Equilibria
1. Reversible Reactions & Dynamic Equilibrium
Reversible reaction: a reaction that can proceed both forwards and backwards as per the conditions applied (shown by ⇌). Equilibria only apply to reversible reactions.
Dynamic equilibrium: established when the rate of the forward reaction equals the rate of the backward reaction.
Two conditions:
- The reaction must be reversible.
- The system must be closed → energy can be exchanged in and out of the system, but matter cannot.
At equilibrium nothing looks like it changes (constant concentrations) but both reactions are still going on at the same rate.
2. Le Chatelier's Principle
- Equilibrium shifts to the right ⇒ concentration of products increases.
- Equilibrium shifts to the left ⇒ concentration of reactants increases.
| # | Change | Equilibrium shifts | Result |
|---|---|---|---|
| 1 | [reactants] ↑ | to the right | products ↑, reactants ↓ |
| 2 | [reactants] ↓ | to the left | reactants ↑, products ↓ |
| 3 | [products] ↑ | to the left | reactants ↑, products ↓ |
| 4 | [products] ↓ | to the right | products ↑, reactants ↓ |
| 5 | temperature ↑ | the endothermic reaction proceeds | heat absorbed |
| 6 | temperature ↓ | the exothermic reaction proceeds | heat released |
| 7 | pressure ↓ | side with more moles of gas | ↑ no. of particles → ↑ collisions → ↑ pressure |
| 8 | pressure ↑ | side with fewer moles of gas | ↓ no. of particles → ↓ collisions → ↓ pressure |
3. Choosing Conditions — Haber Process
4 mol gas → 2 mol gas: forward reaction exothermic (and fewer moles); backward reaction endothermic
Use a lower temperature as the forward reaction is exothermic → we use 450
°C.
→ Compromise between yield and rate. Any lower: yield is good but the rate of reaction
is too slow.
Use a high pressure as there are fewer moles of gas on the product side → we use 200
atm.
→ Going higher increases the cost of maintenance and machinery (vessels/pipes, safety, money) —
good yield, good rate at 200 atm.
Pump/extract out ammonia → equilibrium shifts to the right → more ammonia produced. Easy to separate as ammonia condenses before H₂ and N₂ because it has a higher m.p. and b.p. (hydrogen bonding).
Pump in hydrogen and nitrogen continuously → equilibrium shifts to the right → more ammonia produced. (So true dynamic equilibrium is never really established in the plant.)
Activation energy decreases → rate of reaction increases. Yield does NOT increase.
4. Choosing Conditions — Contact Process
3 mol gas → 2 mol gas: forward reaction exothermic; backward endothermic. (Makes H₂SO₄.)
Lower T favours the exothermic forward reaction → we use 450 °C: compromise between yield and rate; any lower, yield is good but rate is too slow.
High pressure would favour fewer moles of gas (right) but we still use only 1–2 atm: we already get 99.5 % yield at this pressure, and anything higher is useless as it only increases costs.
Not really necessary as we have 99.5 % yield already.
Activation energy decreases → rate increases (yield does not increase).
| Haber | Contact | |
|---|---|---|
| Reaction | N₂ + 3H₂ ⇌ 2NH₃ | 2SO₂ + O₂ ⇌ 2SO₃ |
| ΔH | −92 | −196 |
| Temperature | 450 °C | 450 °C |
| Pressure | 200 atm | 1–2 atm |
| Catalyst | iron | V₂O₅ |
| Extra | remove NH₃ (condense), feed reactants | no separation needed, 99.5 % yield |
5. Past-Paper Questions — Le Chatelier
V²⁺ + H₂O ⇌ V³⁺ + ½H₂ + OH⁻. What would favour V²⁺?
Need a shift to the left → add OH⁻ (or remove a right-hand species is wrong).
Answer: D
CH₃CO₂CH₃ + H₂O ⇌ CH₃CO₂H + CH₃OH; hydrolysis slow in neutral solution but measurable in acid. Function of HCl?
