Chemical Equilibrium Notes

Chemical Equilibrium: Definition & Characteristics

• State where concentrations/pressures of all species remain constant with time in a closed system.

• Equilibrium is dynamic: forward and reverse reaction rates are equal; microscopic change continues despite macroscopic constancy.

• Position of equilibrium can lie "far to the right" (products predominant) or "far to the left" (reactants predominant).

Equilibrium Condition (Dynamic Equilibrium)

• Key criterion: $r<em>{fwd}=r</em>{rev}$ ⇒ concentrations constant.

• Disturbance (e.g. adding reactant) temporarily changes rates; system shifts until rates re-equalise.

Equilibrium Constant (K)

• Law of mass action for $jA+kB \rightleftharpoons lC+mD$ :
  $K = \frac{[C]^l[D]^m}{[A]^j[B]^k}$

• Properties
  • Depends only on temperature; independent of initial composition.
  • No units (by convention).

• Manipulations
  • Reverse reaction ⇒ $K<em>{rev}=1/K$ • Multiply equation by $n$ ⇒ $K</em>{new}=K^{n}$

• Multiple equilibrium positions (sets of concentrations) share the same $K$.

Relations Involving Pressures (K_p versus K)

• For gases, equilibrium can be expressed with partial pressures:
  $K<em>p = \frac{(P</em>C)^l(P<em>D)^m}{(P</em>A)^j(P_B)^k}$

• Link between constants:
  $K_p = K(RT)^{\Delta n}$
  where $\Delta n=(l+m)-(j+k)$ (change in moles of gas).

Heterogeneous Equilibria

• Pure solids & liquids have constant concentrations; they are omitted from $K$ and $K<em>p$ expressions. Example: $\text{CaCO}</em>3(s) \rightleftharpoons \text{CaO}(s)+\text{CO}<em>2(g),\; K=[\text{CO}</em>2]$

Applications of K

• Extent of reaction:
  • $K \gg 1$ ⇒ products dominate.
  • $K \ll 1$ ⇒ reactants dominate.

• Reaction Quotient $Q$ (same form as $K$ but uses initial concentrations) predicts shift:
  • $QK$ ⇒ shift left.
  • $Q=K$ ⇒ at equilibrium.

• ICE (Initial-Change-Equilibrium) tables streamline equilibrium calculations.

• Small-K approximations: when $K$ is very small, the change in large initial concentrations can be neglected (verify afterward).

Solving Equilibrium Problems (concise procedure)

1. Write balanced equation.

2. Write $K$ (or $K_p$) expression.

3. List initial values.

4. Compute $Q$ to find shift.

5. Define changes (using variable $x$).

6. Substitute equilibrium values into $K$; solve for $x$.

7. Verify results satisfy $K$.

Le Châtelier’s Principle

• If a system at equilibrium experiences a change (concentration, pressure/volume, temperature), it shifts to oppose that change.

Change in Concentration

• Add reactant/product ⇒ shifts to consume added species.

• Remove species ⇒ shifts to replace it.

Change in Pressure/Volume (gas systems)

• Add inert gas at constant volume: no shift (partial pressures unchanged).

• Decrease volume (increase total pressure): equilibrium shifts toward side with fewer moles of gas; increase volume does opposite.

Change in Temperature

• Treat heat as a reactant (endothermic) or product (exothermic).
  • Endothermic (\Delta H>0): heating shifts right; $K$ increases.
  • Exothermic (\Delta H<0): heating shifts left; $K$ decreases.

These bullet-point notes capture the essential principles, relations, and problem-solving steps for chemical equilibrium, suitable for rapid exam review.