How to Calculate pH from Hydrogen Ion Concentration [H+]
Master acid-base chemistry mathematics. Learn how to calculate pH, pOH, [H+], and [OH-] ion concentrations using logarithmic formulas and Kw constants.
How to Calculate pH from Hydrogen Ion Concentration [H+]
The pH scale measures the acidity or basicity (alkalinity) of aqueous solutions. First devised in 1909 by Danish biochemist Søren Sørensen, pH is a base-10 logarithmic scale that compresses wide variations in hydrogen ion concentration into an intuitive 0 to 14 index.
This guide details the mathematical equations for pH and pOH, the autoionization of water, and connects to the CalculatorAll pH Calculator.
The Core Acid-Base Equations
- pH from [H⁺]:
pH = -log₁₀[H⁺] - [H⁺] from pH:
[H⁺] = 10^(-pH) - pOH from [OH⁻]:
pOH = -log₁₀[OH⁻] - Water Autoionization Constant (at 25°C):
pH + pOH = 14.00 - Ion Product of Water:
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴
Worked Example: 0.0025 M Hydrochloric Acid (HCl)
Hydrochloric acid is a strong monoprotic acid that dissociates 100% in water, meaning [H⁺] = 0.0025 M (2.5 × 10⁻³ mol/L):
- Calculate pH:
pH = -log₁₀(0.0025) = -(-2.602) = 2.60 (Acidic). - Calculate pOH:
pOH = 14.00 - 2.60 = 11.40. - Calculate Hydroxide Concentration [OH⁻]:
[OH⁻] = 10^(-11.40) = 3.98 × 10⁻¹² M.
The Logarithmic pH Scale in Everyday Solutions
Because the pH scale is logarithmic, each whole pH step represents a 10-fold change in acidity:
| Solution | Typical pH | [H⁺] Concentration (M) | Classification |
|---|---|---|---|
| Battery Acid (H₂SO₄) | 0.5 | 0.316 M | Strongly Acidic |
| Gastric Stomach Acid | 1.5 – 2.0 | 0.01 – 0.03 M | Strongly Acidic |
| Lemon Juice / Vinegar | 2.4 | 4.0 × 10⁻³ M | Moderately Acidic |
| Black Coffee | 5.0 | 1.0 × 10⁻⁵ M | Weakly Acidic |
| Pure Deionized Water | 7.0 | 1.0 × 10⁻⁷ M | Neutral |
| Human Blood Plasma | 7.35 – 7.45 | ~4.0 × 10⁻⁸ M | Slightly Alkaline |
| Household Bleach | 12.5 | 3.16 × 10⁻¹³ M | Strongly Alkaline |
Try the numbers with our calculator
Use your own assumptions instead of relying on a generic example.
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