Chemical Equilibrium Notes

Reversible Reactions and Equilibrium

• Reversible Reactions: Reactions that can proceed in both forward and reverse directions.
  • Represented by the symbol $⇌$.
  • Example: $"H2O(l) ⇌ H2O(g)"$ (water evaporation/condensation).
• Incomplete Reactions: Reversible reactions appear incomplete because they don't achieve 100% yield.
  • Example: $N2(g) + 3H2(g) ⇌ 2NH3(g)$, where 1 mol of nitrogen and 3 mol of hydrogen do not produce 2 mol of ammonia.
• Chemical Equilibrium: The point at which the rates of the forward and reverse reactions are equal, resulting in a constant concentration of reactants and products.
  • Reactants and products are both present at equilibrium.
• Conditions for Reversibility: Reactions can be reversed if reactants and products stay in contact under the right conditions.
  • Example: $CuSO4(s) + 5H2O(l) ⇌ CuSO4.5H2O(s)$

Equilibrium Process

• Rechargeable Batteries: Utilize reversible reactions; forward releases energy, backward absorbs energy.
• Forward and Backward Reaction Rates:
  • Initially, reactants form products.
  • Products collide and act as reactants (backward reaction).
  • As product concentration increases, the backward reaction rate increases.
  • As reactant concentration decreases, the forward reaction rate decreases.
• Equilibrium Attainment: Equilibrium is reached when the forward and backward reaction rates become equal.
• Activation Energy: The energy barrier that must be overcome for a reaction to occur. Both forward and reverse reactions have activation energies.

Dynamic Equilibrium

• Dynamic Equilibrium: A state where the reaction is continuously proceeding in both directions at the same rate.
• Characteristics:
  • Reactants and products are present in the equilibrium mixture.
  • Intramolecular bonds are continually breaking and forming.
• Macroscopic Properties at Equilibrium: Observable properties remain constant.
  • Color
  • pH
  • Temperature
  • Gas pressure

Open vs. Closed Systems

• Open System: Exchanges both matter and energy with surroundings.
• Closed System: Exchanges only energy with surroundings.
• Equilibrium in Closed Systems: Only closed systems can reach equilibrium because products must remain in the system to reverse the reaction.
• Open Vessel Reaction: Example: The reaction between $CaCO3$ and $HCl$ in an open vessel does not reach equilibrium because the product, $CO2$, escapes.

Homogeneous vs. Heterogeneous Equilibrium

• Homogeneous Equilibrium: All reactants and products are in the same state (gaseous, aqueous, or liquid).
• Heterogeneous Equilibrium: Reactants and products are in different states.
• Extent of Reaction: Indicates how far a reaction proceeds toward products at equilibrium.
  • Strong acids like $HCl$ ionize almost completely (high extent): $HCl(aq) + H2O(l) ⇌ H3O^+(aq) + Cl^–(aq)$
  • Weak acids like $CH3COOH$ ionize only slightly (low extent): $CH3COOH(aq) + H2O(l) ⇌ H3O^+(aq) + CH3COO^–(aq)$
• Rate vs. Extent: Extent is not the same as rate.

Equilibrium Constant (K)

• Equilibrium Constant (K): A mathematical constant associated with a system at equilibrium; temperature-dependent.

• General Reaction: For a general reaction $aA + bB + … ⇌ pP + qQ + …$, the equilibrium constant $K$ is expressed as:

  $K = \frac{{\left[P\right]^p \left[Q\right]^q …}}{{\left[A\right]^a \left[B\right]^b …}}$

• Example Equations:

  • For $PCl5(g) ⇌ PCl3(g) + Cl2(g)$, $K = \frac{{\left[PCl3\right]\left[Cl2\right]}}{{\left[PCl5\right]}}$
  • For $CO(g) + 2H2(g) ⇌ CH3OH(g)$, $K = \frac{{\left[CH3OH\right]}}{{\left[CO\right]\left[H2\right]^2}}$

• K Value: The value of $K$ is different for different reactions.

Reaction Quotient (Q) or Concentration Fraction (CF)

• Reaction Quotient (Q): The ratio of concentrations of products to reactants at any point in a reaction.

• Approaching Equilibrium: The value of $Q$ changes over time and approaches the value of $K$.

• Equilibrium:

  • When the reaction has reached equilibrium, the reaction quotient will remain constant, and will be equal to the equilibrium constant.

• General System: Consider the system $aA + bB + … ⇌ cC + dD$, then:

  $Q = \frac{{\left[C\right]^c \left[D\right]^d}}{{\left[A\right]^a \left[B\right]^b}}$

• Interpreting Q:

  • If Q > K, the system shifts left (more reactants form).
  • If Q < K, the system shifts right (more products form).
  • If $Q = K$, the system is at equilibrium.

Equilibrium Constant Units

• Units of K: Equilibrium constants have units that depend on the expression. Each concentration must have a unit in molar (M).

