TAHA Engineering Toolsby TAHA Knowledge Lab

Chemical Engineering

pH & pOH Calculator

pH, pOH, [H⁺] and [OH⁻] from any one of them, using pH + pOH = pKw, with pKw for the temperature and an optional activity coefficient.

Inputs

Calculate from
A pH scale from 0 to 14 with pOH from 14 to 0 above it; neutral is marked at 7 = pKw ÷ 2.0246810121414121086420pHpOHneutral: pH = pKw ÷ 2acidicbasicpH + pOH = pKw (pKw ≈ 14.00 at 25 °C)
pH and pOH run in opposite directions and always add up to pKw. Below pKw ÷ 2 the solution is acidic, above it basic. The scale is shown for pKw = 14 (about 25 °C); at other temperatures pKw and the neutral point move. Each pH unit is a factor of 10 in [H⁺]. Diagram not to scale.

Scientific notation is fine, for example 1e-3 or 2.5e-9.

Leave 1 for the simple concentration-based calculation. Enter a value (for example from the Debye–Hückel or Davies equation) to work with activities. 0.05 to 1.5.

Result

pH
3
pOH
11
Hydrogen ion concentration [H⁺]
0.001
Hydroxide ion concentration [OH⁻]
1 × 10⁻¹¹
pKw used
14
Neutral pH at this pKw (pKw ÷ 2)
7
The solution is
Acidic (pH below 7)
Working
pH = −log₁₀(γ × [H⁺]) = −log₁₀(1 × 0.001) = 3 pOH = pKw − pH = 14 − 3 = 11 [H⁺] = 10^(−pH) ÷ γ = 0.001 mol/L [OH⁻] = 10^(−pOH) ÷ γ = 1 × 10⁻¹¹ mol/L Check: γ²[H⁺][OH⁻] = 10^(−pKw) = 1 × 10⁻¹⁴

pH = 3 and pOH = 11 (pKw 14): [H⁺] = 0.001 mol/L, [OH⁻] = 1 × 10⁻¹¹ mol/L.

  • γ = 1: this is the concentration-based value, often written p[H]. A pH meter measures activity, which differs from concentration, especially above about 0.01 mol/L of dissolved ions.
  • pKw used: 14.00 (approximate value at 25 °C). Neutral water has pH = pKw ÷ 2, which is 7 only near 25 °C.

Educational estimate — check the assumptions below.

About this calculator

pH tells how acidic a water-based solution is. It is the negative base-10 logarithm of the hydrogen-ion activity. pOH is the same for hydroxide ions. In water the two are linked by the ionic product of water: pH + pOH = pKw.

pKw is about 14.00 at 25 °C but changes with temperature (it is 13.26 at 50 °C), so “neutral” is pH 7 only near room temperature. This calculator converts between [H⁺], [OH⁻], pH and pOH for the pKw you choose. It is a conversion tool, not an equilibrium solver: it does not work out the pH of weak acids, buffers or mixtures.

Formula

pH = −log₁₀(aH⁺)    aH⁺ = γ × [H⁺] ÷ c°    pOH = −log₁₀(γ × [OH⁻] ÷ c°)

pH + pOH = pKw    [H⁺] = 10−pH ÷ γ    [OH⁻] = 10−pOH ÷ γ    neutral pH = pKw ÷ 2

[H⁺], [OH⁻] = ion concentrations (mol/L), c° = 1 mol/L, γ = activity coefficient (1 for the simple concentration-based calculation), a = activity, pKw = −log₁₀ Kw.

Worked example

  • [H⁺] = 1.0 × 10⁻³ mol/L, pKw 14.00, γ = 1: pH = −log₁₀(0.001) = 3.000; pOH = 14.00 − 3.000 = 11.000; [OH⁻] = 10⁻¹¹ mol/L. Acidic.
  • pH 7.40 at 25 °C with pKw 13.99: pOH = 6.59; [H⁺] = 10⁻⁷·⁴ = 3.98 × 10⁻⁸ mol/L.
  • Neutral water at 50 °C (pKw 13.26) has pH = 13.26 ÷ 2 = 6.63: it is neutral, not acidic.

Assumptions and limitations

  • With γ = 1 the calculation uses concentrations instead of activities. This is close only for dilute solutions (roughly below 0.01 mol/L of dissolved ions).
  • One activity coefficient γ is used for both H⁺ and OH⁻, and the activity of water is taken as 1.
  • The [H⁺] or [OH⁻] entered must be the actual ion concentration in the solution. For a strong acid or base it equals the acid or base concentration only in moderately dilute solutions; for weak acids, weak bases, buffers, mixtures, concentrated or very dilute solutions it does not, and an equilibrium calculation is needed.
  • The published pKw values are for pure water at 0.1 MPa (Bandura & Lvov 2006, Table 4). Dissolved salts and pressure change pKw.
  • A calculation tool only, not chemical handling advice. Follow the safety data sheet for acids and bases.

References

  • Bandura, A. V. and Lvov, S. N. (2006), “The Ionization Constant of Water over Wide Ranges of Temperature and Density”, J. Phys. Chem. Ref. Data 35 (1), 15–30 — pKw values in Table 4.
  • IUPAC, Quantities, Units and Symbols in Physical Chemistry (the “Green Book”): definition of pH from the hydrogen-ion activity.