Reaction Quotient and Le Châtelier’s Principle
Quick Notes
- Q (reaction quotient) shows the ratio of product to reactant concentrations at any given time.
- K (equilibrium constant) shows the ratio of product to reactant concentrations at equilibrium.
- If Q ≠ K, the system is not at equilibrium and will shift to restore it:
- If Q < K → reaction proceeds in forward direction (more products form).
- If Q > K → reaction proceeds in reverse direction (more reactants form).
- Changes in concentration affect Q.
- Changes in temperature affect K.
Full Notes
Q, K, and Le Châtelier’s Principle
Le Châtelier’s Principle describes how a system at equilibrium responds to stress (see Topic 7.9). The reaction will shift to oppose the change and re-establish equilibrium.But how can we know which direction the system will shift in? That’s where Q (reaction quotient) and K (equilibrium constant) come in.
Q vs. K: Predicting the Direction of Shift
- K is the ratio of product to reactant concentrations at equilibrium.
- Q is the ratio of those concentrations at any moment, even if the system is not at equilibrium.
When a system is disturbed or 'stressed':
- If Q < K
The system shifts right to form more products. - If Q > K
The system shifts left to form more reactants. - If Q = K
No shift occurs.
In other words, Q tells us where the reaction system is, and K tells us where it's going.
How This Links to Le Châtelier’s Principle
Le Châtelier’s Principle says: When a system at equilibrium is disturbed, it will shift in the direction that opposes the change and restores equilibrium.
This is exactly what happens when Q ≠ K.
The system adjusts and concentrations or pressures shift. Q changes until Q = K again – and the system reaches a new equilibrium.
Examples of Disturbances
- Add reactant
denominator in Q increases → Q decreases → typically shifts right. - Add product
numerator in Q increases → Q increases → typically shifts left. - Remove reactant
denominator decreases → Q increases → shifts left. - Remove product
numerator decreases → Q decreases → shifts right. - Pressure/volume changes (gases) affect Qp.
When the total gas moles differ for reactants and prodcuts; the system shifts toward the side that reduces the imposed change (e.g, shifts in direction of fewer moles at higher pressure).
What About Temperature?
Temperature changes are different — they actually change the value of K, not just Q.
- For endothermic reactions (+ΔH): Increasing Temperature increases K
system shifts right. - For exothermic reactions (-ΔH): Increasing Temperature decreases K
system shifts left.
After a temperature change Q remains the same initially, but K has changed. The system is now out of equilibrium (Q ≠ K), and will shift to re-establish Q = K.
How Q and K Predict Reaction Direction
| Condition | Direction | Interpretation |
|---|---|---|
| Q < K | Shift right (forward) | Too many reactants, not enough products |
| Q > K | Shift left (reverse) | Too many products, not enough reactants |
| Q = K | No shift | System at equilibrium |
Reaction: N2(g) + 3H2(g) ⇌ 2NH3(g) K = 0.5
Initial concentrations: [N2] = 1.0 M, [H2] = 3.0 M, [NH3] = 1.0 M
Calculate Q:
Q = [NH3]2 / ([N2][H2]3) = (1.0)2 / (1.0 × 27) = 1 / 27 ≈ 0.037
Since Q < K, the reaction will shift right to form more NH3 until equilibrium is reestablished.
Summary
- Q vs. K is a powerful diagnostic for predicting the direction of reaction shift.
- Q < K overall the forward direction proceeds; Q > Koverall the reverse direction proceeds.
- Concentration changes affect Q; temperature changes affect K.
- The system always adjusts to restore Q = K, demonstrating Le Châtelier’s Principle in quantitative terms.