CHEM1011 · Chemistry 1a
Chemical Equilibrium: K, Q and Le Chatelier
Week 5 introduces dynamic equilibrium, the equilibrium-constant expression K and the reaction quotient Q, and the ICE-table method for solving equilibrium concentrations — including the small-x approximation flagged Mastery. Le Chatelier's principle predicts the response to disturbances. This is the topic examined in In-Term Test 1, so the ICE-table calculation and a Q-versus-K direction call are near-certain assessment items.
What this chapter covers
- 01Dynamic equilibrium: forward rate = reverse rate, concentrations constant while reactions continue
- 02Equilibrium constant K = ([C]ᶜ[D]ᵈ)/([A]ᵃ[B]ᵇ); pure solids and liquids omitted; K depends only on temperature
- 03Reaction quotient Q (same form, current concentrations): Q < K net forward, Q > K net reverse, Q = K at equilibrium
- 04ICE tables: Initial / Change (in x) / Equilibrium, substitute into K and solve
- 05The small-x approximation when K is small (valid if x < ~5% of the initial), checked by back-substitution (Mastery)
- 06Manipulating K: reverse → 1/K, scale coefficients by m → Kᵐ, add reactions → multiply K's
- 07Le Chatelier's principle: response to added/removed species, pressure/volume, and temperature
- 08Only a temperature change alters the value of K; Kp = Kc(RT)^Δn for gas equilibria (Mastery)
Equilibrium concentrations from an ICE table with the small-x approximation
- +1Write the expression and ICE table. Kc = [PCl₃][Cl₂]/[PCl₅]. Initial: 0.50, 0, 0. Change: −x, +x, +x. Equilibrium: 0.50 − x, x, x.
- +1Substitute: Kc = x²/(0.50 − x) = 4.0 × 10⁻⁴. Because Kc is small, assume x ≪ 0.50, so 0.50 − x ≈ 0.50.
- +1Then x² = 4.0 × 10⁻⁴ × 0.50 = 2.0 × 10⁻⁴, giving x = √(2.0 × 10⁻⁴) = 1.41 × 10⁻² mol L⁻¹ = [Cl₂].
- +1Check the approximation: x/0.50 = 0.0141/0.50 = 2.8%, which is below 5%, so the approximation is valid. Equilibrium: [Cl₂] = [PCl₃] = 0.014 mol L⁻¹, [PCl₅] ≈ 0.49 mol L⁻¹.
Key terms
- Dynamic equilibrium
- The state where the forward and reverse reaction rates are equal, so concentrations stay constant even though both reactions continue at the molecular level.
- Equilibrium constant (K)
- K = ([C]ᶜ[D]ᵈ)/([A]ᵃ[B]ᵇ) at equilibrium, with pure solids and liquids omitted. K depends only on temperature; K ≫ 1 favours products, K ≪ 1 favours reactants.
- Reaction quotient (Q)
- The same expression as K but using current (non-equilibrium) concentrations. Q < K means net forward reaction, Q > K net reverse, Q = K at equilibrium.
- ICE table
- A bookkeeping table of Initial, Change (in terms of x with stoichiometric coefficients) and Equilibrium concentrations, substituted into K to solve for x.
- Small-x approximation
- When K is small, assume the change x is negligible against the initial concentration (initial − x ≈ initial) to avoid the quadratic; valid only if x is under about 5% of the initial, checked by back-substitution (Mastery).
- Le Chatelier's principle
- A system at equilibrium shifts to partially oppose a disturbance: add reactant → shift forward; increase pressure → shift toward fewer gas moles; raise temperature → shift in the endothermic direction (and change K).
Chemical Equilibrium: K, Q and Le Chatelier FAQ
What is the difference between K and Q, and how do I use them?
K is the equilibrium constant, evaluated with equilibrium concentrations, and is fixed at a given temperature. Q has the identical form but uses whatever concentrations you have right now. Compare them to predict direction: Q < K means the reaction runs net forward (toward products), Q > K means net reverse, and Q = K means the mixture is already at equilibrium. This Q-versus-K call is a classic In-Term Test 1 item.
When can I use the small-x approximation instead of the quadratic?
Only when K is small enough that the change x is tiny compared with the initial concentration. You assume initial − x ≈ initial, solve the simplified expression, then back-check that x is under about 5% of the initial. If it passes, keep the approximate answer; if x comes out larger than 5%, the approximation is invalid and you must solve the full quadratic x = (−b ± √(b²−4ac))/2a.
Does anything other than temperature change the value of K?
No. Adding or removing species, or changing the volume/pressure, shifts the position of equilibrium (Le Chatelier) but leaves K unchanged — the system re-establishes the same K. Only a temperature change alters the numerical value of K: for an endothermic forward reaction raising T increases K, for an exothermic one it decreases K. Watching for this distinction on a concentration-versus-time graph is a common exam skill.
Can Sia help me with equilibrium and ICE-table problems?
Yes. Sia can set up the K expression, build the ICE table, decide whether the small-x approximation is safe (and check it), or solve the full quadratic, and it can walk a Le Chatelier prediction with the Q-versus-K reasoning. It explains the method and checks your working; it does not do graded assessment, and UNSW academic-integrity rules apply.
Exam move
Because this topic is examined in In-Term Test 1 and again in the final, drill the ICE-table method until it is mechanical: write the K expression (omitting pure solids/liquids), lay out Initial/Change/Equilibrium in x with the correct stoichiometric coefficients, substitute, and solve. Make the small-x decision explicit every time — use it only when K is small, and always back-check the under-5% condition, falling back to the quadratic when it fails. Practise the Q-versus-K direction call as a separate reflex, and rehearse manipulating K (reverse → 1/K, scale → Kᵐ, add → multiply). For Le Chatelier, be able to read a concentration-versus-time graph, name each disturbance, and say whether K itself changed (only temperature does). Keep the Kp = Kc(RT)^Δn conversion ready for gas equilibria. When an ICE algebra step slips, ask Sia to re-solve it both ways and compare.
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