Equilibrium Constant Calculations
ICE Table Examples
ICE tables are used to solve equilibrium problems. They stand for Initial, Change, Equilibrium.
General Form:
| Reactant A | Reactant B | Product C | |
|---|---|---|---|
| Initial | $ x_A $ | $ x_B $ | $ x_C $ |
| Change | $ -ax $ | $ -bx $ | $ +cx $ |
| Equilibrium | $ x_A - ax $ | $ x_B - bx $ | $ x_C + cx $ |
where:
- $ x_A $ , $ x_B $ , $ x_C $ are the initial concentrations of A, B, and C respectively.
- $ a $ , $ b $ , $ c $ are the stoichiometric coefficients from the balanced chemical equation.
- $ x $ represents the change in concentration to reach equilibrium.
Example 1: Simple Equilibrium
Consider the reaction: $ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) $
Let’s say we start with 1.0 M $ N_2 $ and 1.5 M $ H_2 $ , and the equilibrium constant $ K_c = 0.50 $ .
| $ N_2 $ | $ 3H_2 $ | $ 2NH_3 $ | |
|---|---|---|---|
| Initial | 1.0 M | 1.5 M | 0 M |
| Change | $ -x $ | $ -3x $ | $ +2x $ |
| Equilibrium | $ 1.0 - x $ | $ 1.5 - 3x $ | $ 2x $ |
We can now write the expression for $ K_c $ :
$ K_c = \frac{[NH_3^2}{[N_2[H_2^3} = \frac{(2x)^2}{(1.0 - x)(1.5 - 3x)^3} = 0.50 $
This equation can be solved for $ x $ (often requiring the quadratic formula or approximation methods). Once $ x $ is found, the equilibrium concentrations can be calculated.
Example 2: Equilibrium with an Initial Product Concentration
(Equilibrium Constant Calculations)
Example 3: Weak Acid/Base Equilibria
Example 4: Solubility Equilibria
Important Notes:
- ICE tables are most useful when the $ K $ value is small, allowing for simplifying assumptions (e.g., $ x $ is negligible compared to initial concentrations).
- Always check your assumptions. If the assumption is invalid, you will need to solve the resulting equation without simplification (often using the quadratic formula or a numerical solver).
- Units of $ K $ are important and depend on the form of the equilibrium expression.