Chemistry
pH and pOH calculator
Enter any one of pH, pOH, [H⁺] and [OH⁻] and get the other three, with the classification of the solution. All values refer to 25 °C.
What pH measures
pH is the negative base-ten logarithm of the hydrogen ion concentration: pH = −log[H⁺]. The logarithmic scale exists because the concentrations involved span fourteen orders of magnitude, from about 1 mol/L in concentrated acids to 10⁻¹⁴ in strong bases, and writing them out would be impractical. The consequence is that each pH unit is a factor of ten: a solution at pH 3 is ten times more acidic than one at pH 4 and a hundred times more than one at pH 5.
Pure water dissociates to a tiny extent, and at 25 °C the product of the two ion concentrations is always 10⁻¹⁴. Everything else follows from this: if [H⁺] rises, [OH⁻] must fall in proportion, and the sum pH + pOH stays 14. Neutral sits at 7 because that is the point where the two concentrations are equal, both at 10⁻⁷ mol/L.
The value 7 as neutral holds only at 25 °C, however. The ion product of water rises with temperature, and at 50 °C pure water has a pH of 6.63 while remaining perfectly neutral: it still has equal concentrations of H⁺ and OH⁻. That is why a pH figure without a temperature is incomplete, even though school practice always assumes 25 °C.
Common mistakes
- Treating the scale as linear: between pH 2 and pH 5 there is not a factor of 2.5 but a factor of a thousand. This is what leads people to underestimate the difference between two solutions.
- Applying the strong-acid formula to a weak acid: 0.1 M acetic acid does not have pH 1, because it dissociates only slightly. Weak acids need the dissociation constant Ka.
- Forgetting that in diprotic acids the H⁺ concentration does not equal that of the acid: sulfuric acid releases two per molecule.
Frequently asked questions
How do you calculate pH from a concentration?
pH = −log₁₀[H⁺]. A solution with 0.001 mol/L of H⁺ ions has pH 3. In the other direction, [H⁺] = 10⁻ᵖᴴ.
Why do pH and pOH always add to 14?
Because at 25 °C the ion product of water is [H⁺]·[OH⁻] = 10⁻¹⁴. Taking the negative logarithm of both sides makes the two values sum to 14. At other temperatures the constant changes and the sum is no longer exactly 14.
How do you calculate the pH of a strong acid?
A strong monoprotic acid is fully dissociated, so the H⁺ concentration equals that of the acid: the pH is the negative logarithm of that concentration. 0.01 M HCl has pH 2.
Can pH be negative or greater than 14?
Yes, for very concentrated solutions, although it is rare outside the laboratory. 2 M hydrochloric acid has a pH of about −0.3. In that range, however, formulas based on concentrations lose accuracy and activities should be used instead.
How this calculation works
Definitions: pH = −log₁₀[H⁺] and pOH = −log₁₀[OH⁻], with concentrations in mol/L. Inverses: [H⁺] = 10⁻ᵖᴴ and [OH⁻] = 10⁻ᵖᴼᴴ. Ion product of water at 25 °C: Kw = [H⁺]·[OH⁻] = 1.0·10⁻¹⁴, so pH + pOH = 14. Strong monoprotic acid of concentration C: [H⁺] = C, so pH = −log C. Strong monobasic base: [OH⁻] = C, so pOH = −log C and pH = 14 + log C. Classification at 25 °C: pH < 7 acidic, pH = 7 neutral, pH > 7 basic.
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