ICE Tables in Equilibrium Calculations

Explore practical examples of using ICE tables to solve equilibrium problems in chemistry.
By Jamie

Understanding ICE Tables in Equilibrium Calculations

ICE tables, which stand for Initial, Change, and Equilibrium, are a systematic way to track the concentrations of reactants and products during a chemical reaction. They are particularly useful in finding equilibrium concentrations and calculating equilibrium constants. Below are three diverse examples that illustrate how to effectively use ICE tables in equilibrium calculations.

Example 1: Determining Equilibrium Concentrations of a Simple Reaction

Context

This example involves the equilibrium reaction between nitrogen dioxide (NO₂) and dinitrogen tetroxide (N₂O₄), which is a common reaction in atmospheric chemistry.

NO₂ (g) ⇌ N₂O₄ (g)

Example

  1. Initial Concentrations: Let’s say we start with 0.50 M of NO₂ and no N₂O₄.
  2. Change in Concentration: At equilibrium, let x be the amount of NO₂ that reacts. Therefore, the changes in concentration will be:

    • NO₂: decreases by x
    • N₂O₄: increases by x
  3. Equilibrium Concentrations:

    • NO₂: 0.50 - x
    • N₂O₄: 0 + x
  4. ICE Table:

    Species Initial (M) Change (M) Equilibrium (M)
    NO₂ 0.50 -x 0.50 - x
    N₂O₄ 0 +x x
  5. Equilibrium Constant Expression: The equilibrium constant (Kc) for this reaction is given by:

    Kc = [N₂O₄] / [NO₂]²

  6. Substituting Equilibrium Concentrations:

    Kc = x / (0.50 - x)²

Notes

The value of x can be solved if a specific value for Kc is provided. This example illustrates a straightforward application of ICE tables to find equilibrium concentrations.

Example 2: Complex Equilibrium with Multiple Changes

Context

In this example, we will look at the equilibrium reaction of the formation of ammonia from nitrogen and hydrogen gases:

N₂ (g) + 3H₂ (g) ⇌ 2NH₃ (g)

Example

  1. Initial Concentrations: Assume we start with 1.00 M of N₂ and 3.00 M of H₂, and no NH₃ is present.
  2. Change in Concentration: At equilibrium, let y be the amount of N₂ that reacts, which will affect the concentrations as follows:

    • N₂: decreases by y
    • H₂: decreases by 3y
    • NH₃: increases by 2y
  3. Equilibrium Concentrations:

    • N₂: 1.00 - y
    • H₂: 3.00 - 3y
    • NH₃: 0 + 2y
  4. ICE Table:

    Species Initial (M) Change (M) Equilibrium (M)
    N₂ 1.00 -y 1.00 - y
    H₂ 3.00 -3y 3.00 - 3y
    NH₃ 0 +2y 2y
  5. Equilibrium Constant Expression: The equilibrium constant (Kc) is given by:

    Kc = [NH₃]² / ([N₂][H₂]³)

  6. Substituting Equilibrium Concentrations:

    Kc = (2y)² / ((1.00 - y)(3.00 - 3y)³)

Notes

This example highlights how to tackle more complex reactions using ICE tables. The challenge lies in carefully tracking the stoichiometric coefficients during changes in concentration.

Example 3: Reaction Quotient and Shift in Equilibrium

Context

This example explores how to use ICE tables to determine the direction of the shift in equilibrium when a change in concentration occurs. The reaction is:

A (g) ⇌ B (g)

Example

  1. Initial Concentrations: Initially, we have 0.70 M of A and 0.30 M of B.
  2. Change in Concentration: Suppose we increase the concentration of B to 0.50 M. We want to find out how the equilibrium shifts.

  3. ICE Table Before Change:

    Species Initial (M) Change (M) Equilibrium (M)
    A 0.70 -x 0.70 - x
    B 0.30 +x 0.30 + x
  4. Initial Reaction Quotient (Q):

    Q = [B] / [A] = 0.30 / 0.70 = 0.43

  5. Equilibrium Constant (K): Assume K is 0.50. Since Q < K, the reaction will shift to the right to form more B.

  6. New ICE Table After Change:

    Species Initial (M) Change (M) Equilibrium (M)
    A 0.70 -y 0.70 - y
    B 0.50 +y 0.50 + y

Notes

This example demonstrates the use of ICE tables not only for calculating equilibrium concentrations but also for predicting the direction of a reaction based on changes in concentration and the comparison of Q and K values.