Effect of Conditions on Equilibrium Constants
Learning Objectives (OCR Spec 5.1.2)
By the end of this lesson you should be able to:
- Explain that temperature is the only factor that changes the value of Kc or Kp
- Describe how increasing temperature changes K differently for exothermic and endothermic reactions
- Explain why concentration and pressure changes do not affect K
- Explain why catalysts do not affect K (or equilibrium position)
The Key Idea
A crucial take-home message of OCR Year 2 equilibrium: only temperature changes the value of K. Concentration changes, pressure changes, and catalysts affect rate and/or equilibrium position, but they do not change the numerical value of Kc or Kp.
| Change | Affects position? | Affects K value? |
|---|
| Concentration | Yes | No |
| Pressure (gas) | Yes (if gas moles differ) | No |
| Temperature | Yes | Yes |
| Catalyst | No (reaches equilibrium faster) | No |
Why Temperature Changes K
Temperature changes K because it changes the ratio of forward to reverse rate constants.
- Both k_forward and k_reverse obey the Arrhenius equation: k = A e^(-Ea/RT). Raising T increases both rate constants.
- But the forward and reverse activation energies (Ea,f and Ea,r) are not equal. They differ by the enthalpy change of reaction: DH = Ea,f - Ea,r.
- The exponential term is more sensitive to changes in Ea for the step with the larger Ea. This means k_forward and k_reverse change at different rates.
Since K = k_forward / k_reverse (at equilibrium), K changes as T changes.
Exothermic Forward Reaction (DH < 0)
- Ea,r > Ea,f (reverse has higher barrier).
- Raising T speeds up k_reverse more than k_forward.
- Ratio k_f/k_r decreases — K decreases.
- Equilibrium shifts backwards (Le Chatelier: heat is a product; adding heat shifts equilibrium away from product).
Endothermic Forward Reaction (DH > 0)
- Ea,f > Ea,r.
- Raising T speeds up k_forward more than k_reverse.
- Ratio k_f/k_r increases — K increases.
- Equilibrium shifts forwards.
Summary Table
| Reaction type | Effect of raising T on K |
|---|
| Exothermic forward (DH < 0) | K decreases |
| Endothermic forward (DH > 0) | K increases |
And cooling has the opposite effect.
Why Concentration Does NOT Change K
Imagine a system at equilibrium with [A] = [B] = 1.0 mol dm^-3 and K = 1.0. If you suddenly add more A so [A] = 2.0, then:
- Reaction quotient Q = [B]/[A] = 1.0/2.0 = 0.5 < K.
- System responds by converting A to B until Q returns to K.
- Eventually: [A] = 1.5, [B] = 1.5, so Q = 1.0 = K once more.
The ratio defining K is restored — but the individual concentrations are now different. K itself is unchanged. The equilibrium position has shifted towards products, but K remains 1.0.
Why Pressure Does NOT Change Kp
Pressure changes the partial pressures of all gases, but the equilibrium constant Kp depends only on temperature. Increasing total pressure (by compressing the container) causes the system to shift to the side with fewer moles of gas, but the Kp value does not change.
Example
N2(g) + 3H2(g) <-> 2NH3(g), Kp (at fixed T).
- Compress the mixture (raise p_total). Q initially falls because NH3 is on the side with fewer moles.
- System shifts forward until the partial pressures re-satisfy Kp = p_NH3^2/(p_N2 x p_H2^3).
- Kp is the same number before and after — only the individual partial pressures have changed.
Why Catalysts Do NOT Change K or Equilibrium Position
A catalyst lowers the activation energies of both the forward and reverse reactions by the same amount. So:
- k_forward increases by a certain factor.
- k_reverse increases by the same factor.
- Their ratio k_f/k_r = K is unchanged.
- The equilibrium position is unchanged.
- The rate of reaching equilibrium is faster (both directions).