Unit 2: CH02 Syllabus Node

Dynamic Equilibria & Equilibrium Constant Kc

Dynamic equilibrium, Le Chatelier shifts, homogeneous Kc mathematical expressions, ICE calculation tables, and temperature effects on Kc.

Dynamic Equilibrium Rate vs Time Graph Time Reaction Rate Forward Rate (Reactants used up) Reverse Rate (Products accumulate) t_eq (Equilibrium Established) Dynamic Equilibrium Plateau Forward Rate = Reverse Rate Macroscopic concentrations constant

1. The Concept of Dynamic Equilibrium

Dynamic Equilibrium

A reversible reaction in a closed system where the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of reactants and products remain constant.

Equilibrium is dynamic because reactions continue occurring at the microscopic level in both directions simultaneously at identical rates.

2. Le Chatelier's Principle

Le Chatelier's Principle

If a chemical system at equilibrium is subjected to a change in conditions, the system adjusts to oppose that change and restore equilibrium.

Condition Changed Equilibrium Shift Opposing Response of the System
Increase Temperature Shifts in the endothermic direction (\(+\Delta H\)) Absorbs thermal energy to lower system temperature.
Decrease Temperature Shifts in the exothermic direction (\(-\Delta H\)) Releases thermal energy to raise system temperature.
Increase Pressure Shifts to side with fewer gas moles Reduces total gas molecules to lower pressure.
Decrease Pressure Shifts to side with more gas moles Increases total gas molecules to raise pressure.
Add Catalyst No shift in position Increases rates of forward and reverse reactions equally.

3. The Equilibrium Constant (\(K_c\))

For a general homogeneous reversible reaction:

\[ a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D} \]

The equilibrium constant expression is:

\[ K_c = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b} \]

Where square brackets \([\text{X}]\) denote equilibrium concentrations in \(\text{mol dm}^{-3}\).

Determining Units of \(K_c\)

Substitute \(\text{mol dm}^{-3}\) for each concentration term and cancel algebraically:

  • If numerator and denominator have equal powers, \(K_c\) has no units.
  • For \(\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)\): \[ \text{Units} = \frac{(\text{mol dm}^{-3})^2}{(\text{mol dm}^{-3}) \times (\text{mol dm}^{-3})^3} = \frac{1}{(\text{mol dm}^{-3})^2} = \mathbf{\text{mol}^{-2}\text{dm}^6} \]

4. ICE Calculation Tables (Initial, Change, Equilibrium)

Worked Example: Esterification Equilibrium
In an esterification reaction: CH3COOH + C2H5OH <=> CH3COOC2H5 + H2O Initially, 1.00 mol of ethanoic acid is mixed with 1.00 mol of ethanol in a sealed flask of volume V dm^3. At equilibrium at 298 K, 0.670 mol of ethyl ethanoate is present. Calculate the value of Kc.

Step 1: Construct the ICE Table:

Row CH3COOH C2H5OH CH3COOC2H5 H2O
Initial (mol)1.001.000.000.00
Change (mol)-0.670-0.670+0.670+0.670
Equilibrium (mol)0.3300.3300.6700.670
Concentration (mol/V)0.330 / V0.330 / V0.670 / V0.670 / V

Step 2: Substitute into \(K_c\) expression:

\[ K_c = \frac{[\text{CH}_3\text{COOC}_2\text{H}_5][\text{H}_2\text{O}]}{[\text{CH}_3\text{COOH}][\text{C}_2\text{H}_5\text{OH}]} = \frac{(0.670 / V)(0.670 / V)}{(0.330 / V)(0.330 / V)} \]

The volume terms \(V\) cancel out completely:

\[ K_c = \frac{0.670 \times 0.670}{0.330 \times 0.330} = \frac{0.4489}{0.1089} = \mathbf{4.12} \text{ (no units)} \]

5. The Effect of Conditions on the Value of \(K_c\)

Vital OxfordAQA Rule: Temperature Alone Changes Kc
  • Temperature: If temperature change shifts equilibrium in the forward direction, \(K_c\) increases. If it shifts equilibrium in the reverse direction, \(K_c\) decreases.
  • Concentration / Pressure: Changing concentrations or total pressure shifts the position of equilibrium, but does not change the numerical value of \(K_c\).
  • Catalysts: Catalysts speed up forward and reverse rates equally; they alter neither the position of equilibrium nor the value of \(K_c\).

6. Practice Questions

Practice Problem (2 Marks)
For the exothermic reaction: 2SO2(g) + O2(g) <=> 2SO3(g) (Delta H = -197 kJ mol^-1) State and explain what happens to the value of Kc when the temperature is increased.

Answer:

  • The value of \(K_c\) decreases. (1 mark)
  • Explanation: Because the forward reaction is exothermic, an increase in temperature shifts the equilibrium in the endothermic reverse direction to absorb heat. This reduces the concentration of products and increases reactants, decreasing the value of the fraction. (1 mark)