pH is the measure of how acidic or basic a solution is. Understanding how to calculate it from first principles is fundamental to chemistry, biology, medicine, and environmental science.
The pH Formula
pH is defined as the negative base-10 logarithm of the hydrogen ion concentration:
pH = −log₁₀[H⁺]
Where [H⁺] is the concentration of hydrogen ions in moles per litre (mol/L or M).
Example 1: [H⁺] = 0.001 M (10⁻³ M):
- pH = −log(0.001) = −(−3) = 3 (acidic)
Example 2: [H⁺] = 1 × 10⁻⁷ M (pure water):
- pH = −log(10⁻⁷) = 7 (neutral)
Example 3: [H⁺] = 1 × 10⁻¹¹ M:
- pH = 11 (basic/alkaline)
The pH Scale
| pH | Classification | Example |
|---|---|---|
| 0–2 | Strongly acidic | Battery acid, stomach acid (1–2) |
| 3–4 | Acidic | Vinegar (2.4), orange juice (3.5) |
| 5–6 | Mildly acidic | Black coffee (5), rainwater (5.6) |
| 7 | Neutral | Pure water |
| 8–9 | Mildly basic | Seawater (8), baking soda (8.3) |
| 10–12 | Basic | Milk of magnesia (10.5) |
| 13–14 | Strongly basic | Bleach (12.5), drain cleaner (14) |
Calculating [H⁺] from pH
The reverse calculation — finding ion concentration from pH:
[H⁺] = 10^(−pH)
Example: pH = 4.5:
- [H⁺] = 10^(−4.5) = 3.16 × 10⁻⁵ mol/L
The Relationship Between pH and pOH
In aqueous solutions at 25°C:
pH + pOH = 14
pOH = −log₁₀[OH⁻]
If you know the hydroxide ion concentration instead of hydrogen ions:
Example: [OH⁻] = 1 × 10⁻³ M:
- pOH = −log(10⁻³) = 3
- pH = 14 − 3 = 11 (basic)
Calculating pH of Strong Acids
Strong acids (HCl, HNO₃, H₂SO₄) dissociate completely in water:
[H⁺] = Concentration of acid (for monoprotic acids)
pH = −log[acid concentration]
Example: 0.05 M HCl:
- [H⁺] = 0.05 M
- pH = −log(0.05) = 1.30
For H₂SO₄ (diprotic): [H⁺] = 2 × [H₂SO₄]
Calculating pH of Weak Acids (Using Ka)
Weak acids partially dissociate. Use the acid dissociation constant Ka:
[H⁺] = √(Ka × C)
pH = −log(√(Ka × C)) = ½ × (pKa − log C)
Where C = initial acid concentration, Ka = dissociation constant.
Example: 0.1 M acetic acid (Ka = 1.8 × 10⁻⁵):
- [H⁺] = √(1.8 × 10⁻⁵ × 0.1) = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³
- pH = −log(1.34 × 10⁻³) = 2.87
(Compared to strong acid: 0.1 M HCl would have pH = 1.0 — much more acidic)
Calculating pH of Strong Bases
Strong bases (NaOH, KOH) dissociate completely:
[OH⁻] = concentration of base
pOH = −log[OH⁻]
pH = 14 − pOH
Example: 0.02 M NaOH:
- pOH = −log(0.02) = 1.70
- pH = 14 − 1.70 = 12.30
Buffer Solutions
A buffer resists pH change. The Henderson-Hasselbalch equation calculates buffer pH:
pH = pKa + log([A⁻]/[HA])
Where [A⁻] = conjugate base concentration, [HA] = weak acid concentration.
Example: Acetic acid/acetate buffer, pKa = 4.74, equal concentrations:
- pH = 4.74 + log(1) = 4.74 + 0 = 4.74
Buffers work best within ±1 pH unit of the pKa.
Practical Applications
Blood pH: Maintained at 7.35–7.45 by bicarbonate buffering. Below 7.35 = acidosis; above 7.45 = alkalosis.
Swimming pools: Optimal pH 7.2–7.8. Below 7.0 irritates eyes and corrodes equipment; above 7.8 reduces chlorine effectiveness.
Soil pH: Affects nutrient availability. Most plants thrive at 6.0–7.0; blueberries prefer 4.5–5.5.
Use our logarithm calculator to quickly compute −log values for pH and pOH calculations.