# The equilibrium constant > IB Chemistry HL · R2: How much / how fast / how far? > Source: https://www.owlsprep.com/study/ib-chemistry-hl-u5-the-equilibrium-constant/ This sub-topic covers how to write, manipulate, and calculate equilibrium constants ($K_c$, $K_p$) for reversible reactions at equilibrium, interpret their magnitude, and apply stoichiometric rules to adjust $K$ for modified reactions. **Prerequisites:** [Dynamic chemical equilibrium](https://www.owlsprep.com/study/ib-chemistry-hl-u5-dynamic-equilibrium/); [Reaction stoichiometry](https://www.owlsprep.com/study/ib-chemistry-hl-u1-stoichiometric-calculations/) ## Learning objectives - Write correct expressions for $K_c$ and $K_p$ for homogeneous and heterogeneous equilibria - Calculate equilibrium constants from initial and equilibrium quantities - Manipulate $K$ values for reversed, scaled, or combined reactions - Interpret the magnitude of $K$ in terms of reaction extent ## Writing Equilibrium Constant Expressions For the general equilibrium reaction $aA + bB \rightleftharpoons cC + dD$, $K$ is defined as the ratio of product activities over reactant activities, each raised to the power of their stoichiometric coefficients. For dilute solutions, activity ≈ concentration ($[X]$) for $K_c$; for gases, activity ≈ partial pressure ($P_X$) for $K_p$. **Equilibrium Constant** — A temperature-dependent constant that describes the ratio of products to reactants at equilibrium, independent of initial reaction concentrations. *Notation:* $K_c$ (mol dm⁻³ⁿ), $K_p$ (kPaⁿ / atmⁿ) > **info** > > Pure solids and pure liquids have constant activity = 1, so they are **always omitted** from equilibrium constant expressions. **Worked example:** Write the $K_c$ expression for the heterogeneous equilibrium: $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$ 1. 1. Identify species that are not pure solids: only gaseous $CO_2$ is included 2. 2. Omit $CaCO_3$ and $CaO$ (pure solids, activity = 1) 3. $$K_c = [CO_2]$$ > **Exam tip:** Always check the state symbols of all species when writing a K expression, don't forget to omit solids and liquids. *Calculator:* allowed ## Manipulating Equilibrium Constants When the stoichiometry of a reaction is modified (reversed, scaled, or combined with another reaction), the equilibrium constant must be adjusted based on the original $K$ value for the original reaction. - Reversed reaction: $K_{reverse} = \frac{1}{K_{forward}}$ - Reaction scaled by factor $n$: $K_{new} = (K_{original})^n$ - Two reactions added together: $K_{total} = K_1 \times K_2$ **Worked example:** Given $N_2(g) + O_2(g) \rightleftharpoons 2NO(g)$ has $K_c = 4.8 \times 10^{-31}$ at 25°C. Calculate $K_c$ for $NO(g) \rightleftharpoons \frac{1}{2}N_2(g) + \frac{1}{2}O_2(g)$ 1. 1. The target reaction is the original reaction reversed, then multiplied by $\frac{1}{2}$ 2. 2. First reverse the original K, then raise to the power of $\frac{1}{2}$ (square root) 3. $$K_c = \left(\frac{1}{4.8 \times 10^{-31}}\right)^{1/2} = \sqrt{2.1 \times 10^{30}} = 1.4 \times 10^{15}$$ > **Exam tip:** This is a common multiple choice question: remember scaling raises K to the power n, do not multiply K by n. *Calculator:* allowed ## Calculating K from Initial and Equilibrium Data To calculate K, you need the equilibrium concentrations of all included species. If only initial quantities and one equilibrium quantity are given, use an ICE (Initial, Change, Equilibrium) table to find all unknown equilibrium values. **ICE Table** — A table to organise concentration data, using stoichiometry to find unknown equilibrium concentrations *Notation:* I = Initial, C = Change, E = Equilibrium **Worked example:** 0.100 mol $PCl_5$ is placed in a 1.00 dm³ container. At equilibrium, 0.060 mol $PCl_5$ remains. For $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$, calculate $K_c$. 1. 