Equilibrium Constant and Relevant Concepts

Lesson 2.5d: The Equilibrium Constant

Key Terms

  • Law of Chemical Equilibrium

    • At equilibrium, the rates of the forward and reverse reactions are equal, leading to a constant ratio between concentrations of products and reactants.

  • Equilibrium Constant (Kc)

    • A constant that expresses the ratio of product concentrations to reactant concentrations at equilibrium at a certain temperature.

  • ICE Table

    • An aid used in stoichiometry to keep track of the Initial, Change, and Equilibrium concentrations of species in a reaction.

  • Percent Reaction

    • A measure of the extent of a reaction expressed as a percentage of reactants that are converted into products at equilibrium.

  • Reaction Quotient (Qc)

    • A ratio of the concentrations of products to reactants at any point in time, which indicates the direction a reaction will proceed to reach equilibrium.

  • Le Châtelier’s Principle

    • States that if a system at equilibrium is disturbed, the system will adjust to counteract the disturbance and re-establish equilibrium.

  • Common Ion Effect

    • The decrease in the solubility of an ionic compound in a solution that already contains one of its constituent ions.

Concentrations of Reactants & Products

  • Example Reaction:
    • ext{N}_2 ext{O}_4 (g) ⇌ 2 ext{NO}_2 (g)
  • The equilibrium concentrations can provide insights into the reaction progression.
  • Concentration is represented by square brackets indicating molarity (mol/L).

Law of Chemical Equilibrium

  • At equilibrium, the concentrations of reactants and products reach a constant ratio, and both forward and backward reactions occur at equal rates.

Equilibrium Constant (Kc)

  • For a reaction at equilibrium at a set temperature, the equilibrium constant formula is defined as:
    • General Reaction:
    • aP + bQ ⇌ cR + dS
    • Equilibrium Expression:
    • K_c = rac{[ ext{R}]^c[ ext{S}]^d}{[ ext{P}]^a[ ext{Q}]^b}
    • Where
      • P, Q, R, S are the chemical species in the reaction
      • a, b, c, d are the coefficients from the balanced reaction.
  • The value of Kc is constant for a given reaction at a specific temperature, is independent of initial concentrations, and has no units.

Writing the Equilibrium Expression

  • Use the coefficients of the balanced equation to express the concentrations of products over reactants, raised to their coefficients.
  • Note: Solids and pure liquids are not included in the Kc expression as their concentrations do not change.

Equilibrium Constant & Temperature

  • The equilibrium constant ($K_c$) depends solely on temperature. Changing concentrations of reactants/products does not affect $K_c$ but influences reaction rates.
    • Changes in temperature affect the forward and reverse reactions differently due to differing activation energies.

Calculating the Equilibrium Constant (Kc)

  • The equilibrium constant can be calculated using known concentration values when the reaction reaches equilibrium
    • K_c = rac{[ ext{products}]}{[ ext{reactants}]}

Sample Problems

  • Sample Problem 1

    • Write equilibrium expression for:
    • 2 ext{H}_2(g) + ext{N}_2(g) ⇌ ext{N}_2 ext{H}_2(g)
    • K_c = rac{[ ext{N}_2 ext{H}_2]}{[ ext{H}_2]^2[ ext{N}_2]}

  • Sample Problem 2

    • Given:
    • 2 ext{SO}_2(g) + ext{O}_2(g) ⇌ 2 ext{SO}_3(g)
    • At equilibrium:
      • [ ext{SO}_3] = 5.0 imes 10^{-2} ext{ M}
      • [ ext{O}_2] = 3.5 imes 10^{-3} ext{ M}
      • [ ext{SO}_2] = 3.0 imes 10^{-3} ext{ M}
    • Calculate $K_c$:
    • K_c = rac{(5.0 imes 10^{-2})^2}{(3.0 imes 10^{-3})(3.5 imes 10^{-3})}

  • Sample Problem 3

    • Given:
    • ext{H}_2(g) + ext{I}_2(g) ⇌ 2 ext{HI}(g)
      • At 740 K:
      • [ ext{HI}] = 1.37 imes 10^{-2} ext{ M}
      • [ ext{H}_2] = 6.47 imes 10^{-3} ext{ M}
      • [ ext{I}_2] = 5.94 imes 10^{-4} ext{ M}
    • Calculate $K_c$.

  • Using ICE Tables

    • Allows calculation of equilibrium concentrations based on initial concentrations and changes due to the reaction, formatted as:
    • I = ext{Initial concentration}
    • C = ext{Change in concentration}
    • E = ext{Equilibrium concentration}

  • Sample Problem 4

    • For the decomposition of:
    • 2 ext{NOCl}(g) ⇌ 2 ext{NO}(g) + ext{Cl}_2(g)
    • Calculate $K_c$ with given moles of Cl2 at equilibrium.

  • Sample Problem 5

    • Given $K_c = 25.0$ at 1100 K for:
    • ext{H}_2(g) + ext{I}_2(g) ⇌ 2 ext{HI}(g)
    • Find equilibrium concentrations with initial moles in a 1.00 L vessel.

Percent Reaction

  • Percent reaction quantifies how much of a reactant has been converted to products.
  • Use the percent to multiply the initial concentration giving the new concentrations at equilibrium using ICE tables.

Sample Problem 6

  • Calculate $K_c$ for a reaction involving boron nitride and chlorine with given conditions.

Common Ion Effect

  • A significant concept in equilibrium systems, shows the effect of adding a common ion in a solution that shifts equilibrium based on Le Châtelier’s principle.

Qualitatively Interpreting Kc

  • Evaluating the relative positions of equilibrium:
    • If $K > 1$ then products are favored (equilibrium lies to the right).
    • If $K
      eq 1$ then concentrations of reactants and products are approximately equal.
    • If $K < 1$ then reactants are favored (equilibrium lies to the left).

Predicting the Direction of a Reaction

  • Utilize the reaction quotient $Q_c$ to determine the direction a reaction must shift to reach equilibrium by comparing the values of $Q_c$ and $K_c$.
    • If $Q < K$, the reaction will shift towards products.
    • If $Q > K$, the reaction will shift towards reactants.