Difficulty: Intermediate | Prerequisites: Acids and Bases Defined (Ch. 12), logarithms
Water self-ionises into H₃O⁺ and OH⁻ in equal, tiny amounts, and the product of their concentrations is always 1.0 × 10⁻¹⁴ (K_w). The pH scale is just the negative log of the H₃O⁺ concentration: below 7 is acidic, above 7 is basic. Strong acids and bases dissociate completely in water (use a single arrow); weak acids and bases only partially dissociate (use an equilibrium arrow), so most of the original molecule remains intact.
Self-ionisation of water (autoionisation)
The process in which two water molecules transfer a proton between them: H₂O(l) + H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq). One molecule acts as the acid, the other as the base.
Think of it as water molecules constantly, very slightly, breaking apart and recombining on their own.
K_w (ion-product constant of water)
The equilibrium constant for the self-ionisation of water: K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C.
In simple terms, this number is always the same at room temperature, no matter what is dissolved in the water.
pH
The negative base-10 logarithm of the hydronium ion concentration: pH = –log[H₃O⁺]. Lower pH means more acidic; higher pH means more basic.
Think of it as a shorthand scale that converts very small concentrations into manageable numbers from roughly 0 to 14.
pOH
The negative base-10 logarithm of the hydroxide ion concentration: pOH = –log[OH⁻]. At 25 °C, pH + pOH = 14.
In simple terms, pOH does for hydroxide what pH does for hydronium.
Strong acid
An acid that dissociates (ionises) completely in water. Every molecule breaks apart into ions. Also called a strong electrolyte.
Think of it as: if you put 0.1 M HCl in water, you get 0.1 M H⁺ and 0.1 M Cl⁻, with no HCl left.
Strong base
A base that dissociates completely in water, producing metal cations and OH⁻. Also a strong electrolyte.
In simple terms, every unit of NaOH you dissolve becomes Na⁺ and OH⁻ with nothing left undissociated.
Weak acid
An acid that only partially ionises in water. An equilibrium forms between the intact acid and its ions. Also called a weak electrolyte.
Think of it as: most of the acid molecules stay whole; only a small fraction donate their proton.
Weak base
A base that only partially ionises in water. An equilibrium exists between the intact base and the ions it produces.
In simple terms, most of the base molecules remain unreacted, and only a small proportion accept a proton.
Pure water self-ionises: H₂O(l) + H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)
In pure water, [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ M
The product of these concentrations is the ion-product constant: K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴
K_w holds in any aqueous solution at 25 °C, not just pure water. If you know one concentration, you can find the other.
pH = –log[H₃O⁺]
The scale runs from roughly 0 to 14 for typical solutions.
Each whole-number step represents a tenfold change in [H₃O⁺].
pH 1: [H₃O⁺] = 0.10 M
pH 2: [H₃O⁺] = 0.010 M
pH 7: [H₃O⁺] = 1.0 × 10⁻⁷ M (neutral)
pH 14: [H₃O⁺] = 1.0 × 10⁻¹⁴ M
Acidic solution: [H₃O⁺] > [OH⁻], pH < 7
Neutral solution: [H₃O⁺] = [OH⁻], pH = 7
Basic solution: [H₃O⁺] < [OH⁻], pH > 7
pOH = –log[OH⁻]
pH + pOH = 14 at 25 °C
To find [H₃O⁺] from pH: [H₃O⁺] = 10^–pH
To find [OH⁻] from pOH: [OH⁻] = 10^–pOH
HNO₃ at 0.010 M dissociates completely, so [H₃O⁺] = 0.010 M. pH = –log(0.010) = 2.0.
Given pH = 8.6: [H₃O⁺] = 10^–8.6 = 2.5 × 10⁻⁹ M. Then [OH⁻] = K_w / [H₃O⁺] = (1.0 × 10⁻¹⁴) / (2.5 × 10⁻⁹) = 4.0 × 10⁻⁶ M.
Dissociate/ionise completely in solution (strong electrolytes). Use a single forward arrow (→).
Strong acids to memorise: HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄
Strong bases to memorise: LiOH, NaOH, KOH, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂
Example: HNO₃(aq) → H⁺(aq) + NO₃⁻(aq). Starting with 1 mol HNO₃ gives 1 mol H⁺ and 1 mol NO₃⁻, with 0 mol HNO₃ remaining.
Do NOT dissociate completely (weak electrolytes). Use an equilibrium arrow (⇌).
Only a small fraction of molecules ionise.
Example comparison at 0.1 M:
HCl (strong): starts at 0.1 M, ends at 0 M HCl, with 0.1 M H⁺ and 0.1 M Cl⁻.
HF (weak): starts at 0.1 M, ends at 0.092 M HF, with only 0.008 M H⁺ and 0.008 M F⁻.
