Chemical Equilibrium Calculations

Equilibrium Constants and Concentration Tables (ICE Tables)

Chemical equilibrium calculations are essential for predicting the behavior of reactions and determining concentrations of reactants and products at equilibrium. The equilibrium constant (Kc) quantifies the ratio of product and reactant concentrations at equilibrium. ICE tables (Initial, Change, Equilibrium) are a systematic tool used to organize and solve equilibrium problems.

• Equilibrium Constant (Kc): A numerical value expressing the ratio of concentrations of products to reactants at equilibrium, each raised to the power of their stoichiometric coefficients.

• ICE Table: A tabular method to track initial concentrations, changes during reaction, and equilibrium concentrations for all species involved.

• Key Steps:

  • Write the balanced chemical equation.

  • Set up the ICE table for all reactants and products.

  • Use stoichiometry to relate changes in concentration.

  • Apply the equilibrium constant expression using equilibrium concentrations.

Example: Calculation of Equilibrium Constant

Consider the reaction between hydrogen and iodine:

Balanced Equation: H2 + I2 → 2HI

Suppose 0.200 mol of H2 and 0.200 mol of I2 are placed in a 2.00 L flask. At equilibrium, [I2] = 0.020 mol L–1.

Equilibrium Constant Expression:

Substitute equilibrium concentrations:

Summary of ICE Table Use:

• Only equilibrium concentrations are used in the equilibrium constant expression.

• All concentrations must be in mol L–1.

• Changes in concentration follow the stoichiometric ratios of the balanced equation.

• Reactant concentrations decrease (negative change), product concentrations increase (positive change).

Calculating Equilibrium Concentrations from Initial Conditions and Known Kc

When the equilibrium constant and initial concentrations are known, algebraic methods are used to solve for equilibrium concentrations. This often involves setting up an ICE table and solving for unknowns.

• Given: Initial concentrations and equilibrium constant.

• Required: Final equilibrium concentrations.

• Method: Set up variables for changes (e.g., x), write equilibrium expressions, and solve algebraically.

Example: Using Approximations in Equilibrium Calculations

For reactions with very small equilibrium constants, the change in concentration may be negligible compared to the initial concentration. Approximations can simplify calculations.

Reaction: 2H2O → 2H2 + O2

At 1000 °C, Kc = 7.3 × 10–18. Initial [H2O] = 0.100 M.

Equilibrium Constant Expression:

Substitute equilibrium values:

Since Kc is very small, assume 2x << 0.100, so (0.100 – 2x) ≈ 0.100:

Solve for x:

Plug in values:

Therefore, [H2] = 2x = 5.2 × 10–7 M.

• Validity of Approximation: The approximation is valid if the initial concentration is at least 400 times greater than Kc. In this case, 0.100 >> Kc × 400.

• Check: Subtracting 2x from 0.100 yields negligible change, confirming the approximation.

Summary Table: ICE Table Structure

Key Points:

• ICE tables are a powerful tool for solving equilibrium problems.

• Only equilibrium concentrations are used in the equilibrium constant expression.

• Approximations can simplify calculations when changes are negligible compared to initial concentrations.

Example Application: Calculating equilibrium concentrations for reactions with small Kc values, such as the decomposition of water at high temperature.

Additional info: ICE tables are widely used in both introductory and advanced chemistry courses to solve equilibrium problems, including acid-base equilibria and solubility equilibria.