By Tracy McConnell, Updated Aug 30, 2022
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The pH scale—ranging from 0 to 14—quantifies the acidity or alkalinity of a solution. Understanding a solution’s pH is essential in both educational settings and laboratory practice, as it informs us about the species present and predicts how the solution will behave in chemical reactions.
Because pH directly reflects the concentration of hydronium ions (H₃O⁺) in water, it can be used to calculate the concentration of other ions in the system. The following equations provide the foundation for these calculations.
The relationship between pH and hydronium ion concentration is expressed as:
pH = − log₁₀[H₃O⁺]
Here, the brackets denote molarity. When [H₃O⁺] is known, pH can be determined; conversely, a measured pH allows calculation of [H₃O⁺].
In a 1.0 L sample of 0.1 M hydrochloric acid (HCl), the hydronium concentration is 1 × 10⁻¹ M.
pH = − log₁₀(1 × 10⁻¹) = −(−1) = 1.00
If a solution has a pH of 4.3, rearranging the pH equation gives:
[H₃O⁺] = 10^−pH = 10^−4.3 ≈ 5.01 × 10⁻⁵ M
For basic solutions, the concentration of hydroxide ions [OH⁻] is more readily measured. Using the ion‑product constant for water (K_w = 1 × 10⁻¹⁴ at 25 °C), we find:
[H₃O⁺] = K_w / [OH⁻]
With [OH⁻] = 4.0 × 10⁻¹¹ M:
1. [H₃O⁺] = (1 × 10⁻¹⁴) / (4.0 × 10⁻¹¹) = 2.5 × 10⁻⁴ M
2. pH = − log₁₀(2.5 × 10⁻⁴) ≈ 3.60
pH values are typically reported to the nearest tenth or hundredth, reflecting the precision of the measurement. When applying the logarithm, only the digits after the decimal point are considered significant, ensuring consistency with experimental uncertainty.
The acid dissociation constant quantifies the extent to which an acid ionizes in water. Weak acids have small K_a values, meaning most of the acid remains undissociated, whereas strong acids have large K_a values and ionize almost completely.
Example: Carbonic acid (H₂CO₃) is a weak, diprotic acid with
H₂CO₃(aq) ⇌ HCO₃⁻(aq) + H⁺(aq) K_a₁ = 4.3 × 10⁻⁷
and a second dissociation step:
HCO₃⁻(aq) ⇌ CO₃²⁻(aq) + H⁺(aq) K_a₂ = 4.8 × 10⁻¹¹
In contrast, nitric acid (HNO₃) is a strong acid with K_a ≈ 40, illustrating its near‑complete dissociation.
