7.3 Reaction Quotient

Q vs K Equilibrium Direction

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Q vs KLog ScaleDirection Arrow5 Reactions
Topic 7.3

Reaction Quotient and Equilibrium Constant

Represent the reaction quotient Qc or Qp for a reversible reaction, and the corresponding equilibrium expressions Kc = Qc or Kp = Qp.

The reaction quotient Qc describes the relative concentrations of reaction species at any time. For gas-phase reactions it may instead be written in terms of partial pressures as Qp. The reaction quotient tends toward the equilibrium constant, such that at equilibrium Kc = Qc and Kp = Qp.

For a A + b B ⇌ c C + d D, the law of mass action gives

Kc = [C]c[D]d / ([A]a[B]b) and Kp = (PC)c(PD)d / ((PA)a(PB)b)

Both are on the AP equation sheet.

Rules for writing the expression:

  • Products over reactants, each raised to its stoichiometric coefficient.
  • Include aqueous species (concentration) and gases (concentration or partial pressure).
  • Exclude pure solids and pure liquids. Their "concentration" — a fixed density — does not change as the reaction proceeds, so they are folded into K.
  • Exclude solvent water in a dilute aqueous equilibrium, for the same reason.

Q versus K. They have identical mathematical form. The only difference is when the values are measured: Q at any moment, K only at equilibrium. That shared form is exactly why Q can be compared to K to predict direction (7.10).

Units. AP treats K and Q as unitless. Do not attach units.

Key points

  • Q and K have identical form; only the timing differs.
  • Pure solids and pure liquids never appear in the expression.
  • Coefficients become exponents — a coefficient of 3 becomes a cube.
  • K depends only on temperature.

Equations

  • on the exam sheetFor a A + b B ⇌ c C + d D.
  • on the exam sheet

Common mistakes

  • Including a solid or pure liquid. For CaCO₃(s) ⇌ CaO(s) + CO₂(g), K = P(CO₂). That is the whole expression.
  • Reactants over products. Always products on top.
  • Using coefficients as multipliers instead of exponents.
  • Including liquid water as a solvent. It is excluded from dilute aqueous K expressions.

Worked example

Write the Kc expression for each: (a) 2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g) (b) CaCO₃(s) ⇌ CaO(s) + CO₂(g) (c) NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq) (d) Ag₂CrO₄(s) ⇌ 2 Ag⁺(aq) + CrO₄²⁻(aq)

(a) Kc = [SO₃]² / ([SO₂]²[O₂])
All species are gases; note the squares from the coefficients.

(b) Kc = [CO₂]
Both solids are excluded. The equilibrium expression contains a single term. (In pressure terms, Kp = PCO₂.)

(c) Kc = [NH₄⁺][OH⁻] / [NH₃]
Liquid water is the solvent and is excluded. This expression is Kb for ammonia.

(d) Ksp = [Ag⁺]²[CrO₄²⁻]
The solid is excluded, leaving only the product terms. This is a solubility product (7.11).

Full notes for topic 7.3 →