What pH measures
pH expresses how acidic or basic a water solution is, through the concentration of hydrogen ions: pH = −log10[H⁺]. Because the scale is logarithmic, each unit is a factor of ten. A solution at pH 3 has ten times more hydrogen ions than one at pH 4 and ten thousand times more than pure water at pH 7.
The formulas
- pH = −log10[H⁺] and pOH = −log10[OH⁻]
- pH + pOH = 14 at 25 °C, since [H⁺] × [OH⁻] = 10⁻¹⁴
- Strong acid (HCl, HNO3): fully dissociated, [H⁺] ≈ concentration × number of H⁺ per molecule
- Strong base (NaOH, KOH): [OH⁻] ≈ concentration × number of OH⁻, then pH = 14 − pOH
- Weak acid: solve Ka = [H⁺]² ÷ (C − [H⁺]), with Ka = 10^−pKa
The calculator also includes water’s own ions, so very dilute solutions correctly approach pH 7.
Worked example: vinegar
Household vinegar contains about 5% acetic acid, around 0.83 M, with a pKa of 4.76.
- Ka = 10^−4.76 = 1.74 × 10⁻⁵.
- Solving the equation gives [H⁺] ≈ 0.0038 M.
- pH = −log10(0.0038) = 2.42.
- Only about 0.46% of the acetic acid molecules are dissociated, which is what makes it a weak acid.
pH of everyday substances
| Substance | Typical pH |
|---|---|
| Stomach acid | 1 to 2 |
| Lemon juice | about 2 |
| Vinegar | about 2.4 |
| Coffee | about 5 |
| Rain | about 5.6 |
| Pure water (25 °C) | 7.0 |
| Blood | 7.35 to 7.45 |
| Seawater | about 8.1 |
| Baking soda in water | about 8.3 |
| Household ammonia | about 11.5 |
| Bleach | 12 to 13 |
Strong versus weak
A strong acid such as hydrochloric acid gives up all its protons: 0.01 M HCl has a pH of 2. A weak acid at the same concentration gives up only a small share: 0.01 M acetic acid has a pH of about 3.4. The lower the pKa, the stronger the acid.
Limits of the calculation
- Activity: above about 0.1 M, ions interact and the real pH differs from the concentration-based value.
- Temperature: pure water is pH 7 only at 25 °C; at 37 °C it is about 6.8.
- Polyprotic acids such as phosphoric or citric acid release a second proton at higher pH. The calculator uses the first step, which sets the pH of their solutions in most cases.
- Safety: concentrated acids and bases cause burns. Always add acid to water, not water to acid.