• Example:

  • For $K = \frac{{\left[NH3\right]^2}}{{\left[N2\right]\left[H2\right]^3}}$, the unit is $\frac{{M^2}}{{M \cdot M^3}} = M^{-2}$

• Calculation Example: For the reaction $PCl3(g) + Cl2(g) ⇌ PCl5(g)$ at 20 °C, given $\left[PCl3\right] = 1.50 \times 10^{-3} M$, $\left[Cl2\right] = 8.25 \times 10^{-2} M$, $\left[PCl5\right] = 1.67 M$:

  $K = \frac{{\left[PCl5\right]}}{{\left[PCl3\right]\left[Cl2\right]}} = \frac{{1.67}}{{1.50 \times 10^{-3} \times 8.25 \times 10^{-2}}} = 1.35 \times 10^4 M^{-1}$

• Calculating Equilibrium Concentrations: For the reaction $Ag^+(aq) + 2NH3(aq) ⇌ Ag(NH3)<em>2^+(aq)$, given $Kc = 1.60 \times 10^4 M^{-2}$ at 25 °C, $\left[NH3\right] = 5.00 \times 10^{-3} M$, $\left[Ag(NH3)</em>2^+\right] = 0.401 M$:

  $K = 1.60 \times 10^4 = \frac{{\left[Ag(NH3)_2^+\right]}}{{\left[Ag^+\right]\left[NH3\right]^2}}$

  $\left[Ag^+\right] = \frac{{0.401}}{{1.60 \times 10^4 \times (5.00 \times 10^{-3})^2}} = 1.00 M$

Extent of Reaction and Equilibrium Yield

• Extent of Reaction: The equilibrium constant indicates the extent of reaction.
• Equilibrium Yield: The amount of products present at equilibrium.
• K Value: Fixed for a particular reaction at a constant temperature.
  • Unaffected by adding reactants or products, changes in pressure, or catalysts.
  • Dependent on temperature.
• Temperature Effects:
  • Exothermic Reactions: As temperature increases, $K$ decreases, and the amount of products at equilibrium decreases.
  • Endothermic Reactions: As temperature increases, $K$ increases, and the amount of products at equilibrium increases.

Calculating Equilibrium Constants

• Calculating K:
  • Equilibrium constants can be calculated if amounts and volumes are known (convert to concentration).
  • Substitute known values into the equilibrium expression to find the unknown.

Le Chatelier's Principle

• Le Chatelier’s Principle: When a change is made to a system at equilibrium, the system will adjust to partially oppose the change.
• Types of Changes:
  • Adding or removing reactants/products
  • Decreasing or increasing the volume of a gaseous system
  • Increasing or decreasing the temperature
  • Adding a catalyst

Effect of Adding/Removing Reactants/Products

• Adding a Reactant:
  • Temporarily increases the concentration of the reactant.
  • The system acts to decrease the concentration of that reactant (by reacting with other reactants).
  • Net forward reaction (equilibrium shifts right).
• Removing a Reactant:
  • Temporarily decreases the concentration of the reactant.
  • The system acts to increase the concentration of that reactant (by converting products into reactants).
  • Net backward reaction (equilibrium shifts left).
• Adding a Product:
  • Temporarily increases the concentration of the product.
  • The system acts to decrease the concentration of the product (by converting products into reactants).
  • Net backward reaction (equilibrium shifts left).
• Removing a Product:
  • Temporarily decreases the concentration of the product.
  • The system acts to increase the concentration of the product (by converting reactants into products).
  • Net forward reaction (equilibrium shifts right).

Effect of Volume Changes on Gaseous Systems

• Decreasing Volume:
  • Temporarily increases the concentration of all reactants and products.
  • The system acts to decrease the concentration of particles.
  • If more reactant particles than product particles, equilibrium moves to the right.
  • If equal numbers of reactant and product particles, equilibrium does not move.
  • If fewer reactant particles than product particles, equilibrium moves to the left.
• Increasing Volume:
  • Temporarily decreases the concentration of all reactants and products.
  • The system acts to increase the concentration of particles.
  • If more reactant particles than product particles, equilibrium moves to the left.
  • If fewer reactant particles than product particles, equilibrium moves to the right.

Effect of Volume Changes on Aqueous System

• Increasing Volume by Adding Water (Dilution): The concentration of all reactants and products will be decreased initially. The system will oppose the change according to the stoichiometry of the reaction.
• Example: Consider the equilibrium $Fe^{3+}(aq) + SCN^–(aq) ⇌ FeSCN^{2+}(aq)$. If this solution is diluted, the concentration of all species are momentarily lowered. According to Le Chatelier’s principle, the reverse reaction will be favored.

Effect of Adding Inert Gas

• Adding Inert Gas at Constant Volume: Increases the pressure of a gaseous system. The concentrations of reactants and products are unaffected. Therefore, there is no effect on the position of equilibrium.

Effect of Temperature Changes

• Only Temperature Affects K: The only change that can affect the value of $K$ is temperature.
• Enthalpy (ΔH): The value of $"\Delta H"$ influences the direction in which equilibrium moves.
• Exothermic Reactions:
  • Consider $N<em>2 + 3H</em>2 ⇌ 2NH_3 ; \"\Delta H" = –92 \"kJ mol"^{-1}$
  • Increasing temperature is like adding a product (heat), so the position of equilibrium moves to the left.
  • Decreasing temperature is like removing a product (heat), so the position of equilibrium moves to the right.
  • Exothermic reactions are favored by decreasing the temperature.
• Endothermic Reactions:
  • Consider $NH<em>4NO</em>3(s) + aq ⇌ NH<em>4^+ + NO</em>3^–(aq) ; \"\Delta H" = +25 \"kJ mol"^{-1}$
  • Increasing temperature is like adding a reactant (heat), so the position of equilibrium moves to the right.
  • Decreasing temperature is like removing a reactant, so the position of equilibrium moves to the left.
  • Endothermic reactions are favored by increasing the temperature.

Catalysts and Equilibrium

• Effect of a Catalyst: The addition of a catalyst does not change the position of equilibrium.
• Reaction Rate: It does, however, allow equilibrium to be reached more quickly, as it lowers the activation energy and increases the rate of both forward and backward reactions.