How to use the ph calculator
- Choose the solution: strong acid, weak acid, strong base or weak base.
- Enter the concentration in mol/L. You can write numbers like 1e-3.
- For a weak acid or base, enter Ka or Kb, or switch to pKa or pKb. Look up the constant for your own substance; the default is only an example.
- Read the pH, pOH and percent ionized. The page also solves the equilibrium again with water included and shows that pH.
Formula
weak acid: Ka = x^2 / (C - x), so x = (-Ka + sqrt(Ka^2 + 4 Ka C)) / 2
pH = -log10[H+] and pOH = 14 - pH (at 25 C)
percent ionized = x / C x 100
strong acid with water: [H+] = (C + sqrt(C^2 + 4 Kw)) / 2, with Kw = 1.0e-14
For a weak base the same equation uses Kb, and x is the hydroxide concentration. The full equilibrium with water is the cubic y^3 + K y^2 - (K C + Kw) y - K Kw = 0, solved here by repeated halving, so you can see when ignoring water matters.
A 0.10 mol/L weak acid with Ka 1.8e-5
Solving x^2 / (0.1 - x) = 1.8e-5 gives x = 0.001332671, so pH = -log10(0.001332671) = 2.875 and pOH = 11.125. The share ionized is 0.001332671 / 0.1 = 1.333%. Putting x back in the equilibrium expression returns 0.000018 exactly, and the version that includes water gives pH 2.875 too.
The same numbers as a weak base with Kb 1.8e-5 give a pH of 11.125. A 0.01 mol/L strong acid has pH 2.000, and a 1e-8 mol/L strong acid has pH 6.978 rather than 8, because the water supplies hydrogen ions of its own. A very weak acid, 0.001 mol/L with Ka 1e-9, gives pH 6.0002 without water and 5.9981 with it.
Strong and weak
A strong acid or base is treated as fully dissociated, so the ion concentration equals the starting concentration. A weak acid or base ionizes only in part, and the share that ionizes depends on both its constant and its concentration: more dilute solutions ionize a larger share.
Many textbooks use the shortcut x = sqrt(Ka x C), which is fine when less than about 5% ionizes. This page solves the full quadratic, so it also works when the shortcut would be off, and it flags those cases.
When water matters
Water makes about 1e-7 mol/L of hydrogen ions by itself. When an acid produces fewer ions than that, the usual equation misses part of the picture. The page warns when the ions made are below 1e-6 mol/L and shows the pH that includes water. To prepare a solution of a given strength, the Solution Dilution Calculator finds the volumes, and the Moles to Grams Calculator converts amounts.
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Assumptions and limits
- The temperature is 25 C, where pH + pOH = 14 and Kw = 1.0e-14. Other temperatures shift these values.
- One acid or base with a single ionization step is in water, with no other acids, bases or buffers.
- Ions act ideally. In concentrated solutions, activity effects change the real pH.
- The constants are whatever you enter. The default values are examples, not data for a particular substance.
Frequently asked questions
What is the difference between Ka and pKa?
pKa is the negative base 10 logarithm of Ka. A smaller pKa means a stronger acid. Switch the strength setting to enter pKa directly; for example, pKa 4.74 means Ka is about 1.8e-5.
Why is the pH of a very dilute strong acid not simply minus the log of its concentration?
Below roughly 1e-6 mol/L, the hydrogen ions from the water are as numerous as those from the acid, so both have to be counted. The page does that for strong acids and bases.
What does percent ionized tell me?
It is the share of the original acid or base that has reacted with water at equilibrium. A weak acid at 0.10 mol/L with Ka 1.8e-5 is about 1.3% ionized.
Can I use it for acids with more than one proton?
Only for the first ionization step. Acids such as sulfuric or phosphoric acid have later steps that this single-equilibrium model does not include.