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Chemical Equilibrium: Expressions, Calculations, and Applications

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Chemical Equilibrium

Equilibrium Constants and Chemical Equations

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The equilibrium constant (K) quantifies the ratio of product and reactant concentrations at equilibrium.

  • Equilibrium Constant Expression: For a general reaction aA + bB → cC + dD, the equilibrium constant is given by:

  • Manipulating Equilibrium Constants: Reversing a reaction inverts the equilibrium constant, and multiplying the coefficients by a factor raises K to that power.

  • Example: For the synthesis and decomposition of ammonia: Equilibrium constant for ammonia synthesis and decomposition Equilibrium constant for fractional reaction

Relating Kc and Kp

For reactions involving gases, equilibrium constants can be expressed in terms of concentrations (Kc) or partial pressures (Kp). The relationship is:

  • , where is the change in moles of gas.

  • Example Calculation: Calculation of Kc from Kp Calculation of Kp from Kc

Finding Equilibrium Constants from Experimental Data

Experimental measurements of concentrations at equilibrium allow calculation of K using ICE tables (Initial, Change, Equilibrium).

  • ICE Table Example: ICE table for CO and H2 reaction ICE table with changes for CO and H2 reaction ICE table with change for CO ICE table with equilibrium concentrations

  • Equilibrium Constant Calculation: Calculation of Kc for CO and H2 reaction

ICE Tables for Other Reactions

ICE tables are used for a variety of reactions to track changes and calculate equilibrium concentrations and constants.

  • Example: Methane Decomposition ICE table for CH4 decomposition ICE table with changes for CH4 decomposition ICE table with stoichiometric changes ICE table with equilibrium concentrations

  • Equilibrium Constant Calculation: Calculation of Kc for CH4 decomposition

Reaction Quotient (Q) and Predicting Direction

The reaction quotient (Q) is calculated using initial concentrations or partial pressures. Comparing Q to K predicts the direction of the reaction:

  • If Q < K, the reaction proceeds to the right (toward products).

  • If Q > K, the reaction proceeds to the left (toward reactants).

  • Example: Calculation of Qp for ICl formation

Finding Unknown Equilibrium Concentrations

If all but one equilibrium concentration is known, use the equilibrium constant expression to solve for the unknown.

  • Example: Given concentrations and Kc for COF2 reaction Conceptual plan for finding CO2 concentration Calculation of CO2 concentration

Solving for Equilibrium Concentrations with Initial Data

When only initial concentrations and the equilibrium constant are known, use ICE tables and algebraic methods (including quadratic equations) to solve for equilibrium concentrations.

  • Example: Nitrogen and Oxygen Reaction ICE table for N2 and O2 reaction Calculation of Qc for N2 and O2 reaction ICE table with variable x for N2 and O2 reaction ICE table with equilibrium expressions Quadratic formula Solving for x in equilibrium Calculated equilibrium concentrations Calculation of Kc with equilibrium values

  • Example: Dinitrogen Tetraoxide and Nitrogen Dioxide ICE table for N2O4 and NO2 reaction Calculation of Qc for N2O4 and NO2 reaction ICE table with variable x for N2O4 and NO2 reaction ICE table with equilibrium expressions Quadratic formula Solving for x in equilibrium Calculated equilibrium concentrations Calculation of Kc with equilibrium values

Equilibrium Partial Pressures

For reactions involving gases, partial pressures can be used in ICE tables and equilibrium expressions.

  • Example: Iodine and Chlorine Reaction ICE table for I2 and Cl2 reaction Calculation of Qp for I2 and Cl2 reaction ICE table with variable x for I2 and Cl2 reaction ICE table with equilibrium expressions Solving for x and equilibrium partial pressures Calculation of Kp with equilibrium values

Small Equilibrium Constants and Approximations

When K is very small, the reaction does not proceed far toward products. Approximations can simplify calculations, but must be checked for validity.

  • Example: Hydrogen Disulfide Decomposition ICE table for H2S decomposition Calculation of initial concentration for H2S ICE table with variable x for H2S decomposition ICE table with equilibrium expressions Solving for x and checking approximation Calculated equilibrium concentrations Calculation of Kc with equilibrium values

  • Example: Lower Initial Concentration ICE table for lower initial H2S Calculation of initial concentration for lower H2S ICE table with variable x for lower H2S

Summary Table: ICE Table Structure

ICE tables are a fundamental tool for equilibrium calculations. They organize the initial, change, and equilibrium values for each species in a reaction.

Step

Description

Initial

Starting concentrations or partial pressures

Change

Change in each species (based on stoichiometry)

Equilibrium

Final concentrations or partial pressures at equilibrium

Quadratic equations and approximations are often used to solve for unknowns in equilibrium calculations.

Additional info: These notes expand on the original examples by providing definitions, formulas, and stepwise explanations for equilibrium calculations, including the use of ICE tables, reaction quotients, and the relationship between Kc and Kp.

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