The Power of Hydrogen: Answer Key

Self-ionization is the process by which water molecules react with one another to form hydronium and hydroxide. One water molecule effectively hands a proton to another, producing H₃O⁺ and OH⁻. The ions rapidly recombine, establishing a dynamic equilibrium. No acid or base is needed. The process arises from water’s own molecular behavior.
pH does not describe a fixed characteristic of water. It measures where the ongoing self-ionization equilibrium currently sits: the balance between H⁺/H₃O⁺ and OH⁻ at a given moment. Adding acid or base drags that balance to a new position, and pH reports where it settled. It is a measurement of equilibrium, not a simple tally of chemical added.
It is not acidic. Neutral means [H⁺] = [OH⁻], not “pH = 7.” At 100°C, Kw increases, so both [H⁺] and [OH⁻] are higher than 10⁻⁷ - but they are equal. The neutral point shifts to ≈6.14 while the water remains perfectly neutral.
pH tells you the current hydrogen concentration: the intensity right now. Alkalinity tells you how much acid the water can absorb before the pH moves significantly. A high-pH solution with little buffering capacity can shift sharply when acid is added, while a moderately alkaline solution with strong bicarbonate buffering can resist change. They are functionally different.
pH 4: [H⁺] = 10⁻⁴ mol/L, pOH = 10, [OH⁻] = 10⁻¹⁰ mol/L. Check: 4 + 10 = 14.

pH 10: [H⁺] = 10⁻¹⁰ mol/L, pOH = 4, [OH⁻] = 10⁻⁴ mol/L. Check: 10 + 4 = 14.

pH 4 vs pH 7 = 3 pH units difference. 10³ = 1,000 times more H⁺ at pH 4.
(a) pOH = 14 − 9 = 5. (b) [OH⁻] = 10⁻⁵ mol/L. (c) [H⁺] = 10⁻⁹ mol/L.
pH 2.5 → 3.5 = 1 pH unit = 10× decrease in [H⁺]. The technician sees “one point” and thinks the change is small because the pH scale is logarithmic. In reality, about 90% of the hydrogen has already been consumed. The next dose walks into an empty room.
At pH 1.0: [H⁺] = 0.1 mol/L. Volume: 1,000 gal × 3.785 L/gal = 3,785 L. Moles H⁺: 3,785 × 0.1 = 378.5 mol. KOH reacts 1:1, so 378.5 mol × 56.1 g/mol = 21,234 g ÷ 453.6 g/lb = 46.8 lb. At pH 2.0: [H⁺] = 0.01 mol/L. Moles: 3,785 × 0.01 = 37.85 mol. Mass: 37.85 × 56.1 = 2,123 g = 4.68 lb. One pH unit difference → 10× less chemical needed.
Two consequences from the chapter: (1) Protective oxide films on metals rely on hydroxide to form and persist - a pH drop collapses hydroxide concentration, dissolving the film faster than it rebuilds, accelerating corrosion. (2) Mineral scale precipitation depends on hydroxide availability - a pH rise shifts equilibrium toward carbonate formation, and scale deposits where it wasn’t forming before. Even a small pH change matters because each unit represents a 10× shift in both [H⁺] and [OH⁻], reorganizing which reactions are thermodynamically favored.

The Blueprint of Water