Acids, bases, and the pH scale

Water molecules don’t always stay intact. Every so often one splits into two ions, and the balance between those ions affects nearly every molecule in a cell.

Water splits, just a little

A tiny fraction of water molecules break apart, or dissociate, into a hydrogen ion (H⁺) and an OH⁻ ion, called a hydroxide ion:

H₂O ⇌ H⁺ + OH⁻

Square brackets around a symbol stand for its concentration in moles per liter, so [H⁺] means “the hydrogen ion concentration.” In pure water, [H⁺] and [OH⁻] are equal, and each is 10⁻⁷ M.

As a reminder, 10⁻⁷ means 1 divided by 10 seven times, or 0.0000001. Each step in the exponent (the small raised number) is a factor of 10, so 10⁻⁶ M is ten times more concentrated than 10⁻⁷ M.

One rule ties the two ions together. At 25 °C, multiplying [H⁺] by [OH⁻] always gives 10⁻¹⁴. In pure water, 10⁻⁷ × 10⁻⁷ = 10⁻¹⁴ (to multiply powers of ten, add the exponents). So when one ion’s concentration rises, the other’s must fall.

Acids and bases

Some substances release hydrogen ions when they dissolve in water, raising [H⁺]. These are acids. Acids differ in how completely they dissociate:

• Hydrochloric acid (the acid in your stomach) breaks apart completely: HCl → H⁺ + Cl⁻. The one-way arrow shows that essentially no intact HCl remains. An acid that dissociates completely is a strong acid.
• Carbonic acid breaks apart only partly, so some of it stays intact: H₂CO₃ ⇌ H⁺ + HCO₃⁻ (a bicarbonate ion). The two-way arrow shows the reaction runs both ways. An acid that dissociates only partly is a weak acid.

Other substances have the opposite effect and lower [H⁺]. These are bases, and they can work in different ways:

• By adding OH⁻. Sodium hydroxide releases hydroxide ions: NaOH → Na⁺ + OH⁻. The extra OH⁻ combines with H⁺ to form water, so [H⁺] drops.
• By taking H⁺ from water. Ammonia pulls an H⁺ off a water molecule: NH₃ + H₂O ⇌ NH₄⁺ (an ammonium ion) + OH⁻. That also raises [OH⁻] and lowers [H⁺].

The pH scale

Acids and bases can shift [H⁺] across many powers of ten, so scientists track it with a simpler number. Write [H⁺] as a power of ten, drop the minus sign from the exponent, and you have the solution’s pH: [H⁺] = 10⁻⁷ M means a pH of 7.

Formally, pH is the negative logarithm (base 10) of the H⁺ concentration:

pH = −log₁₀[H⁺]

A base-10 logarithm is the exponent you’d put on 10 to get a number, so the logarithm of 10⁻⁷ is −7, and the minus sign in front turns it into 7. (This “base” is a math word, unrelated to chemical bases.)

• At pH 7, [H⁺] equals [OH⁻], and the solution is neutral. Pure water is neutral.
• Below pH 7, there’s more H⁺ than OH⁻, and the solution is acidic.
• Above pH 7, there’s more OH⁻ than H⁺, and the solution is alkaline (basic).

Each pH unit is a tenfold step

Each step of 1 pH unit is a 10-fold change in [H⁺], much as each step on the Richter scale for earthquakes means ten times stronger shaking. Unlike the Richter scale, though, pH runs backward: the higher the number, the fewer hydrogen ions.

Check yourselfA sample’s hydroxide ion concentration is 10⁻⁵ M. What is its pH, and is it acidic or alkaline?

[H⁺] = 10⁻¹⁴ ÷ 10⁻⁵ = 10⁻⁹ M, so the pH is 9. That’s above 7, so the sample is alkaline.