The pH scale: measuring acidity
Learn what pH really measures, why the scale is logarithmic, how to calculate pH from [H⁺], and what the numbers mean in everyday life.
Quick answer
pH = −log[H⁺]: the negative base-10 logarithm of the hydrogen-ion concentration. Lower pH means more acidic; each unit is a tenfold change in [H⁺].
Example: For 0.010 M HCl (strong acid, fully dissociated), [H⁺] = 0.010 M and pH = −log(0.010) = 2.00.
What you will learn
- Define pH as the negative logarithm of [H⁺].
- Calculate pH from hydrogen-ion concentration and vice versa.
- Explain why the scale is logarithmic and what each unit means.
- Identify acidic, basic, and neutral pH values at 25 °C.
Why a logarithmic scale
Hydrogen-ion concentrations span an enormous range — from about 10 M in concentrated acid to 10⁻¹⁴ M in concentrated base. Writing all those zeros is impractical, so chemist Søren Sørensen (1909) introduced the logarithm:
The negative sign keeps everyday values positive: [H⁺] = 10⁻³ M becomes pH 3. Because it is base-10 log, each pH unit represents a tenfold change in [H⁺]. Going from pH 7 to pH 4 multiplies acidity by 10³ = 1000.
Reading the scale
At 25 °C, water autoionizes with Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, so:
- [H⁺] > 10⁻⁷ M (pH < 7): acidic — H⁺ dominates
- [H⁺] = 10⁻⁷ M (pH = 7): neutral — H⁺ and OH⁻ are equal
- [H⁺] < 10⁻⁷ M (pH > 7): basic — OH⁻ dominates
Familiar landmarks: stomach acid pH ~1.5–2, lemon juice ~2, pure water 7, blood 7.4, baking soda solution ~8.3, household ammonia ~11, drain cleaner ~13–14. Remember that pH 7 is neutral only at 25 °C — neutrality means [H⁺] = [OH⁻], whatever the number.
Calculating pH and [H⁺]
For strong acids, [H⁺] equals the acid concentration (complete dissociation): 0.010 M HCl → [H⁺] = 0.010 M → pH = −log(1.0 × 10⁻²) = 2.00.
To go backward: [H⁺] = 10^(−pH). A solution of pH 4.50 has [H⁺] = 10^(−4.50) = 3.2 × 10⁻⁵ M.
For weak acids, first find [H⁺] from the Ka equilibrium ([H⁺] ≈ √(Ka × C)), then take the log. Significant figures follow the log rules: the decimal places in pH match the significant figures in [H⁺] — pH 2.00 (two decimal places) corresponds to 0.010 M (two sig figs).
Measuring pH
pH is measured two ways: indicator paper/strips for quick estimates (compare the color to a chart, ±1 pH unit) and pH meters for precision (±0.01). A pH meter's glass electrode develops a voltage proportional to [H⁺]; it must be calibrated with standard buffers before use.
Note that pH electrodes measure activity rather than raw concentration — in very concentrated solutions the two diverge, which is one reason the simple pH math is reserved for dilute solutions.
Variables and units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Hydrogen-ion concentration | M | Molar concentration of hydrogen ions | |
| Water constant | M² | Ion product of water, 1.0 × 10⁻¹⁴ at 25 °C |
Common mistakes
0–14 covers dilute aqueous solutions at 25 °C. Concentrated acids go negative, concentrated bases exceed 14, and non-aqueous solvents have their own scales. The familiar range is a useful convention, not a boundary of nature.
Backwards and wrong: lower pH means more acidic, and the scale is logarithmic. pH 3 has 10³ = 1000 times the [H⁺] of pH 6. Each single unit is a factor of ten.
pH measures the current H⁺ concentration of a solution. A weak acid at high concentration can have a lower pH than a strong acid at low concentration. Strength (Ka) and pH ([H⁺]) are related but different quantities.
Real-world applications
Agriculture: soil pH decides which nutrients plants can absorb.
Medicine: blood pH is held at 7.4; small deviations are emergencies.
Food industry: pH controls preservation, flavor, and safety.
Water treatment: pH adjustment is step one in purification.
Frequently asked questions
Is pH 7 always neutral?
pH 7 is neutral only at 25 °C, where Kw = 1.0 × 10⁻¹⁴ makes [H⁺] = [OH⁻] = 10⁻⁷ M. At higher temperatures Kw is larger, so neutral pH drops (about 6.1 at 100 °C). 'Neutral' means [H⁺] = [OH⁻], not 'pH 7' universally.
Can pH be negative or greater than 14?
Yes. pH is defined for any aqueous [H⁺]: concentrated acids give negative pH values (12 M HCl has pH ≈ −1.1), and concentrated bases exceed 14. The 0–14 range is a convenience for dilute solutions, not a law.
How is pH measured in practice?
pH paper and indicator strips give quick estimates (±1 unit); pH meters with glass electrodes give precise readings (±0.01). Meters need calibration with buffer standards, while strips need only a color chart.
How much more acidic is pH 3 than pH 5?
Each pH unit is a factor of 10 in [H⁺]: pH 3 has ten times the H⁺ of pH 4 and a hundred times that of pH 5. Small pH differences mean large concentration differences — which is why the body regulates blood pH so tightly.