The pH scale is a logarithmic measure of the acidity or basicity (alkalinity) of an aqueous solution, defined mathematically as the negative base-10 logarithm of the molar concentration of hydronium ions (H₃O⁺, often written loosely as H⁺) present in the solution:

pH = −log₁₀[H₃O⁺]

Because of the negative sign in this definition, pH and hydronium ion concentration are inversely related: as [H₃O⁺] increases, its logarithm becomes a larger positive number, and the negative of that logarithm — the pH — becomes correspondingly smaller. Conversely, as [H₃O⁺] decreases, pH increases. This inverse relationship is the entire basis of using pH as a convenient, compressed scale for concentrations that can otherwise span many orders of magnitude (from about 1 M down to 10⁻¹⁴ M in typical aqueous solutions).

A few worked examples make the relationship concrete:

• [H₃O⁺] = 1 × 10⁻¹ M (0.1 M) → pH = 1 (strongly acidic)
• [H₃O⁺] = 1 × 10⁻² M (0.01 M) → pH = 2
• [H₃O⁺] = 1 × 10⁻⁴ M (0.0001 M) → pH = 4 (weakly acidic)
• [H₃O⁺] = 1 × 10⁻⁷ M → pH = 7 (neutral, as in pure water)

Notice that each ten-fold increase in hydronium ion concentration corresponds to a decrease of exactly one pH unit, which is exactly what "higher the hydronium ion concentration, lower is the pH" describes, and is why this is the correct statement.

The other options fail for clear reasons: pH is not independent of ion concentration — it is defined entirely in terms of [H₃O⁺], so the two are intrinsically linked by the logarithmic formula above; and the claim that lower hydronium ion concentration gives lower pH (or, equivalently, that higher concentration gives higher pH) reverses the actual inverse relationship — a solution with fewer hydronium ions is less acidic and therefore has a higher pH, not a lower one, and vice versa.