Calculating Equilibrium Concentrations
The ICE Table Method | Chemical Equilibrium
1. The Problem
Often, we know the Initial Concentrations of reactants and the Equilibrium Constant ($K_c$), and we need to find the concentrations of all species when equilibrium is reached. To solve this, we use a systematic approach.
2. The ICE Table Method
ICE stands for Initial, Change, and Equilibrium. It organizes the data to solve for the unknown variable $x$.
- Write the balanced chemical equation.
- I (Initial): Write initial concentrations (Molarity) of reactants and products (usually 0).
- C (Change): Define change in terms of $x$. Reactants decrease ($-ax$), Products increase ($+bx$). Coefficients matter!
- E (Equilibrium): Sum of I and C rows ($Initial \pm x$).
3. Worked Example
Problem: 0.1 M of $H_2$ and 0.1 M of $I_2$ are mixed at 700K. $K_c = 57.0$. Calculate equilibrium concentrations.
Equation: $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$
| Condition | $H_2$ | $I_2$ | $2HI$ |
|---|---|---|---|
| Initial (M) | 0.10 | 0.10 | 0 |
| Change (M) | $-x$ | $-x$ | $+2x$ |
| Equilibrium (M) | $0.10 - x$ | $0.10 - x$ | $2x$ |
Substitute into $K_c$:
$$ K_c = \frac{[HI]^2}{[H_2][I_2]} \implies 57 = \frac{(2x)^2}{(0.1-x)(0.1-x)} $$ $$ 57 = \left( \frac{2x}{0.1-x} \right)^2 $$Taking square root (Perfect Square Method):
$$ \sqrt{57} \approx 7.55 = \frac{2x}{0.1-x} $$ $$ 0.755 - 7.55x = 2x \implies 9.55x = 0.755 \implies x \approx 0.079 \, M $$Final Concentrations:
- $[H_2] = [I_2] = 0.10 - 0.079 = 0.021 \, M$
- $[HI] = 2(0.079) = 0.158 \, M$
4. Approximation Method (Small K)
If $K_c$ is very small ($K < 10^{-3}$), the reaction proceeds very little. Thus, $x$ is very small.
This simplifies the math by avoiding complex quadratic equations.
Check: If $x$ is less than 5% of the initial concentration, the assumption is valid.
Practice Quiz
Test your ability to set up and solve equilibrium problems.
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