7.4 Calculating the Equilibrium Constant

The equilibrium constant (K) is a number that quantifies the ratio of product to reactant activities at equilibrium for a balanced reaction—Kc uses concentrations, Kp uses partial pressures (law of mass action). You calculate K by plugging equilibrium concentrations or pressures into the equilibrium expression (often using an ICE table)—that’s exactly what AP LO 7.4.A expects you to do. Why we need it: K tells you the extent of reaction (large K → products favored; small K → reactants favored), lets you compare with the reaction quotient Q to predict which direction the system will shift, and is essential for solving equilibrium problems (including heterogeneous equilibria, temperature dependence, and gas-phase Kp via the ideal gas law). For practice and step-by-step examples (ICE tables, Q vs K, Kc ↔ Kp), see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and more practice questions (https://library.fiveable.me/practice/ap-chemistry).

Write the equilibrium expression from the balanced equation using the law of mass action: Kc = (products)^(stoich coeff) / (reactants)^(stoich coeff). Use equilibrium concentrations [ ] for Kc and partial pressures P for Kp (same algebraic form). Omit pure solids and liquids (heterogeneous equilibria) because their activities ≈ 1. If reaction: aA + bB ⇌ cC + dD, then Kc = [C]^c [D]^d / ([A]^a [B]^b) Kp = (PC)^c (PD)^d / (PA)^a (PB)^b Remember: use equilibrium values (from ICE tables or measured data)—that’s what AP Topic 7.4 tests (calculate Kc or Kp from equilibrium concentrations/pressures). You can compare to the reaction quotient Q (same form) to predict shift. For worked examples and practice, check the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and more unit review (https://library.fiveable.me/ap-chemistry/unit-7); hundreds of practice problems are at (https://library.fiveable.me/practice/ap-chemistry).

Kc uses molar concentrations [ ] (M) in the equilibrium expression; Kp uses partial pressures (atm) for gaseous species. Use Kc when you’re given equilibrium concentrations or working with solutions; use Kp when you’re given partial pressures or the problem is stated in gases. For gas-phase reactions you can convert between them: Kp = Kc(RT)Δn, where Δn = moles of gaseous products − moles of gaseous reactants, R = 0.08206 L·atm·mol−1·K−1, and T is in K. Remember: pure solids and pure liquids don’t appear in either expression (their activity ≈ 1). K (either form) depends only on temperature—don’t include Kc or Kp units on the exam answer unless asked. On the AP exam you’ll be expected to calculate Kc or Kp from experimental concentrations or pressures (CED 7.4.A), often using an ICE table and the ideal gas law if you need to convert P ↔ [ ]. For a quick review see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and more practice problems at (https://library.fiveable.me/practice/ap-chemistry).

Step-by-step: 1. Write the balanced equation and the equilibrium-constant expression (law of mass action). Put products over reactants, each raised to its stoichiometric coefficient. (Exclude pure solids/liquids.) 2. Decide Kc (concentrations) or Kp (partial pressures). AP expects you to use whichever experimental data are given. 3. If you’re given equilibrium concentrations directly, just substitute them into the expression and compute K. Example: for aA + bB ⇌ cC + dD, Kc = [C]^c[D]^d / [A]^a[B]^b. 4. If you’re given initial concentrations and one equilibrium value, build an ICE table, use stoichiometry to find all equilibrium concentrations, then substitute to compute Kc. 5. Watch units (K is unitless on the exam) and significant figures. For gaseous systems given as pressures, use Kp and the same expression with partial pressures. For more examples and practice problems that match the AP CED, see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and 1000+ practice questions (https://library.fiveable.me/practice/ap-chemistry).

K is defined by the law of mass action using the concentrations (or partial pressures) of species at equilibrium—not the initial amounts—because K describes the ratio of product to reactant activities when the system has reached dynamic equilibrium. Initial concentrations tell you where the system started, but reactions shift until forward and reverse rates are equal; only the equilibrium concentrations satisfy K’s expression. If you plug initial values into K you’re really calculating the reaction quotient Q. Comparing Q to K tells you which direction the system will shift (QK → reverse), which is an essential AP skill (Topic 7.3–7.4). Use ICE tables to convert initial concentrations to equilibrium concentrations and then substitute those equilibrium values into the Kc or Kp expression (CED 7.4.A.1). For worked examples and practice problems, see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and the AP Chem practice question bank (https://library.fiveable.me/practice/ap-chemistry).