1. Moles = concentration for 1 dm³ volume: Initial $[PCl_5] = 0.100$, others = 0 2. 2. Change in $[PCl_5] = -(0.100 - 0.060) = -0.040$. Stoichiometry gives $\Delta[PCl_3] = \Delta[Cl_2] = +0.040$ 3. 3. Equilibrium concentrations: $[PCl_5] = 0.060$, $[PCl_3] = [Cl_2] = 0.040$ 4. $$K_c = \frac{[PCl_3][Cl_2]}{[PCl_5]} = \frac{(0.040)(0.040)}{0.060} = 0.027 \text{ mol dm}^{-3}$$ *Calculator:* allowed ## Interpreting the Magnitude of K The value of K tells us how far the reaction proceeds at equilibrium at a given temperature. It gives no information about how fast the reaction reaches equilibrium. - $K > 10^3$: Equilibrium lies far right, mostly products, reaction almost complete - $10^{-3} < K < 10^3$: Significant amounts of both reactants and products - $K < 10^{-3}$: Equilibrium lies far left, mostly reactants, reaction barely proceeds > **warning** > > K only changes with **temperature**. It is not affected by catalysts, changes in concentration, or changes in pressure. **Check your understanding** Test your understanding 1. What does $K = 2.1 \times 10^{-4}$ tell you about the equilibrium? - The reaction is very slow - Mostly reactants at equilibrium - Mostly products at equilibrium - Equal amounts of reactants and products *Answer:* Mostly reactants at equilibrium *Why:* Correct! K does not describe reaction rate, and K < 10⁻³ means mostly reactants at equilibrium. ## Common pitfalls - **Wrong:** Including pure solids/liquids in the K expression - Why it fails: Students forget that pure solids/liquids have constant activity that does not change - Correct: Always omit pure solids and pure liquids from K expressions - **Wrong:** Multiplying K by n when a reaction is scaled by n - Why it fails: Confusing stoichiometric scaling of the reaction with how K is defined - Correct: Raise the original K to the power of the scaling factor n - **Wrong:** Using initial concentrations instead of equilibrium concentrations to calculate K - Why it fails: Rushing the calculation and forgetting K only applies to equilibrium - Correct: Use an ICE table to find all equilibrium concentrations before calculating K - **Wrong:** Claiming K always increases when temperature increases - Why it fails: Forgetting K change depends on the enthalpy of the forward reaction - Correct: K increases with T for endothermic forward reactions, decreases for exothermic forward reactions - **Wrong:** Claiming K depends on initial concentrations of reactants - Why it fails: Misunderstanding the definition of an equilibrium constant - Correct: K depends only on temperature and reaction stoichiometry, not initial concentrations ## Cheatsheet | Rule Type | Outcome | | --- | --- | | Reverse reaction | Knew = 1/Koriginal | | Scale by n | Knew = (Koriginal)n | | Add two reactions | Ktotal = K1 × K2 | | Heterogeneous equilibrium | Omit pure solids / pure liquids | | K >> 1 (K > 10³) | Mostly products at equilibrium | | K << 1 (K < 10⁻³) | Mostly reactants at equilibrium | | What changes K? | Only temperature and stoichiometry | ## What's next The equilibrium constant is the foundation for all subsequent equilibrium topics in IB Chemistry HL. The skills you learned writing K expressions, manipulating K values, and calculating K from experimental data are used repeatedly in acid-base equilibria, solubility equilibria, and when applying Le Chatelier's principle to predict equilibrium shifts. Mastery of this sub-topic is essential for earning high marks on extended response questions in Paper 2, which often combine multiple equilibrium concepts. - [AHL: Advanced stoichiometry and titration calculations](https://www.owlsprep.com/study/ib-chemistry-hl-u5-ahl-advanced-stoichiometry-and-titration/) - [AHL: Rate laws and reaction order](https://www.owlsprep.com/study/ib-chemistry-hl-u5-ahl-rate-laws-and-reaction/) --- From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/ib-chemistry-hl-u5-the-equilibrium-constant/