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.