CHEM 106: 2/26/25

Equilibrium Concepts

  • Definition of Equilibrium: A state where the forward and reverse reactions occur at the same rate in a closed system at a constant temperature.

    • Closed System: No mass can enter or leave.

    • Dynamic Nature: Despite reaching equilibrium, molecular interactions (both forming products and reactants) continue at the microscopic level.

  • Key Characteristics of Equilibrium:

    • The rates of the forward and reverse reactions are equal.

    • Composition of the reaction mixture remains constant over time.

    • Can only be defined at a constant temperature.

Equilibrium Constant Expression

  • General Form: For a reaction [ aA + bB \leftrightarrow cC + dD ]the equilibrium constant expression is written as: [ K = \frac{[C]^c[D]^d}{[A]^a[B]^b} ]

    • [C]: concentration of product C at equilibrium, raised to the power of its stoichiometric coefficient.

    • [A]: concentration of reactant A at equilibrium.

    • K: equilibrium constant.

Manipulating Equilibrium Constants

  • Adding Reactions: When adding two equations together, the equilibrium constants multiply:

    • If Reaction 1 has equilibrium constant ( K_1 ) and Reaction 2 has ( K_2 ), then: [ K = K_1 \times K_2 ]

  • Reversing Reactions: The equilibrium constant for a reverse reaction is the inverse of the forward reaction: [ K_{reverse} = \frac{1}{K_{forward}} ]

  • Multiplying Coefficients: If all coefficients in a reaction are multiplied by a factor ( b ), the equilibrium constant is raised to that power: [ K_{new} = K_{original}^b ]

Example Problem

  • Combining Reactions: Given Reaction 1: [ C(s) + 2H_2O(g) \leftrightarrow CO_2(g) + 2H_2(g) ] with ( K_{p1} = 3.85 ) and Reaction 2: [ H_2(g) + CO_2(g) \leftrightarrow H_2O(g) + CO(g) ] with ( K_{p2} = 0.71 )

    • Combine to write Reaction 3 and find its equilibrium constant: [ K_{p3} = K_{p1} \times (K_{p2})^2 ]

ICE Tables for Equilibrium Calculations

  • ICE Table Setup: Refers to Initial, Change, Equilibrium concentrations.

    • Initial Concentrations: Given values at the start of the reaction.

    • Change: Change during the reaction, determined by stoichiometry.

    • Equilibrium: Final concentrations after reaching equilibrium.

  • Example: For the synthesis of methanol: [ CO(g) + 2H_2(g) \leftrightarrow CH_3OH(g) ] Initial concentrations provided: 1.75 M (CO), 0.8 M (H2), 0.65 M (methanol). Equilibrium concentration of CO is 1.60 M; find equilibrium concentrations of other reactants/products.

Reaction Quotient vs. Equilibrium Constant

  • Reaction Quotient (Q): Calculated at any point, potentially not at equilibrium. [ Q = \frac{[products]}{[reactants]} ]

  • Equilibrium Constant (K): Calculated using equilibrium concentrations.

  • Evaluation:

    • If ( Q < K ): Reaction shifts right to produce more products.

    • If ( Q > K ): Reaction shifts left to produce more reactants.

    • If ( Q = K ): System is at equilibrium, no net change.