How pH Is Calculated: Formula, Scale, and Hydrogen-Ion Concentration
Understand how pH is calculated from hydrogen ion concentration, how the logarithmic scale works, and how to convert between pH and [H⁺] for acids and bases.
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What Is pH?
pH is a logarithmic scale measuring the concentration of hydrogen ions (H⁺) in a solution. It tells you how acidic or basic a substance is.
Formula: pH = −log₁₀[H⁺]
Where [H⁺] is the molar concentration of hydrogen ions in mol/L (molarity).
Reverse: [H⁺] = 10^(−pH)
The pH Scale
Calculating pH from [H⁺]
Example 1: [H⁺] = 0.001 mol/L = 10⁻³ mol/L pH = −log₁₀(10⁻³) = −(−3) = pH 3
Example 2: [H⁺] = 0.0000001 mol/L = 10⁻⁷ mol/L pH = −log₁₀(10⁻⁷) = pH 7 (neutral — pure water)
Example 3: [H⁺] = 3.2 × 10⁻⁵ mol/L pH = −log₁₀(3.2 × 10⁻⁵) = −(log₁₀(3.2) + log₁₀(10⁻⁵)) = −(0.505 − 5) = pH 4.50
Calculating [H⁺] from pH
[H⁺] = 10^(−pH)
Example: pH = 6.8 [H⁺] = 10^(−6.8) = 1.585 × 10⁻⁷ mol/L
pOH and the Relationship with pH
pOH = −log₁₀[OH⁻]
At 25°C: pH + pOH = 14 (the water constant at standard temperature)
If pH = 3: pOH = 14 − 3 = 11, meaning [OH⁻] = 10⁻¹¹ mol/L
Logarithmic Nature: What pH Units Mean
Because pH is logarithmic, each whole-number change = 10× change in [H⁺]: - pH 3 is 10× more acidic than pH 4 - pH 3 is 100× more acidic than pH 5 - pH 2 (stomach acid) is 1,000× more acidic than pH 5 (coffee)
Buffer Systems
A buffer resists pH change when acid or base is added. The Henderson-Hasselbalch equation describes buffer pH:
pH = pKₐ + log([A⁻]/[HA])
Where pKₐ is the acid's dissociation constant, [A⁻] is conjugate base concentration, and [HA] is acid concentration. Biological systems (blood pH ~7.4) are maintained by carbonic acid-bicarbonate buffers.
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Frequently Asked Questions
- What is the formula for calculating pH?
- pH = −log₁₀[H⁺], where [H⁺] is hydrogen ion concentration in mol/L. If [H⁺] = 0.0001 mol/L = 10⁻⁴, then pH = 4. Conversely, [H⁺] = 10^(−pH). A pH of 7 corresponds to [H⁺] = 10⁻⁷ = 0.0000001 mol/L — pure neutral water.
- How much more acidic is pH 3 than pH 5?
- pH 3 has 100× more hydrogen ions than pH 5. Each unit on the logarithmic scale represents a 10× difference in [H⁺] concentration. pH 3 vs. pH 5 is 2 units = 10² = 100× difference. This is why even small pH changes represent large shifts in actual acidity.
- What is neutral pH and why is water pH 7?
- At 25°C, pure water partially dissociates: H₂O → H⁺ + OH⁻. This produces exactly 10⁻⁷ mol/L of H⁺ and 10⁻⁷ mol/L of OH⁻. pH = −log(10⁻⁷) = 7. pH 7 is considered neutral because [H⁺] = [OH⁻]. Note: at higher temperatures, water's neutral pH drops slightly (pH 6.77 at 50°C).
- What is pH 7.4 in the human body?
- Blood pH is maintained at 7.35–7.45, with 7.4 as the typical value. This is slightly basic. The body uses the carbonic acid-bicarbonate buffer system and kidneys to maintain this narrow range. pH below 7.35 (acidosis) or above 7.45 (alkalosis) represents dangerous conditions requiring immediate treatment.
Last updated 7/28/2026