Equilibrium

Equilibrium Basics

  • Definition: Equilibrium in a reaction system occurs when the forward and reverse reactions happen at the same rate, causing no net change in the concentrations of reactants and products over time.

  • Concept of Dynamic Equilibrium: Although the concentrations remain constant, both the forward and reverse reactions continue to take place.

  • Chemical Representation: The forward reaction is represented as: aA + bB ⇆ cC + dD, where:

    • Left side: Reactants (A, B)

    • Right side: Products (C, D)

  • Equilibrium Constant (Keq): Describes the ratio of the concentrations of products to reactants at equilibrium; applicable only for aqueous and gaseous species (solids and pure liquids excluded).

Reaction Quotients

  • General Formula: Qc = [C]^c [D]^d / [A]^a [B]^b

  • Real-Time Calculation: The reaction quotient can be measured at any point during the reaction, comparing it to the equilibrium constant to determine the state of the system.

Example Calculation of Keq

  • For the reaction A + 2B ⇆ C + D, using given equilibrium concentrations:

    [ Kc = \frac{[C][D]}{[A][B]^2} ]

    • If [A] = 0.0115M, [B] = 0.0253M, [C] = 0.109M, [D] = 0.0110M,

    • Then calculated [ Kc = \frac{(0.109)(0.0110)}{(0.0115)(0.0253^2)} \approx 163. ]

kP vs kC

  • Kp: Equilibrium expression for gaseous systems, using partial pressures instead of concentrations. Relation between Kp and Kc is given by:

    • [ Kp = Kc (0.08206 , \text{Latm/molK})^m ]

    • where m is the change in moles of gas (moles of products - moles of reactants).

Manipulating Equilibrium Expressions

  • Reverse Reaction: Reversing the reaction will take the reciprocal of Kc.

  • Multiplying: Multiplying a reaction by a coefficient squares the Kc value. Example:

    • Original: 2NO(g) + O2(g) ⇆ 2NO2(g)

    • Reversed: 2NO2(g) ⇆ 2NO(g) + O2(g) where Kc becomes 1/Kc.

    • Multiplied by 2: 4NO(g) + 2O2(g) ⇆ 4NO2(g) resulting in Kc squaring.

Calculating Kc from Individual Reactions

  • Given:

    • Kc1 for HF ⇆ H+ + F- is 6.8x10^-4.

    • Kc2 for H2C2O4 ⇆ 2H+ + C2O42- is 3.8x10^-6.

  • Target Reaction: C2O42- + 2HF ⇆ 2F- + H2C2O4 requires manipulation to solve:

    1. Reverse Kc2: New Kc2' = 1/(3.8x10^-6) = 2.6x10^5.

    2. Double Kc1: New Kc1'' = (6.8x10^-4)^2 = 4.6x10^-7.

    3. Combine Kc Values: Kc for target reaction is Kc2' * Kc1' = (2.6x10^5)(4.6x10^-7) = 0.12.

Comparison of Q and K for Reaction Direction

  • When Q < K: Reactants need to produce more products; equilibrium shifts right.

  • When Q = K: The system is at equilibrium; no shift occurs.

  • When Q > K: Products must convert back to reactants; equilibrium shifts left.

Equilibrium and Gibbs Free Energy

  • Equation: [ ΔG = ΔG^o + RT , ln K ]

  • At equilibrium: Q=K means [ ΔG=0 ] leading to [ ΔG^o = -RT , ln Q ].

Calculating Equilibrium Concentrations Using ICE Tables

  1. Set up initial concentrations:

    • Example: 0.850M reactant, change=x leading to concentrations:

    • Initial: [Reactants] = 0.850M, [Products] = 0

    • Change: [Reactants] = 0.850-x, [Products] = x

  2. Relate to Kc:

    • [ Kc = \frac{x}{0.850-x} ]

    • Given Kc: Solve for x with algebraic techniques.

  3. Calculate final concentrations.

Le Chatelier's Principle

  • Principle: If an external change is imposed on a system at equilibrium, the system shifts to counteract that change:

    • Addition: Shift away from added substance.

    • Removal: Shift towards removed substance.

    • Pressure Changes: Shifts toward the side with fewer moles of gas for compression or more for expansion.

    • Temperature Changes: Shifts away from the side to which heat is added (e.g., increases in temperature favor endothermic reactions).

Simplifications in Equilibrium Calculations

  • Simplification possible when initial concentration is 1000x greater than K value.