What is pH and How to Calculate It

The pH scale is one of the most important concepts in chemistry. It measures how acidic or basic (alkaline) a solution is, on a scale from 0 to 14. Understanding pH is essential for chemistry, biology, environmental science, and even cooking.

The pH Scale

The Math Behind pH

pH from [H⁺] Concentration

pH is the negative logarithm of the hydrogen ion concentration:

pH = −log₁₀[H⁺]

Example 1

If [H⁺] = 0.001 M (which is 10⁻³ M):

• pH = −log₁₀(10⁻³) = 3 (acidic)

Example 2

If [H⁺] = 2.5 × 10⁻⁵ M:

• pH = −log₁₀(2.5 × 10⁻⁵) = 4.60 (acidic)

Working Backwards: [H⁺] from pH

[H⁺] = 10⁻ᵖᴴ

If pH = 9: [H⁺] = 10⁻⁹ = 0.000000001 M

pOH and the [H⁺]/[OH⁻] Relationship

At 25°C, pH and pOH are related:

pH + pOH = 14

And the ion product of water:

[H⁺] × [OH⁻] = 10⁻¹⁴ (at 25°C)

Example

If pH = 4:

• pOH = 14 − 4 = 10
• [H⁺] = 10⁻⁴ M
• [OH⁻] = 10⁻¹⁰ M

Strong vs. Weak Acids

Strong Acids

Completely dissociate in water. The [H⁺] equals the acid concentration.

Common strong acids: HCl, H₂SO₄, HNO₃, HBr, HI, HClO₄

Example: 0.01 M HCl

• [H⁺] = 0.01 M
• pH = −log(0.01) = 2.0

Weak Acids

Only partially dissociate. You need the acid dissociation constant (Ka) to calculate pH.

Example: 0.1 M acetic acid (Ka = 1.8 × 10⁻⁵)

Using the approximation for weak acids:

1. Set up the equilibrium: Ka = [H⁺][A⁻]/[HA]
2. Assume x = [H⁺]: 1.8 × 10⁻⁵ = x²/0.1
3. x = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³
4. pH = −log(1.34 × 10⁻³) = 2.87

Buffer Solutions

A buffer resists changes in pH when small amounts of acid or base are added. Buffers consist of:

• A weak acid and its conjugate base, OR
• A weak base and its conjugate acid

The Henderson-Hasselbalch Equation

pH = pKa + log₁₀([A⁻]/[HA])

Example: Acetate Buffer

Mix 0.1 M acetic acid (pKa = 4.74) with 0.15 M sodium acetate:

pH = 4.74 + log(0.15/0.1) = 4.74 + 0.176 = 4.92

Why pH Matters

In Biology

• Blood pH must stay between 7.35 – 7.45 (slightly basic)
• Enzymes work best at specific pH ranges
• Stomach acid (pH ~1.5) is essential for digestion

In Environmental Science

• Rain is naturally slightly acidic (pH ~5.6 due to CO₂)
• Acid rain has pH < 5.0 — harmful to ecosystems
• Ocean acidification: pH has dropped from 8.2 to 8.1 since pre-industrial times

In Everyday Life

• Swimming pools should be pH 7.2 – 7.8
• Soil pH affects plant growth (most prefer 6.0 – 7.0)
• Shampoo is typically pH 4.5 – 5.5 to match scalp acidity

Quick Reference

Calculate pH, pOH, [H⁺], and [OH⁻] instantly with our pH Calculator. Enter any value and get all the others — plus classification and real-world examples.