Calculating Equilibrium Concentrations
Learning Objective 7.7.A
Identify the concentrations or partial pressures of chemical species at equilibrium based on the initial conditions and the equilibrium constant.
Quick Notes
- ICE tables (Initial, Change, Equilibrium) can be used to calculate equilibrium concentrations.
- The equilibrium constant K can be used to find unknown concentrations at equilibrium.
- Q can be compared to K to determine direction of reaction shift:
- If Q < K → Reaction shifts right (toward products)
- If Q > K → Reaction shifts left (toward reactants)
- If Q = K → system is already at equilibrium
Full Notes
Using ICE Tables to Find Equilibrium Concentrations
To calculate concentrations at equilibrium:
- Write the balanced equation.
- Set up an ICE table with rows for:
- Initial concentrations/pressures
- Change (use variables like −x or +2x)
- Equilibrium
- Can use values in terms of x.
- Write the K expression and substitute the equilibrium terms.
- Solve for x and substitute back to get the actual concentrations.
Example Problem
For the reaction: H2(g) + I2(g) ⇌ 2HI(g),
Kc = 50.0 at a certain temperature.
Initial concentrations: [H2] = 1.00 M,
[I2] = 1.00 M,
[HI] = 0.00 M.
Step 1: ICE Table
| Species | Initial (M) | Change | Equilibrium (M) |
|---|---|---|---|
| H2 | 1.00 | −x | 1.00 − x |
| I2 | 1.00 | −x | 1.00 − x |
| HI | 0.00 | +2x | 2x |
Step 2: Write K expression
Kc = [HI]2 / ([H2][I2])
50.0 = (2x)2 / ((1.00 − x)(1.00 − x)) = 4x2 / (1 − x)2
Step 3: Solve the equation
50(1 − x)2 = 4x2 → 50 − 100x + 50x2 = 4x2 → 46x2 − 100x + 50 = 0.
Solve (quadratic) for x, then substitute to get equilibrium concentrations.
Check: x ≈ 0.78 → [HI] = 1.56 M, [H2] = [I2] ≈ 0.22 M, which satisfies Kc ≈ 50.
Using Q vs K to Predict Direction
- Q is the current products/reactants ratio (see Reaction Quotient, Q).
- If Q < K: Reaction proceeds right in forward direction.
- If Q > K: Reaction proceeds left in reverse direction.
- If Q = K: the system is at equilibrium.
Summary
- Use ICE tables with a correct K expression to find unknown equilibrium values.
- Set up the algebra (often a quadratic) and solve for the variable(s).
- Compare Q and K to predict the direction a system will shift to reach equilibrium.