Equilibrium Constants Study Notes

Section 13.2: Equilibrium Constants

Overview of Equilibrium Constants

• Equilibrium Constants conceptually focus on both homogeneous and heterogeneous reactions.

• Objective: Derive reaction quotients and calculate equilibrium constants using concentrations and pressures.

  • Define how equilibrium constants relate to properties of chemical systems.

Reaction Quotient (Q)

• Definition: A mathematical expression that indicates how far a reversible reaction is from equilibrium; provides a numerical assessment towards equilibrium.

  • Calculation: Derived from the stoichiometry of the reaction.

  • Two forms exist based on whether concentrations or partial pressures are used:

  • Using concentrations:
    $Q_C = rac{[ ext{Products}]^{ ext{coefficients}}}{[ ext{Reactants}]^{ ext{coefficients}}}$

  • Using partial pressures:
    $Q<em>P = rac{P</em>{ ext{Products}}^{ ext{coefficients}}}{P_{ ext{Reactants}}^{ ext{coefficients}}}$

• Stoichiometric Coefficients: Act as exponents in calculations.

• Disclaimer: The rigorous derivation involving relative values resulting in dimensionless quantities is not covered in this section for simplicity.

Direction of Reactions and Equilibrium

• Reactions can progress from products to reactants or reactants to products depending on initial conditions.

• Two possible scenarios for Q as equilibrium is approached:

  • Case 1: Start with all reactants;

  • No initial products: (Q = 0)

  • Case 2: Start with all products;

  • No initial reactants: (Q = ext{Infinity})

• At equilibrium: (Q = K)

• Q and K Values:

  • (Q < K): Excess reactants → reaction proceeds forward (towards products).

  • (Q > K): Excess products → reaction proceeds backward (towards reactants).

  • (Q = K): System in equilibrium where concentrations remain constant.

Law of Mass Action

• Statement: At constant temperature, the equilibrium constant for a reaction remains unchanged regardless of the concentration of the reactants and products.

• Allows prediction of reaction direction from calculated (Q) compared to known (K).

• Notation:

  • Capital italicized K denotes equilibrium constant, distinct from lowercase k rate constants that refer to reaction speed.

Equilibrium Graphical Representation

• Graph Explanation: Graphs can depict Q's convergence to K under different starting conditions: all reactants, all products, or a mixture.

• Key Point: Different starting compositions may lead to the same equilibrium constant K, but these do not produce the same final concentrations unless the initial conditions are the same.

Homogeneous and Heterogeneous Equilibria

• Homogeneous Equilibrium: All reactants and products are in the same phase (solution).

  • Omits solids and liquids in K calculations:

  • Only includes aqueous and gaseous components.

• Heterogeneous Equilibrium: Involves reactants and products in different phases.

  • The equilibrium constant K_P includes only gaseous reactants/products, omitting solids and liquids:

  • Solids and liquids do not contribute as they are constants.

Relationship Between KP and KC

• KP is not directly equal to KC, but they are related through the ideal gas law.

• Ideal Gas Law Rearrangement:

  • Pressure (P) relates to molarity (C): (P = C imes RT)

• Conversion from KP to KC:

  • (KP = KC imes RT^{ ext{Δn}}), where Δn = change in moles (moles of products - moles of reactants).

  • Proper units and R value (liters.atm/(moles.K)) must be used.

Coupled Equilibria

• Definition: Systems involving multiple equilibrium reactions sharing reactants or products.

• Rules for manipulating K values:

  1. Reversing a Reaction: To reverse a reaction, take the reciprocal of K.

  • Example: If (KC = \frac{B}{A}), then for the reverse (KC' = \frac{A}{B}=\frac{1}{K_C}).

  1. Changing Stoichiometric Coefficients: Multiply all species by a constant factor results in raising K to that factor.

  • If multiplied by x: (KC' = (KC)^x).

  1. Adding Reactions: K for the resulting reaction is the product of the individual K values:

  • If two reactions with K1 and K2, then (K{ ext{total}} = K1 imes K_2).

Summary

• Understanding equilibrium constants involves calculating reaction quotients based on given initial conditions and predicting reaction direction using the Law of Mass Action. The relationships between K values in homogeneous and heterogeneous equilibria reflect the behavior of collections of reactions sharing components under various conditions. Coupled equilibria present additional complexity that can be navigated by manipulating the K values accordingly.