AP Chemistry · Unit 7 · Topic 7.3
Reaction Quotient and Equilibrium Constant
Before calculating anything, write a ratio that matches the reaction. Most mistakes with equilibrium constants begin before the numbers enter the calculator.
One expression, two uses
For \(aA+bB\rightleftharpoons cC+dD\), products appear in the numerator and reactants in the denominator. Their balanced coefficients become powers. Evaluating this expression for any current composition gives Q. Evaluating it for an equilibrium composition gives K. Q changes as a disturbed sample reacts; K is fixed for a specified reaction at a fixed temperature.
Why phases matter
Pure solids and pure liquids have activity approximately equal to one in the usual AP model, so their factors do not appear explicitly. This omission does not mean they are chemically unimportant. A solid must actually be present if the equilibrium description requires it. Dissolved substances and gases normally remain in the expression.
Match the representation
| Reaction | Appropriate quotient |
|---|---|
| \(H_2(g)+I_2(g)\rightleftharpoons2HI(g)\) | \(Q_c=[HI]^2/([H_2][I_2])\) |
| \(CaCO_3(s)\rightleftharpoons CaO(s)+CO_2(g)\) | \(Q_p=P_{CO_2}/P^\circ\) |
| \(AgCl(s)\rightleftharpoons Ag^+(aq)+Cl^-(aq)\) | \(Q\approx[Ag^+][Cl^-]/(c^\circ)^2\) |
Here \(c^\circ=1\ \mathrm M\) and \(P^\circ\) is the specified standard pressure. Normalization makes the thermodynamic quotient dimensionless.
A complete numerical comparison
For the HI reaction, let [HI] = 0.240 M, [H₂] = 0.0800 M, and [I₂] = 0.120 M. Then
If \(K_c=12.0\) at this temperature, net forward reaction is favored. HI is not “too small” in isolation: its squared concentration is too small relative to the reactant product. That distinction matters when several concentrations change together.
Connect pressure and concentration carefully
For ideal gases, partial pressure is proportional to molar concentration through \(P=cRT\). In conventional classroom notation, \(K_p=K_c(RT)^{\Delta n_{\mathrm{gas}}}\), with consistent units and standard-state conventions. The HI reaction has zero change in gaseous stoichiometric moles, so these factors cancel. Do not use the liquid or solid coefficients when finding that gas-only difference.
Test whether measurements represent K
Measure a reaction mixture at several times. Ratios that drift are Q values, not independent equilibrium constants. A reproducible plateau from several starting compositions is stronger evidence for K. Record temperature because a new temperature can produce a genuinely different equilibrium ratio.
Three useful safeguards
Balance the equation first, include phase labels, and identify whether the data are current or equilibrium values. Do not replace partial pressure with total pressure unless only one gas is present. In dilute-solution AP calculations, concentration values approximate activities; concentrated ionic solutions may require a more refined model.
Practice with answers
- For \(2SO_2+O_2\rightleftharpoons2SO_3\), write Qc. \([SO_3]^2/([SO_2]^2[O_2])\).
- Does doubling the mass of an existing pure solid double its activity? No, not in this model.
- When does Q equal K? When the composition is an equilibrium composition at the stated temperature.
Factual reference: OpenStax Chemistry 2e, 13.2. Organization, worked values, comparison table, and questions are independently authored.
Official curriculum reference: College Board AP Chemistry course page. The explanation and worked example are independently written for this study site.