HCl does not alter either side of the equilibrium — it only speeds it up: catalytic action (H⁺ catalyst for ester hydrolysis).
Answer: C
OCl⁻(aq) + H₂O ⇌ OH⁻(aq) + HOCl(aq). UV breaks down OCl⁻ → Cl⁻ + ½O₂ (this second reaction is not reversible). Highest [HOCl]?
Only the first is an equilibrium. Remove OH⁻ → shifts right → more HOCl: acidify (H⁺ + OH⁻ → H₂O).
B, D ✗ act on the complete (non-reversible) UV reaction, so no shift C ✗ extra OH⁻ shifts LEFT
Answer: A
N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92. Temperature increased — which is correct?
Rate depends on temperature: both forward and backward rates increase, whatever the equilibrium position does.
Answer: A
T increased at constant pressure — volume of the mixture?
Forward endothermic → T↑ shifts right (absorbs heat) → 2 mol NO₂ from 1 mol N₂O₄ → more gas → volume ↑. Plus thermal expansion of gases. Both reasons.
A ✗ ignores thermal expansion C, D ✗ shift is to the right, not left
Answer: B
Which change makes the purple mixture paler (less I₂)?
Need shift right (uses up I₂). Forward is endothermic ⇒ increase T. Pressure: 2 mol gas each side ⇒ no effect.
A, C ✗ pressure has no effect B ✗ lower T shifts left (more I₂)
Answer: D
Percentage yield of Z rises with pressure and is higher at lower temperature. Which statement is correct?
Answer: D
% NH₃ at equilibrium vs pressure for 400 °C and 500 °C.
Yield ↑ with pressure (4 → 2 mol) ⇒ curves rise. Exothermic ⇒ lower T (400 °C) higher yield ⇒ 400 °C curve above 500 °C.
B ✗ labels swapped C, D ✗ yield decreasing with pressure
Answer: A
Conditions for greatest % of N₂O₄?
Right side has fewer moles ⇒ high pressure; forward exothermic ⇒ low temperature.
Answer: B (high P, low T)
(a)(i) State Le Chatelier's principle. If a change is made to a system at equilibrium, the equilibrium shifts to oppose that change. [2]
(ii) Conditions for higher yield, with explanation:
- Temperature: lower. The forward reaction is exothermic, so it is favoured by lower T (it releases heat, opposing the fall in T).
- Pressure: higher. There are fewer moles of gas on the product side (3 → 1), so higher pressure shifts right, increasing methanol yield and so decreasing the pressure.
6. The Equilibrium Constant Kc
For a reversible reaction wA + xB ⇌ yC + zD we define:
Writing Kc and deducing its units
- A higher Kc usually means a high concentration of products, so equilibrium lies in favour of the right-hand side.
- Solids have no concentration — never include them in Kc (liquid solutions and gases are included; a solid is left out completely). e.g. A(s) + 2B(g) ⇌ C(g): Kc = [C]/[B]².
Kc belongs to one version of the equation
Take NO + ½O₂ ⇌ NO₂ (Kc1), 2NO + O₂ ⇌ 2NO₂ (Kc2), 2NO₂ ⇌ 2NO + O₂ (Kc3):
| Kc1 | Kc2 | Kc3 |
|---|---|---|
| [NO₂][NO][O₂]½ | [NO₂]²[NO]²[O₂] | [NO]²[O₂][NO₂]² |
Kc2 = 1/Kc3 = (Kc1)²
Kc3 = 1/Kc2 = 1/(Kc1)²
7. Calculating Kc (I-C-E tables)
2.5 mol H₂ and 2.5 mol I₂ in a 4 dm³ vessel; equilibrium mixture contains 4 mol HI. Find Kc.
| H₂ | I₂ | 2HI | |
|---|---|---|---|
| Initial | 2.5 | 2.5 | 0 |
| Change | −2 | −2 | +4 |
| Equilibrium | 0.5 | 0.5 | 4 |
0.5 mol X₂ and 0.5 mol Y₂ react; 0.6 mol XY at equilibrium. Find Kc.
| X₂ | Y₂ | 2XY | |
|---|---|---|---|
| I | 0.5 | 0.5 | 0 |
| C | −0.3 | −0.3 | +0.6 |
| E | 0.2 | 0.2 | 0.6 |
Past-paper: Kc
2HI ⇌ H₂ + I₂.