This difference is critical for pH calculations. For a strong acid, [H⁺] equals the initial acid concentration. For a weak acid, [H⁺] is much smaller than the initial concentration.
pH formula
pH = –log[H₃O⁺] (equivalently, pH = –log[H⁺])
pOH formula
pOH = –log[OH⁻]
Relationship between pH and pOH
pH + pOH = 14 (at 25 °C)
Ion-product constant of water
K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ (at 25 °C)
Reverse pH to find concentration
[H₃O⁺] = 10^–pH
[OH⁻] = 10^–pOH
Finding one ion concentration from the other
[OH⁻] = K_w / [H₃O⁺] and [H₃O⁺] = K_w / [OH⁻]
Pool maintenance relies on pH monitoring: chlorine disinfection is most effective in a narrow pH range (7.2 to 7.8), and the readings are direct applications of –log[H₃O⁺]. Stomach acid (HCl) is a strong acid at roughly pH 1.5 to 3.5, which is why antacids (weak bases) work by partially neutralising it rather than eliminating all H⁺.
Students often think that pH can only range from 0 to 14. It can go below 0 or above 14 for very concentrated solutions. The 0 to 14 range applies to typical dilute aqueous solutions.
Students sometimes assume that "strong" means "concentrated" and "weak" means "dilute." Strength is about the degree of dissociation (complete vs. partial), not the amount dissolved. You can have a dilute solution of a strong acid or a concentrated solution of a weak acid.
Students frequently forget to use K_w to find the other ion concentration. If you know [H₃O⁺], you must divide K_w by it to find [OH⁻], not subtract.
Students often mix up the direction of the pH scale. A lower pH number means a higher concentration of H₃O⁺ (more acidic), not less.
⚠️ Memorise the six strong acids (HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄) and the strong bases (LiOH, NaOH, KOH, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂). If it is not on the list, treat it as weak.
⚠️ Be comfortable converting between pH, [H₃O⁺], pOH, and [OH⁻] in any direction. Multi-step conversion problems are a staple.
⚠️ For strong acids, [H⁺] equals the molarity you started with. For weak acids, it does not. This distinction drives most calculation errors on exams.
⚠️ Remember that pH + pOH = 14 only at 25 °C. If an exam specifies a different temperature, K_w changes.
Fill in the blank: K_w = [H₃O⁺][OH⁻] = ______ at 25 °C. (1.0 × 10⁻¹⁴)
True or false: A solution with pH 3 has ten times the [H₃O⁺] of a solution with pH 4. (True)
Fill in the blank: A strong acid dissociates ______ in water, while a weak acid dissociates only ______. (completely; partially)
True or false: pH + pOH = 14 at all temperatures. (False, only at 25 °C)
Fill in the blank: HF is a ______ acid because it does not fully ionise in water. (weak)
Q: A solution of HNO₃ has a concentration of 0.010 M. Calculate the pH.
A: HNO₃ is a strong acid, so it dissociates completely. [H₃O⁺] = 0.010 M. pH = –log(0.010) = 2.0.
Q: A solution has a pH of 8.6. What is the [H₃O⁺]? What is the [OH⁻]?
A: [H₃O⁺] = 10^–8.6 = 2.5 × 10⁻⁹ M. [OH⁻] = K_w / [H₃O⁺] = (1.0 × 10⁻¹⁴) / (2.5 × 10⁻⁹) = 4.0 × 10⁻⁶ M.
Q: A solution has [OH⁻] = 0.10 M. What is [H₃O⁺]? Is this solution acidic, neutral, or basic?
A: [H₃O⁺] = K_w / [OH⁻] = (1.0 × 10⁻¹⁴) / (0.10) = 1.0 × 10⁻¹³ M. Since [OH⁻] > [H₃O⁺], the solution is basic.
Q: You dissolve 0.1 M HCl and 0.1 M HF separately. Both are acids. Why does the HCl solution have a lower pH?
A: HCl is a strong acid and dissociates completely, so [H⁺] = 0.1 M. HF is a weak acid and only partially dissociates, so [H⁺] is much less than 0.1 M (about 0.008 M). A higher [H⁺] gives a lower pH.
Q: Name the six strong acids.
A: HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄.
The pH scale is the foundation for every calculation in the rest of this chapter: titrations use pH to find the endpoint, buffers are designed to hold pH steady, and the pH of ionic compound solutions depends on whether dissolved ions come from strong or weak parents. The distinction between strong and weak also connects to equilibrium constants (K_a and K_b), which you will use extensively in later chapters.
pH, pOH, pH scale, self-ionisation of water, autoionisation, K_w, ion-product constant, hydronium concentration, hydroxide concentration, –log, strong acid, strong base, weak acid, weak base, strong electrolyte, weak electrolyte, HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄, NaOH, KOH, Ca(OH)₂, HF, NH₃, pH calculations, CHEM 2, general chemistry, Chapter 12