In-Depth Notes on Reaction Quotient (Q) and Equilibrium Constant (K)

Understanding the Reaction Quotient (Q) and the Equilibrium Constant (K)

  • Purpose:
    • To understand the relationship between reaction quotient (Q) and equilibrium constant (K).
    • To predict the spontaneous direction of reactions based on Q and K.

Key Definitions

  • Reaction Quotient (Q):

    • The ratio of the concentrations of products to reactants at any given point in time in a reaction.
    • For a general reaction:
      aA + bB \rightleftharpoons cC + dD
    • The expression for Q is:
      Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}

  • Equilibrium Constant (K):

    • When a system is at equilibrium, Q equals K:
      Q = K
    • It represents the ratio of concentrations of products to reactants at equilibrium, remaining constant at a given temperature.

Examples of Q and K Calculation

  • Hydrogen and Iodine Reaction:
    • The reaction:
      H2(g) + I2(g) \rightleftharpoons 2HI(g)
    • Example Concentrations Over Time:
    • Initial:
      • [H2] = 0.0175 mol/L
      • [I2] = 0.0175 mol/L
      • [HI] = 0 mol/L
    • After time 1:
      • [H2] = 0.0150 mol/L
      • [I2] = 0.0150 mol/L
      • [HI] = 0.0050 mol/L
    • At equilibrium, calculate Q at different times to observe convergence to K.

Relationships and Equilibrium Laws

  • Law of Equilibrium:

    • At equilibrium, Q has a specific value (K) determined by the concentrations of products and reactants.

  • Forms of Q and K:

    • Numerator: concentrations of products.
    • Denominator: concentrations of reactants.
    • Concentration terms of solids are excluded.
    • In aqueous solutions, the molar concentration of water is also excluded.

Comparing Q to K

  • Equilibrium Conditions:
    • If Q < K: The reaction proceeds from reactants to products.
    • If Q = K: The reaction is at equilibrium.
    • If Q > K: The reaction proceeds from products to reactants.

Spontaneous Reaction Direction

  • Understanding Spontaneity:
    • The direction of the spontaneous reaction can be predicted by Q compared to K:
    • Q < K: reactants will produce products.
    • Q = K: reaction is at equilibrium (no net change).
    • Q > K: products will revert to reactants.

Reaction Equations and Equilibrium Constants

  • Doubling the Reaction Equation:

    • If coefficients are doubled, the new K value will be the square of the original K:
    • For example, from:
      C(s) + \frac{1}{2} O2(g) \rightleftharpoons CO(g) to: 2C(s) + O2(g) \rightleftharpoons 2CO(g)
    • Resulting K relation:
      K{new} = K{original}^2

  • Reversing the Reaction Equation:

    • If a reaction's direction is reversed, the new K is the reciprocal of the original K:
    • For example:
      HCOOH(aq) + H2O(ℓ) \rightleftharpoons HCOO^-(aq) + H3O^+(aq)
      has a K value that relates as follows:
      K{reverse} = \frac{1}{K{forward}}

Summary of Key Points

  • Determining Direction of Spontaneous Reaction:
    • By comparing Q and K:
    • Q < K: proceeds to products
    • Q = K: at equilibrium
    • Q > K: proceeds to reactants
  • Equilibrium Constant Calculation:
    • If concentrations are known, substituting them into the reaction quotient allows for calculation of K at the temperature measured.