Chemical equilibrium Study Guide

📖 Core Concepts Chemical equilibrium – a dynamic balance where forward and reverse reaction rates are equal, so macroscopic properties (color, pressure, pH) stay constant. Equilibrium constant (K) – ratio of product activities to reactant activities, each raised to its stoichiometric coefficient; for gases use partial pressures (Kp), for solutions use concentrations (Kc). Law of Mass Action – for an elementary step α A + β B ⇌ σ S + τ T, $$K = \frac{\{S\}^{\sigma}\{T\}^{\tau}}{\{A\}^{\alpha}\{B\}^{\beta}} = \frac{k^{+}}{k^{-}}$$ Thermodynamic link – $$\Delta G^{\circ} = -RT\ln K$$ At constant T and P, equilibrium corresponds to the minimum Gibbs free energy ( $dG/d\xi = 0$ ). Activity – effective concentration relative to a standard state ( $\{A\}=1$  for pure solids/liquids). Real solutions: $K = Kc\Gamma$, where $\Gamma$ corrects for non‑ideal behavior. Le Chatelier’s principle – a system at equilibrium shifts to counteract any imposed change (concentration, pressure, temperature, or addition of a catalyst). 📌 Must Remember K expression: products over reactants, each to its stoichiometric power. Pure solids/liquids → activity = 1 (omit from K). ΔG°–K relation: $\Delta G^{\circ} = -RT\ln K$. van ’t Hoff: $\displaystyle\frac{d\ln K}{dT}= \frac{\Delta H^{\circ}}{RT^{2}}$ (exothermic: K ↓ with ↑T). Reaction quotient (Q): compare instantaneous activities to K; $Q>K$ → shift left; $Q<K$ → shift right. Catalyst: speeds both directions equally → no change in K. Ksp for dissolution AB(s) ⇌ A⁺ + B⁻: $K{sp}=[A^{+}][B^{-}]$. Buffers: $pH = pKa + \log\frac{[\text{A}^-]}{[\text{HA}]}$ (Henderson–Hasselbalch). 🔄 Key Processes ICE Table (simple equilibrium) Initial concentrations → write. Change: introduce variable x for shift. Equilibrium: substitute I ± C into K expression, solve for x. van ’t Hoff calculation Rearrange: $\ln\frac{K2}{K1}= -\frac{\Delta H^{\circ}}{R}\left(\frac{1}{T2}-\frac{1}{T1}\right)$. Mass‑balance for multi‑component systems Write conservation for each element (e.g., total Na = [Na⁺] + [NaCl] etc.). Combine with K expressions to solve. Solubility‑pH interplay For a metal hydroxide $M(OH)n$, $K{sp} = [M^{n+}][OH^-]^n$. Increase pH → $[OH^-]$ ↑ → $[M^{n+}]$ must ↓ → precipitation. 🔍 Key Comparisons Kc vs. Kp – Kc: concentration basis (mol L⁻¹). Kp: partial‑pressure basis (atm). Use $Kp = Kc(RT)^{\Delta n}$ where $\Delta n$ = moles gas products – moles gas reactants. Pure solid/liquid vs. solutes – Pure phase: activity = 1, omitted from K. Solute: activity ≈ concentration × activity coefficient. Catalyst vs. Temperature change – Catalyst: speeds rate, no effect on K. Temperature: changes K according to van ’t Hoff. ⚠️ Common Misunderstandings “Equilibrium means no reaction” – false; forward and reverse continue at equal rates. “Catalyst changes equilibrium position” – false; only rate. “Ksp = solubility” – Ksp is product of ion concentrations at saturation; solubility is a derived quantity (e.g., $s = \sqrt{K{sp}}$ for AB). “Higher K always means more product” – only true when activities ≈ concentrations; ionic strength can mask true composition. 🧠 Mental Models / Intuition “Tug‑of‑war” – visualize forward and reverse reactions pulling on a rope; equilibrium is the point where forces balance → rates equal, concentrations stop changing. “Energy hill” – the system sits at the lowest Gibbs free‑energy point on the reaction coordinate; any disturbance pushes it uphill, and it rolls back toward the valley (equilibrium). “Le Chatelier as a thermostat” – the system senses a change (temperature, concentration) and “adjusts” to keep the “room temperature” (K) stable. 🚩 Exceptions & Edge Cases Non‑elementary reactions – Law of Mass Action applies strictly to elementary steps; for complex mechanisms use overall equilibrium constant derived from elementary steps. Highly ionic solutions – activity coefficients deviate strongly; $K = Kc\Gamma$ must be used, otherwise calculated K will be off. Polyprotic acids – successive dissociations have distinct $K1$, $K2$; overall acidity is product $βD = K1K2$. Temperature‑dependent $Kw$ – water’s ion product changes with T (e.g., $Kw = 1.0\times10^{-14}$ at 25 °C). 📍 When to Use Which Kc vs. Kp – Use Kc for solutions, Kp for gas‑phase reactions; convert with $(RT)^{\Delta n}$ if needed. ICE table – Ideal for single‑reaction, one‑unknown systems. Mass‑balance + equilibrium equations – Required for systems with multiple equilibria or conserved elements. Activity coefficients – Apply when ionic strength > 0.1 M or when precise quantitative work is needed. van ’t Hoff – Use to predict how K changes with temperature or to estimate ΔH° from two K values. 👀 Patterns to Recognize “Q > K → shift left” pattern appears in every Le Chatelier question. Pure solid/liquid omission – whenever a solid appears in a balanced equation, expect it to be absent from the K expression. Δn in gas equilibria – look for change in total moles of gas; if Δn = 0, then $Kp = Kc$. Polyprotic acid titration curves – plateaus correspond to $K1$ and $K2$ regions. 🗂️ Exam Traps Including solids in K – answer choice that writes $K = \frac{[A^+][B^-]}{[AB]}$ for dissolution of AB(s) is wrong; solid omitted. Mixing up Kc and Kp – selecting $Kp = Kc$ when Δn ≠ 0 is a common distractor. Catalyst effect – a choice stating “adding a catalyst increases K” is false. Temperature direction – for an exothermic reaction, a trap may claim “raising temperature increases K”; correct is the opposite. Sign of ΔG° – remembering $\Delta G^{\circ} = -RT\ln K$: a large K (>1) gives negative ΔG°, but a test may flip the sign. --- Use this guide for a quick, confidence‑boosting review before your exam. Master the core equations, recognize the patterns, and avoid the listed traps!