pH Calculator
Calculate pH from hydrogen ion concentration or vice versa.
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What it does
The pH Calculator converts between pH and hydrogen ion concentration and estimates the pH of strong and weak acids and of buffers. Five modes cover the questions that come up at the bench: pH from a hydrogen ion concentration, concentration from a pH, the pH of a strong acid or base straight from its concentration, the pH of a weak acid from its concentration and pKa, and the pH of a buffer from the Henderson-Hasselbalch equation. Every result reports pH alongside both the hydrogen and hydroxide concentrations, so an answer can be checked against the definition rather than taken on trust. It is aimed at students, bench chemists and anyone sanity-checking an acidity value before an experiment.
How it works
pH is defined as minus the base-10 logarithm of the hydrogen ion concentration, with that concentration in mol/L, so the inverse is a concentration equal to 10 raised to the power of minus pH. The two ion concentrations are tied together by the ion product of water, Kw = [H+][OH-] = 1.0e-14 at 25 C, which is why every result also reports the hydroxide concentration as Kw divided by the hydrogen ion concentration. A strong acid or base has its own mode because it dissociates completely: the hydrogen ion concentration is the concentration multiplied by the number of protons released, so 0.10 M HCl gives pH 1.0000 and 0.050 M H2SO4 about 1.0000 when both protons are counted. That last figure is an approximation, since the second dissociation of sulfuric acid is not quite complete and treating it as fully dibasic understates the pH by a few hundredths in dilute solution. For a weak acid the tool does not use the usual square root approximation. It solves the full equilibrium, hydrogen ion concentration = (-Ka + the square root of (Ka squared + 4 times Ka times c)) / 2 with Ka = 10 raised to the power of minus pKa, which is exact for a monoprotic acid. For buffers it applies the Henderson-Hasselbalch equation, pH = pKa + log10(conjugate base over weak acid).
Worked example
A solution with a hydrogen ion concentration of 1.0e-3 mol/L returns pH = 3.0000 and a hydroxide concentration of 1.0e-14 / 1.0e-3 = 1.0000e-11 mol/L. Going the other way, pH 7 gives 1.0000e-7 mol/L. For 0.10 M acetic acid, pKa 4.76, the exact solution begins with Ka = 1.738e-5: the hydrogen ion concentration is (-1.738e-5 + the square root of ((1.738e-5) squared + 4 times 1.738e-5 times 0.10)) / 2 = 1.3096e-3 mol/L, so pH = 2.8829. The familiar approximation, half of (4.76 + 1.00), gives 2.88 and lands within 0.003 here because only about 1.3 percent of the acid has dissociated. Dilute the acid to 1.0e-6 M and the two methods diverge sharply: the full solution gives 6.0231 while the approximation gives 5.38, a gap of more than half a pH unit. A buffer holding equal concentrations of acetic acid and acetate returns pH = pKa = 4.76. Shifting the ratio to ten parts acetate to one part acid gives 4.76 + 1.00 = 5.76, and inverting it to one to ten gives 3.76.
When to use it
Use it to convert between pH and hydrogen ion concentration when writing up a measurement, to estimate where a weak acid stock will land before standardising it against a meter, or to work out the acid to salt ratio that puts a buffer at a target pH. Three limits deserve to be known before the number is trusted. First, the weak acid mode assumes a single monoprotic acid. For phosphoric acid, with a first pKa of 2.15, for citric acid, or for an amino acid, later dissociations and zwitterionic forms mean the first pKa alone will not give the right answer. Second, the buffer mode applies Henderson-Hasselbalch without checking whether the buffer can actually hold pH. The equation is trustworthy within roughly pKa plus or minus 1, that is a salt to acid ratio between 0.1 and 10. Ask for a ratio of 100 to 1 and the tool still returns a number, but almost no buffering capacity remains and the real pH will swing on the slightest addition of acid. Third, Kw is fixed at the 25 C value while a real measurement is temperature dependent: neutral pH is 6.81 at 37 C and close to 7.5 near 0 C, so a meter reading taken warm and converted here carries that offset. A pH outside the 0 to 14 window is reported as computed and flagged with a warning, because the arithmetic is right but the concentration is by then high enough that pH is no longer well described by concentration alone and activities would be needed instead.
FAQ
- How do I calculate pH from hydrogen ion concentration?
- Take the negative base-10 logarithm of the concentration in mol/L: pH = -log10[H+]. For a concentration of 1.0e-3 mol/L the pH is 3.0000, and the tool shows the matching hydroxide concentration of 1.0e-11 mol/L from Kw / [H+]. Note that pH is dimensionless and that concentration rather than activity is being used.
- How do I go from pH back to [H+]?
- Invert the definition: the concentration equals 10 raised to the power of minus pH. A pH of 7 corresponds to 1.0e-7 mol/L and a pH of 4.76 to 1.74e-5 mol/L. The tool accepts negative and fractional pH values, which is what strong acid stocks require: 1 M HCl has pH 0 and 10 M HCl about pH -1. Direct entry is not needed for those cases any more, because the strong acid mode does it from the concentration: 0.10 M HCl returns pH 1.0000, and 0.050 M H2SO4 about 1.0000 counting both protons. A pH outside the 0 to 14 window is flagged, since at that point activities rather than concentrations govern the reading.
- What is the difference between pH and pKa?
- pH measures the actual hydrogen ion concentration of a particular solution, while pKa is an intrinsic property of an acid: the pH at which half of it is deprotonated. The two coincide for a buffer when the acid and its conjugate base are present in equal amounts, which is why an equimolar acetate buffer sits at 4.76, the pKa of acetic acid. Away from that 1:1 point they diverge.
- Why does the weak acid mode differ from the textbook formula?
- The familiar pH = 0.5(pKa - log10 c) assumes the acid barely dissociates, an assumption that fails as the solution becomes more dilute. This tool solves the full quadratic, (-Ka + √(Ka² + 4·Ka·c)) / 2. At 0.10 M acetic acid the two agree, 2.8829 against 2.88, but at 1.0e-6 M the exact answer is 6.0231 while the approximation gives 5.38, a gap of more than half a pH unit.