Chemical Equilibrium Fundamentals

• Chemical equilibrium is the state in which both reactants and products are present in concentrations which have no further tendency to change with time.

Fundamentals of Chemical Equilibrium

• Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction.
• At equilibrium, the net change in concentrations of reactants and products is zero.
• Equilibrium is dynamic; the forward and reverse reactions continue to occur, but at equal rates.
• Equilibrium can only be established in a closed system.
• A closed system is one in which neither matter nor energy can escape to the surroundings or enter from the surroundings.

Equilibrium Constant (K)

• The equilibrium constant (K) is a numerical value that relates the concentrations of reactants and products at equilibrium.
• For a reversible reaction: aA + bB ⇌ cC + dD, the equilibrium constant expression is: K = ([C]^c [D]^d) / ([A]^a [B]^b).
• The square brackets denote the molar concentrations of the species at equilibrium.
• The exponents (a, b, c, d) are the stoichiometric coefficients from the balanced chemical equation.
• A large value of K indicates that the equilibrium favors the products.
• A small value of K indicates that the equilibrium favors the reactants.
• The value of K is temperature-dependent; changing the temperature alters the value of K.

Types of Equilibrium Constants

• K_c: Equilibrium constant expressed in terms of molar concentrations.
• K_p: Equilibrium constant expressed in terms of partial pressures of gaseous reactants and products.
• The relationship between K_c and K_p: K_p = K_c(RT)^Δn, where R is the ideal gas constant, T is the temperature in Kelvin, and Δn is the change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants).

Reaction Quotient (Q)

• The reaction quotient (Q) is a measure of the relative amounts of products and reactants present in a reaction at any given time.
• The reaction quotient (Q) can be calculated whether the reaction is at equilibrium or not.
• For the reaction aA + bB ⇌ cC + dD, Q = ([C]^c [D]^d) / ([A]^a [B]^b), where the concentrations are initial concentrations, not necessarily equilibrium concentrations.
• Comparing Q and K:
  • If Q < K, the ratio of products to reactants is less than that for the system at equilibrium. Therefore, to reach equilibrium, there is a net conversion of reactants to products.
  • If Q > K, the ratio of products to reactants is greater than that for the system at equilibrium. Therefore, to reach equilibrium, there is a net conversion of products to reactants.
  • If Q = K, the reaction is at equilibrium.

Le Chatelier's Principle

• Le Chatelier's Principle states that if a change of condition is applied to a system in equilibrium, the system will shift in a direction that relieves the stress.
• Changes in conditions include:
  • Concentration: Adding reactants or products.
  • Pressure: Changing the pressure (for reactions involving gases).
  • Temperature: Heating or cooling the system.

Effect of Concentration

• Adding reactants shifts the equilibrium to the right (towards products).
• Removing reactants shifts the equilibrium to the left (towards reactants).
• Adding products shifts the equilibrium to the left (towards reactants).
• Removing products shifts the equilibrium to the right (towards products).
• Inert gases have no effect on the equilibrium position.

Effect of Pressure

• Changing the pressure only affects gaseous equilibria where there is a change in the number of moles of gas.
• Increasing the pressure shifts the equilibrium towards the side with fewer moles of gas.
• Decreasing the pressure shifts the equilibrium towards the side with more moles of gas.
• If the number of moles of gas is the same on both sides of the equation, pressure changes have no effect on the equilibrium.

Effect of Temperature

• For endothermic reactions (ΔH > 0), heat can be considered a reactant. Increasing the temperature shifts the equilibrium towards the products. Decreasing the temperature shifts the equilibrium towards the reactants.
• For exothermic reactions (ΔH < 0), heat can be considered a product. Increasing the temperature shifts the equilibrium towards the reactants. Decreasing the temperature shifts the equilibrium towards the products.
• Temperature changes affect the value of the equilibrium constant K.

Effect of a Catalyst

• A catalyst speeds up both the forward and reverse reactions equally.
• A catalyst does not affect the position of equilibrium; it only affects the rate at which equilibrium is reached.
• Catalysts lower the activation energy for both the forward and reverse reactions.

Applications of Chemical Equilibrium

• Haber-Bosch process: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
  • Used for the industrial production of ammonia.
  • High pressure, moderate temperature, and an iron catalyst are used to maximize ammonia production.
• Contact process: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)
  • Used for the industrial production of sulfuric acid.
  • Excess oxygen, moderate temperature, and a vanadium(V) oxide catalyst are used to maximize sulfur trioxide production.