(a) Kc = [H₂]eqm[I₂]eqm[HI]²eqm
(b) At 120 °C: [HI] = 1.47, [H₂] = [I₂] = 0.274 mol dm⁻³.
(c) Why harder to find Kc at room temperature? Iodine is a solid at room temperature, so [I₂(g)] may be too small to measure; also the rate may be too slow, taking too long to reach equilibrium. [2]
CH₃CO₂H + C₂H₅OH ⇌ CH₃CO₂C₂H₅ + H₂O
(i) Dynamic equilibrium: established when the rate of the forward reaction equals the rate of the backward reaction in a reversible reaction.
(ii) Kc = [CH₃CO₂C₂H₅][H₂O][CH₃CO₂H][C₂H₅OH]
(c) 6.0 g ethanoic acid + 6.0 g ethanol + 4.4 g ethyl ethanoate; at equilibrium 0.040 mol acid.
| acid | alcohol | ester | H₂O | |
|---|---|---|---|---|
| initially | 0.1 | 0.13 | 0.05 | 0 |
| change | −0.06 | −0.06 | +0.06 | +0.06 |
| equilibrium | 0.040 | 0.07 | 0.11 | 0.06 |
(iii) Kc has no units because the units cancel out (equal number of concentration terms top and bottom).
I: 2X₂ + Y₂ ⇌ 2X₂Y, Kc = 2. II: X₂Y ⇌ X₂ + ½Y₂. Kc for II?
B ✗ reversed only ½ (no square root) C ✗ reversed only (1/K squared) D ✗ K cannot be negative
Answer: A
1.0 mol AgNO₃ + 1.0 mol FeSO₄ in 1.00 dm³; 0.44 mol Ag⁺ at equilibrium.
Solid Ag is not included (left out of Kc).
| Ag⁺ | Fe²⁺ | Ag(s) | Fe³⁺ | |
|---|---|---|---|---|
| I | 1 | 1 | 0 | 0 |
| C | −0.56 | −0.56 | +0.56 | +0.56 |
| E | 0.44 | 0.44 | — | 0.56 |
Answer: D
500 K, vessel 6.0 dm³; equilibrium 7.2 mol N₂, 12.0 mol H₂; Kc = 6.0 × 10⁻² at 500 K. [NH₃]?
Answer: B
X(aq) ⇌ 2Y(aq); [X] starts 0.50 mol dm⁻³ and falls to 0.25 at equilibrium.
| X | 2Y | |
|---|---|---|
| I | 0.5 | 0 |
| C | −0.25 | +0.5 |
| E | 0.25 | 0.5 |
Answer: C
8. The Equilibrium Constant Kp
For gases it is easier to work with pressures ⇒ Kp.
Partial pressure of A = mole fraction of A × total pressure
- Don't include solids or liquids in Kp.
- The value of an equilibrium constant remains constant if temperature is constant.
- Exothermic: T ↑ ⇒ Kc and Kp ↓ | Endothermic: T ↑ ⇒ Kc and Kp ↑.
- Changing pressure or using a catalyst has NO effect on Kc and Kp.
9. Calculating Kp
Total pressure 1 × 10⁶ Pa, 550 °C. At equilibrium: 0.3 mol PCl₅, 0.7 mol PCl₃, 0.7 mol Cl₂. Find Kp.
2.00 mol N₂O₄ sealed at 350 K. At equilibrium total P = 140 kPa and 1.84 mol N₂O₄ present. (Equation: 2NO₂ ⇌ N₂O₄.)
(i) Kp = p(N₂O₄)eqmp(NO₂)²eqm
| 2NO₂ | N₂O₄ | |
|---|---|---|
| I | 0 | 2 |
| C | +0.32 | −0.16 |
| E | 0.32 | 1.84 |
(ii) n(NO₂) = 0.32 mol.