Quick checklist to tell if your K (Kc or Kp) is right: - Expression: Make sure your equilibrium expression matches the balanced equation and uses concentrations for Kc or partial pressures for Kp. Include each species to the power of its stoichiometric coefficient; omit pure solids/liquids (CED: law of mass action, stoichiometric coefficients, heterogeneous equilibrium). - Numbers: Use equilibrium values (from ICE or experiment), substitute correctly, and keep appropriate sig figs. On the AP free-response you must show the algebra, substitution, and final value (task verb: Calculate). - Units & type: K is unitless in strict thermodynamics, but on the exam label Kc vs Kp. If you computed Kp from Kc, check Kp = Kc(RT)Δn where Δn = moles gas products − moles gas reactants (CED: Kp relation). - Sanity checks: If K ≫ 1, products favored; if K ≪ 1, reactants favored. Compute Q with initial values—if Q → K direction matches expected shift, your value is consistent. You can also re-calculate backwards: assume K and solve equilibrium; results should match given equilibrium concentrations/pressures. - Temperature: Remember K depends on temperature—different T ⇒ different correct K. If you want step-by-step examples and practice, check the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31), the Unit 7 overview (https://library.fiveable.me/ap-chemistry/unit-7) and thousands of practice problems (https://library.fiveable.me/practice/ap-chemistry).

K (Kc or Kp) tells you where equilibrium lies—toward products or reactants—and how far the reaction proceeds. - Large K (≫1, e.g., >10^3): equilibrium lies heavily to the product side. At equilibrium, product concentrations (or partial pressures) are much bigger than reactants—reaction goes “almost to completion.” - Small K (≪1, e.g., <10^-3): equilibrium lies to the reactant side. Reactant concentrations dominate at equilibrium—only a little product forms. - K ≈ 1: significant amounts of both reactants and products at equilibrium. Use the equilibrium expression (law of mass action) and ICE tables to calculate K from measured [ ] or P. To predict direction of shift for a non-equilibrium mixture, compare Q to K: QK → reaction goes reverse. Remember K depends only on temperature (so temperature changes K). This is core AP Topic 7.4 work—see the Topic 7.4 study guide for examples (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and lots of practice problems (https://library.fiveable.me/practice/ap-chemistry).

Short answer: no—you don’t put pure solids or pure liquids explicitly into the K expression. Why: the law of mass action (CED Topic 7.4) uses activities. For pure solids and pure liquids the activity is essentially constant (set = 1), so they don’t appear in the equilibrium expression. Kc and Kp are built from concentrations (aq) or partial pressures (g) of the species that change with the reaction. For heterogeneous equilibria include only gases and aqueous species in the K expression; solids/liquids are omitted (their effect is already contained in the constant). On the AP: when asked to calculate Kc or Kp from equilibrium data, substitute only the measured equilibrium concentrations or partial pressures (use ICE tables, stoichiometric exponents)—don’t include pure solids/liquids. If you want a refresher, see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and more Unit 7 review (https://library.fiveable.me/ap-chemistry/unit-7).

Use the law of mass action but put partial pressures in the expression instead of concentrations. For a general gas reaction aA(g) + bB(g) ⇌ cC(g) + dD(g), Kp = (PC^c · PD^d) / (PA^a · PB^b), where each P is the equilibrium partial pressure (in atm). If you’re given initial pressures and changes, build an ICE (or “I/CE”) table with pressures, solve for the equilibrium pressures, then substitute them into the Kp expression. If you only have equilibrium concentrations (Kc) and need Kp, use the ideal-gas relation: Kp = Kc · (RT)^Δn, where Δn = (c + d) − (a + b), R = 0.08206 L·atm·mol−1·K−1, and T is in K. Remember: only gaseous species appear in Kp, and temperature must match whatever K you’re reporting (K depends on T). This exact skill is in the CED (7.4.A)—practice with ICE tables and conversions to master it (see the Topic 7.4 study guide on Fiveable: https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31). For more mixed practice, try problems at https://library.fiveable.me/practice/ap-chemistry.

In that lab you made a reaction mixture, let it reach equilibrium at a fixed temperature, measured the equilibrium amounts of reactants and products, and plugged those into the law of mass action to get K. Practically: you start with known initial concentrations (or partial pressures), allow the system to equilibrate (constant T), then determine equilibrium concentrations by whatever method fits the system—spectrophotometry (absorbance → [species]), titration (consume product or reactant and back-calc), or gas pressure measurements (use manometer/ideal-gas). Use an ICE table to convert your measured values into equilibrium [ ] (or P) consistent with stoichiometry, then substitute into Kc (or Kp) and report with correct units and sig figs. Remember heterogeneous solids are omitted from K expressions and K is temperature dependent (CED 7.4.A). For a quick refresher and practice on calculating K from data, see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31), the Unit 7 overview (https://library.fiveable.me/ap-chemistry/unit-7), and tons of practice problems (https://library.fiveable.me/practice/ap-chemistry).

