Equilibrium

The Equilibrium State

• Reversible Reactions: All reactions can reverse under suitable conditions, reaching equilibrium.
• Equilibrium Defined: At equilibrium, concentrations of products and reactants remain constant, as the rate of the forward reaction equals the rate of the reverse reaction:
  $\text{rate}<em>{\text{forward}} = \text{rate}</em>{\text{reverse}}$
• Dynamic State: Chemical equilibrium is dynamic; reactions occur continuously, but no net change is observable at a macroscopic level.

The Equilibrium Constant

• Considering a Reaction: For the reaction $2NO<em>2(g) \rightleftharpoons 2NO(g) + O</em>2(g)$
  • At equilibrium:
    $\text{rate}<em>{\text{forward}} = \text{rate}</em>{\text{reverse}}$
• Expression for K: The equilibrium constant (K) is derived from the concentrations of reactants and products:
  $K = \frac{[NO]^2[O<em>2]}{[NO</em>2]^2}$

K and the Extent of Reaction

• Meaning of K: K reflects the ratio of product concentrations to reactant concentrations at equilibrium.
• Small K value: Indicates the reaction yields little product, favoring reactants.
• Large K value: Indicates the reaction produces predominantly products, favoring products.

The Reaction Quotient Q

• Definition of Q: For the general reaction
  $aA + bB \rightleftharpoons cC + dD$
  $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• Equilibrium Comparison: At equilibrium,
  $Q = K$
• Direction of Reaction: The value of Q indicates the direction the reaction must shift to reach equilibrium. If:
  • Q < K: Shift to products
  • Q > K: Shift to reactants
  • $Q = K$: System is at equilibrium.

Heterogeneous Equilibrium

• Definition: Involves reactants and/or products in different phases.
• Concentration Exclusion: Pure solids and liquids are not included in equilibrium expressions.
• Example: For
  $CaCO<em>3(s) \rightleftharpoons CaO(s) + CO</em>2(g)$
  $Q = [CO_2]$

Sample Problems

Writing Reaction Quotients

• Balanced Equations for Reaction Quotients:
  • (a) $4NO<em>2(g) \rightleftharpoons 2N</em>2O<em>4(g)$$Q</em>c = \frac{[N<em>2O</em>4]^2}{[NO_2]^4}$
  • (b) $2Na(s) + 2H<em>2O(l) \rightleftharpoons 2NaOH(aq) + H</em>2(g)$
    $Q<em>c = \frac{[NaOH]^2[H</em>2]}{[Na]^2}$
• Note: Only species with changing concentrations are included in Q.

Determining Direction of Reaction

• Example: For the reaction $N<em>2O</em>4(g) \rightleftharpoons 2NO_2(g)$ at K = 0.21
  • If concentrations are [N2O4] = 0.12 M and [NO2] = 0.55 M:
  • Calculate Q and compare with K. If
    Q > K, reaction moves left.

Le Châtelier’s Principle

• Principle Statement: When a system at equilibrium is disturbed, it shifts to counteract the disturbance.
• Common Disturbances:
  • Change in concentration
  • Change in pressure (via volume change)
  • Change in temperature
• Response:
  • Increase in reactants shifts right (to products)
  • Increase in products shifts left (to reactants)

The Effect of Concentration Changes

• Increase in Reactants: Shifts equilibrium to right, increasing products.
• Decrease in Reactants: Shifts equilibrium to left, increasing reactants.
• Changes in Concentration Have No Effect on K: Only changes in temperature do.

The Effect of Pressure Changes

• Pressure Increase: Shifts equilibrium toward fewer moles of gas.
• Volume Increase: Shifts equilibrium toward more moles of gas.
• Inert Gas Addition: No effect on equilibrium position if volume constant

The Effect of Temperature Changes

• Temperature Increase: For exothermic reactions, K decreases; for endothermic, K increases.
• Temperature Decrease: Opposite effects apply.

Catalysts and Equilibrium

• Catalysts speed up both forward and reverse reactions equally.
• Impact on Equilibrium: Catalysts do not alter the equilibrium position, only the time to reach it.

Solubility and Equilibrium

• Saturated Solutions: At equilibrium with undissolved solute.
• Ksp: The solubility product constant, indicating the solubility of slightly soluble compounds.
• Common Ion Effect: Lowering solubility when a common ion is added.
• Precipitation Prediction: Formed based on Qsp compared to Ksp.