pH Formula
The pH formula pH = -log[H⁺] measures the acidity or basicity of a solution.
Learn to calculate pH and hydrogen ion concentration with examples.
The Formula
pH = -log[H⁺]
The pH scale measures how acidic or basic a solution is. It ranges from 0 (very acidic) to 14 (very basic), with 7 being neutral.
Variables
| Symbol | Meaning |
|---|---|
| pH | The pH value (dimensionless, scale from 0 to 14) |
| [H⁺] | Concentration of hydrogen ions (measured in moles per liter, mol/L) |
| log | Base-10 logarithm |
Example 1
A solution has a hydrogen ion concentration of 0.001 mol/L. What is its pH?
[H⁺] = 0.001 = 10⁻³ mol/L
pH = -log(10⁻³) = -(-3)
pH = 3 (acidic)
Example 2
A solution has a pH of 5.5. What is the hydrogen ion concentration?
Rearrange: [H⁺] = 10⁻ᵖᴴ
[H⁺] = 10⁻⁵·⁵
[H⁺] ≈ 3.16 × 10⁻⁶ mol/L
When to Use It
Use the pH formula to measure or calculate acidity.
- Determining whether a solution is acidic (pH < 7), neutral (pH = 7), or basic (pH > 7)
- Converting between pH and hydrogen ion concentration
- Water quality testing and environmental science
- Biochemistry and medical applications (blood pH is about 7.4)
Key Notes
- The pH scale is logarithmic — each unit represents a tenfold change in H⁺ concentration; pH 3 is 10× more acidic than pH 4, and 100× more acidic than pH 5
- pOH measures hydroxide ion concentration: pOH = −log[OH⁻]; at 25°C, pH + pOH = 14 (the water autoionization constant)
- The 0–14 range is a guideline, not a hard limit — concentrated strong acids can have negative pH values (e.g., pH ≈ −1 for a 10 M HCl solution)
Key Notes
- pH = −log[H⁺]; pOH = −log[OH⁻]; pH + pOH = 14 (at 25°C): Each pH unit represents a 10-fold change in hydrogen ion concentration. pH 3 is 10× more acidic than pH 4, and 100× more acidic than pH 5. The log scale compresses a concentration range of 10¹⁴ into a 0–14 scale.
- Water autoionization: Kw = [H⁺][OH⁻] = 1×10⁻¹⁴ at 25°C: Pure water at 25°C has [H⁺] = [OH⁻] = 10⁻⁷ mol/L, giving pH = 7 (neutral). At higher temperatures, Kw increases — "neutral" pH at 37°C (body temperature) is closer to 6.8.
- Strong vs weak acids: Strong acids (HCl, H₂SO₄, HNO₃) dissociate completely — pH = −log(concentration). Weak acids partially dissociate — use Ka and an ICE table, or the approximation [H⁺] ≈ √(Ka × C) when Ka << C.
- Buffer equation: pH = pKa + log([A⁻]/[HA]): The Henderson-Hasselbalch equation describes buffer solutions. Buffers work best within ±1 pH unit of their pKa. Blood is buffered at pH 7.4 primarily by the carbonic acid/bicarbonate system (pKa ≈ 6.1, with CO₂ driven off by breathing).
- Applications: pH control is critical in enzyme activity (most enzymes have narrow pH optima), drug stability and bioavailability, water treatment, food preservation, soil science, and swimming pool and aquarium maintenance.