density, thermal expansivity, and compressibility of liquid water from 0 °C to 150 °C. Journal of Chemical and Engineering Data 20 (1975) 97-105. The rational fit for the density of liquid water at 1 atm reproduced in every handbook since; it supplies the density the IAPWS ionization equation needs. It puts water’s maximum density at 999.972 kg/m³ near 3.98 °C and gives 958.36 kg/m³ at 100 °C, both of which agree with the published values to about one part in 10⁵.
3. McCarty, C.G. and Vitz, E. pH Paradoxes: Demonstrating That It Is Not True That pH ≡ -log[H⁺]. Journal of Chemical Education 83 (2006) 752-757. Fetched. States that pH is defined as -log a(H⁺), not -log[H⁺]; that 0.01 M HCl has a pH of 2.04 rather than 2.00; and that the pH of 7.6 M HCl is about -1.85 where -log[H⁺] gives -0.88. That last figure is the reason this page will print a negative pH and then tell you not to trust it.
4. CRC Handbook of Chemistry and Physics, “Dissociation constants of inorganic acids and bases”, after Perrin, D.D., Ionization Constants of Inorganic Acids and Bases in Aqueous Solution, 2nd edition, Pergamon, Oxford, 1982. Every inorganic pK_a in the dropdown comes from this table. The table’s own note matters: “all values refer to dilute aqueous solutions at zero ionic strength at the temperature indicated”, which is exactly the condition a real solution is not in.
5. CRC Handbook of Chemistry and Physics, 84th edition (2004), dissociation constants of organic acids, as reproduced in the Saylor Foundation’s General Chemistry: Principles, Patterns and Applications Appendix C. Acetic acid 4.756, formic 3.75, benzoic 4.204, citric 3.13 / 4.76 / 6.40, all at 25 °C.
6. United States Environmental Protection Agency. What is Acid Rain? (epa.gov/acidrain). “Normal rain has a pH of about 5.6; it is slightly acidic because carbon dioxide (CO2) dissolves into it forming weak carbonic acid.” Acid rain “usually has a pH between 4.2 and 4.4”. The same page says “7.0 is neutral”, which is true at 25 °C and is the simplification this page is about.
7. National Oceanic and Atmospheric Administration. Ocean acidification (noaa.gov/education). “The ocean’s average pH is now around 8.1”, having “fallen by 0.1 pH units” since the Industrial Revolution, which NOAA describes as “approximately a 30 percent increase in acidity”. A fall of exactly 0.10 pH units is a 25.89% rise in hydrogen ion concentration and a 30% rise is 0.1139 units, so the pairing is a rounding of a slightly larger fall; the arithmetic is this page’s, and it is the reason a logarithmic scale needs a calculator.
8. U.S. Food and Drug Administration. Approximate pH of Foods and Food Products, the table that accompanies the low-acid canned food regulations in 21 CFR 113 and 114. A work of the United States Government. Every food pH range on this page is quoted from it as a RANGE, because that is how it is published — a single pH for “lemon juice” would be an invention.