Topic 9 · Chemical Equilibria

Chemical Equilibria

1

Dynamic Equilibrium

DefinitionReversible reaction: a reaction that takes place in both the forward and backward directions (⇌)
DefinitionDynamic equilibrium: the state in a reversible reaction where the rate of the forward reaction equals the rate of the backward reaction, such that there is no net change in the concentrations of reactants and products, in a closed system.
DefinitionClosed system: no matter is lost to or gained from the surroundings
timeconcentrationreactantsproductsequilibrium reached timerateforwardbackwardrate f = rate b
  • At equilibrium, [reactants] and [products] are constant, but usually not equal, both reactions are still occurring
  • The same equilibrium is reached whether we start from the reactants or the products
  • In an open system, products escape, so the reaction goes to completion.
2

Equilibrium Constants

For aA + bB ⇌ cC + dD:

ExpressionUnitsUse for
Kc[C]c[D]d[A]a[B]b(mol dm⁻³)(c + d) − (a + b)species in solution or gas, as concentrations
KppCc pDdpAa pBb(atm or Pa)(c + d) − (a + b)gases only, as partial pressures
  • Partial pressure: pA = xA × ptotal, where the mole fraction xA = nA ÷ ntotal
  • Heterogeneous equilibria: leave out pure solids, pure liquids and the solvent, as their concentrations are constant
  • CaCO₃(s) ⇌ CaO(s) + CO₂(g): Kc = [CO₂], Kp = pCO₂
NoteK is changed only by temperature. Concentration, pressure and catalysts do not change K. K says nothing about how fast equilibrium is reached.
Size of KPosition of equilibriumEquilibrium mixture
K ≫ 1lies to the rightmostly products
K ≪ 1lies to the leftmostly reactants
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3

Calculations with K

ICE table: Initial, Change, Equilibrium. Convert equilibrium moles to concentration (÷ V) or partial pressure before substituting into K.

I: initial amountsC: change, in mole ratioE: equilibrium amounts÷ V (or p) → into K

3.1Find Kc from equilibrium amounts

Worked example

CH₃CO₂H(l) + C₂H₅OH(l) ⇌ CH₃CO₂C₂H₅(l) + H₂O(l)

To make the ester ethyl ethanoate, 2.0 mol of ethanoic acid and 2.0 mol of ethanol are mixed. At equilibrium, 1.33 mol of water is present and the total volume is 0.500 dm³. Find Kc.

CH₃CO₂HC₂H₅OHesterH₂O
I / mol2.02.000
C / mol−1.33−1.33+1.33+1.33
E / mol0.670.671.331.33

Divide each by 0.500 dm³ to get concentrations:

Kc = (1.33/0.500)(1.33/0.500)(0.67/0.500)(0.67/0.500) = 3.94 (no units)

Water is a product here, not the solvent, so it is included. V cancels, but working must still show concentrations.

3.2Find Kp from initial partial pressures

Worked example

2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

In the Contact process, SO₂ (1.00 atm) and O₂ (0.50 atm) reach equilibrium in a vessel of fixed volume at 675 K. The total pressure at equilibrium is 1.01 atm. Find Kp.

  • At fixed volume and temperature, partial pressure ∝ moles, so the ICE table can use pressures
  • Let x atm of O₂ react: SO₂ falls by 2x, and SO₃ rises by 2x (mole ratio 2 : 1 : 2)
SO₂O₂SO₃
I / atm1.000.500
C / atm−2x−x+2x
E / atm0.020.010.98

Total: (1.00 − 2x) + (0.50 − x) + 2x = 1.01 → x = 0.49

Kp = pSO₃²pSO₂² pO₂ = (0.98)²(0.02)²(0.01) = 2.40 × 10⁵ atm⁻¹

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4

Le Chatelier's Principle

DefinitionLe Chatelier's Principle: if a change is made to a system in dynamic equilibrium, the position of equilibrium shifts so as to counteract (minimise) that change and re-establish equilibrium.
  • Qc < Kc: too few products → forward reaction favoured, POE shifts right
  • Qc = Kc: system is at equilibrium, no net change
  • Qc > Kc: too many products → backward reaction favoured, POE shifts left
Q = KQ < K: forwardQ > K: backward

Q has the same expression as K but uses concentrations at any moment.

4.1Concentration: A + B ⇌ C + D

Adding A

  1. POE shifts right to consume some of the added A
  2. Forward reaction is favoured
  3. [A] ↓ (but stays higher than before), [B] ↓, [C] and [D] ↑
  4. Kc unchanged
timeconc.ABC, DA addednew eqmold [A]

Removing a product, e.g. D: POE shifts right to produce more D.

4.2Pressure: 2NO₂(g) ⇌ N₂O₄(g)

Decreasing volume (pressure ↑)

  1. Pressure ↑ → POE shifts to the side with fewer gas particles to reduce the pressure
  2. 2 mol gas → 1 mol gas: POE shifts right
  3. Brown colour becomes paler (after first darkening as all gases are compressed)
before: 9 particlesafter: 6 particles
NoteSpecial cases
  • Equal moles of gas on both sides (2HI ⇌ H₂ + I₂): no shift
  • Inert gas at constant volume: partial pressures unchanged → no shift
  • Inert gas at constant pressure: volume ↑, partial pressures ↓ → POE shifts to more gas particles

4.3Temperature: N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ mol⁻¹

Increasing temperature

  1. POE shifts left
  2. The endothermic backward reaction is favoured to absorb the excess heat
  3. [NH₃] ↓ → Kc decreases
timeconc.T raisedNH₃N₂, H₂no sudden jump

T ↑ favours the endothermic direction, T ↓ favours the exothermic direction. Only temperature changes K.

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4

Le Chatelier's Principle (continued)

4.4Catalyst

  1. Rates of forward and backward reactions increase equally
  2. Ea of both directions lowered by the same amount
  3. kf and kb increase by the same factor
  4. Kc = kfkb → no effect on POE or K
  5. Equilibrium is only reached faster
timeconc.with catalystwithoutsame POE
5

The Haber Process

N₂(g) + 3H₂(g) ⇌ 2NH₃(g) ΔH = −92 kJ mol⁻¹

The plant compressor200–250 atm1converteriron, 450 °C2condenserNH₃ liquefies3liquidNH₃unreacted N₂ and H₂ recycledN₂ + 3H₂
Yield of NH₃ at equilibrium
pressure / atm% NH₃ at equilibrium350 °C450 °C550 °C
  • Yield of NH₃ at equilibrium rises with pressure and falls with temperature
  • 200–250 atm and about 450 °C are a compromise between yield, rate and cost

Temperature: 450 °C

  • Forward reaction exothermic: low T shifts POE right → higher yield
  • But at low T, rate is too slow
  • Moderate T: reasonable yield in a reasonable time

Pressure: 250 atm

  • 4 mol gas → 2 mol gas: high p shifts POE right → higher yield, also faster rate
  • But very high p needs costly, thick-walled plant

Catalyst: finely divided Fe

  • Shortens the time to reach equilibrium, yield unchanged
  • Cheaper than other catalysts (e.g. Ru)
  • NH₃ is cooled and condensed and removed: POE shifts right, unreacted N₂ and H₂ recycled
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