(a) Roasting pyrites: 4FeS₂(s) + 11O₂(g) → 2Fe₂O₃(s) + 8SO₂(g) (the board wrote it unbalanced: FeS₂ + O₂ → Fe₂O₃ + SO₂)
(d)(i) Higher temperature: advantage — rates of the forward and backward reactions become fast, so equilibrium is reached faster. Disadvantage — the forward reaction is exothermic, so a higher T shifts equilibrium to the left and decreases the yield of SO₃. [4]
(ii) Kp = (pSO₃)²eqm(pSO₂)²eqm (pO₂)eqm
(iii) 2.00 mol SO₂ + 2.00 mol O₂; at equilibrium P = 2.00 × 10⁵ Pa and 1.80 mol SO₃.
| 2SO₂ | O₂ | 2SO₃ | |
|---|---|---|---|
| I | 2 | 2 | 0 |
| C | −1.8 | −0.9 | +1.8 |
| E | 0.2 | 1.1 | 1.8 |
Note the question uses 400 °C for this step; the board's general conditions list 450 °C.
N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ mol⁻¹; N≡N = 944, H–H = 436.
(a)(i) Bond energy: the minimum energy required to break 1 mole of a bond in gaseous molecules.
(c) At 2.00 × 10⁷ Pa: 1.00 mol N₂ + 3.00 mol H₂; equilibrium has 0.300 mol NH₃.
| N₂ | 3H₂ | 2NH₃ | |
|---|---|---|---|
| I | 1 | 3 | 0 |
| C | −0.15 | −0.45 | +0.3 |
| E | 0.85 | 2.55 | 0.3 |
(d) Partial pressures: N₂ 2.20 × 10⁶; H₂ 9.62 × 10⁵; NH₃ 1.40 × 10⁴ Pa. (i) Kp = (pNH₃)²(pN₂)(pH₂)³
(iii) Same T, smaller container: pressure increases (P ∝ 1/V, T constant) ⇒ equilibrium shifts to fewer moles ⇒ yield of NH₃ increases; Kp — no effect (only T changes K).
2HI ⇌ H₂ + I₂: start with b mol HI, x mol dissociate; total pressure P.
| 2HI | H₂ | I₂ | |
|---|---|---|---|
| I | b | 0 | 0 |
| C | −x | +x/2 | +x/2 |
| E | b−x | x/2 | x/2 |
Answer: D
Which factors change Kp?
Only temperature. Pressure ✗, catalyst ✗ (they change rate/position, not K).
Answer: D (T ✓, pressure ✗, catalyst ✗)
10. Quick Recap — Full Chapter Cheat-Sheet
- Dynamic equilibrium: rate forward = rate backward; needs a reversible reaction in a closed system (energy in/out, no matter).
- Le Chatelier: the equilibrium shifts to oppose the change. Conc ↑ reactants → right; conc ↑ products → left. T ↑ → endothermic direction; T ↓ → exothermic direction. P ↑ → fewer gas moles; P ↓ → more gas moles.
- Catalyst: ↓ Ea, ↑ rate, no change in yield, position or K. T ↑ always ↑ both rates.
- Haber: 450 °C, 200 atm, iron, remove NH₃ (condenses, H-bonding) & recycle. Contact: 450 °C, 1–2 atm, V₂O₅, 99.5 % yield.
- Kc = [products]coef / [reactants]coef (mol dm⁻³, at eqm; omit solids). Kp = same with partial pressures (gases only).
- Partial pressure = mole fraction × total pressure; mole fraction = moles A / total moles.
- Units: work out by cancelling; count terms top vs bottom.
- Reverse ⇒ 1/K; multiply equation by n ⇒ Kn; halve ⇒ √K.
- K changes with temperature only: exo T↑ ⇒ K↓; endo T↑ ⇒ K↑. Pressure/catalyst: no effect. Large K ⇒ equilibrium on the right.
- Always use an I-C-E table; if moles of gas are equal on both sides, volume cancels in Kc.