K (Kc or Kp) depends on temperature because it’s tied to the standard free energy change: ΔG° = -RT ln K. Since ΔG° = ΔH° - TΔS°, changing T changes ΔG° and therefore changes K (Van’t Hoff relationship). So warming or cooling can make products more or less favored at equilibrium. Changing concentrations doesn’t change K because K is a constant for a given reaction at a specific temperature—it reflects the balance set by the reaction’s thermodynamics, not how much stuff you start with. If you change concentrations (or pressure), the system shifts (Le Chatelier) so Q moves toward K, but K itself stays the same at that T. Use ICE tables and Q to predict the direction; use K (from experiment or calculation) to know the equilibrium ratio. For AP exam practice on calculating K and using ICE/Q, see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and more unit resources (https://library.fiveable.me/ap-chemistry/unit-7).

Kp and Kc are both equilibrium constants: Kc uses concentrations (M) and Kp uses partial pressures (atm). For a gas-phase reaction they’re related by Kp = Kc (RT)^{Δn} where R = 0.08206 L·atm·mol⁻¹·K⁻¹, T is absolute temperature (K), and Δn = (sum of stoichiometric coefficients of gaseous products) − (sum for gaseous reactants). Example: for N2(g)+3H2(g) ⇌ 2NH3(g), Δn = 2 − 4 = −2, so Kp = Kc (RT)^{−2}. Remember K values depend on temperature, and only ideal-gas behavior is assumed when using this relation. For heterogeneous equilibria, omit pure solids and liquids from Δn and the equilibrium expression. For more practice and AP-aligned explanations, see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and Unit 7 overview (https://library.fiveable.me/ap-chemistry/unit-7).

Start by writing the balanced chemical equation and the K expression (you’ll need Kc for concentrations, Kp for pressures). Then make an ICE table: 1) Row headings: I (initial), C (change), E (equilibrium). Columns: each species in the balanced equation. 2) Fill I with given equilibrium or initial concentrations (for mixtures after mixing, adjust for volume). If a solid or pure liquid is present, include it in the ICE table for bookkeeping but omit it from the K expression (heterogeneous equilibrium). 3) In the C row, use stoichiometric coefficients: if x reacts, put −ax for reactant with coefficient a and +bx for product with coefficient b. 4) Equilibrium row = I + C. Substitute those equilibrium concentrations into the Kc expression and solve for x. Often you’ll get a quadratic—either solve exactly or use the small-x approximation if K is small (check that x is <5% of initial). 5) Always check units and plug final concentrations into the K expression to compute Kc (or use PV = nRT to convert to partial pressures for Kp). For an AP-focused walkthrough and practice problems, see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and more unit resources (https://library.fiveable.me/ap-chemistry/unit-7).

Good question—we raise each concentration to the power of its stoichiometric coefficient because the equilibrium expression comes from the law of mass action: reaction rates depend on the probability that the required number of particles collide. For aA + bB ⇌ cC + dD, forming products needs c molecules of C (or consuming a of A), so the equilibrium relation reflects those stoichiometric counts as multiplicative probabilities—[A]^a[A]^a... multiplied a times becomes [A]^a. Mathematically, this is tied to how the forward and reverse rate laws (which depend on concentrations) balance at equilibrium, giving Kc or Kp with exponents equal to coefficients. In more rigorous treatments we use activities instead of concentrations, but for AP problems you substitute equilibrium concentrations (or partial pressures) into the K expression and raise them to their coefficients. For practice and examples, see the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31) and more unit review (https://library.fiveable.me/ap-chemistry/unit-7).

K can't be negative. The equilibrium constant K (Kc or Kp) is a ratio of activities (or concentrations/partial pressures) raised to stoichiometric powers; those values are non-negative, so K ≥ 0. In practice K > 0 for any reaction that produces at least tiny amounts of product at equilibrium. A formal K = 0 would mean the numerator is exactly zero (no product at equilibrium), which is not a negative value—it just means the reaction doesn’t produce detectable product. Also, ΔG° = −RT ln K requires K > 0 (ln of a negative number is undefined), so the thermodynamic definition enforces positivity. For more on calculating K from measured equilibrium concentrations or pressures (CED 7.4.A), check the Topic 7.4 study guide (https://library.fiveable.me/ap-chemistry/unit-7/calculating-equilibrium-constant/study-guide/WMmdcS9qD8yHDQwepK31). For practice problems, see Fiveable’s AP Chem practice set (https://library.fiveable.me/practice/ap-chemistry).