##### Chemical Equilibria Part II: The Truth Behind Le Chatelier’s Principle: Temperature effect

- focuschemistry
- November 28, 2017
- Chemical Enquilibria

Le Chatelier’s Principle was first taught in secondary schools, and delved deeper in A levels Chemistry. While many know what the principle is about, few really understand how it works for the effect of a change in temperature.

The effect of temperature on a reversible reaction can be seen through a shift in the position of equilibrium and the value of the equilibrium constant, K (Kc or Kp if expressed in terms of concentration or partial pressure respectively).

Consider a reversible reaction:

k_{f} |
|||

A + B | ⇌ | C | ΔH>0 |

k_{b} |

where kf and kb are the forward and backward rate constants respectively.

__Consider an INCREASE in temperature on the position of equilibrium.__

Many of us know that the position of equilibrium shifts to the right.

** A level Chemistry Teachers’ Reason:** When heat is applied to increase the temperature, the reaction will shift forward (endothermic) to absorb the heat, according to Le Chatelier’s principle.

__Alternative reason (kinetics perspective):__

When temperature increases, the forward and backward rate constants increase, according the Arrhenius equation:

**k = A _{o }exp (-Ea/RT)**

where

k = rate constant; Ao = frequency factor; EA = activation energy; R = gas constant; T = temperature, exp = exponential (or e)

We sometimes hear or read from some literature that says that for every 10^{o}C change in temperature, the rate of reaction doubles. Is that true?

Well, **this is NOT ALWAYS TRUE!**

If we were to perform a ln on the Arrhenius equation, we obtain

**ln k = ln Ao – (Ea/R)(1/T)**

Plotting ln k against 1/T yields the graph with ln Ao as the y-intercept and -Ea/R as the gradient . Notice that EA affects the gradient of the graph? Reactions of higher EA values are more sensitive to temperature changes.

Thus, since an endothermic reaction has a high EA value than an exothermic one, a change in temperature affects endothermic reactions more than exothermic reactions!

Going back to the reversible reaction at the beginning of this blog, we notice that kf is k_{endo} and kb is k_{exo }. Thus an increase in temperature increases kf more than kb.

__This means the NET reaction is in the Forward direction, which is the same conclusion as the typical reason our A level Chemistry teachers taught us!__

__Consider an INCREASE in temperature on the value of equilibrium constant, K__

A Level Chemistry Teachers’ Explanation:

k_{f} |
|||

A + B | ⇌ | C | ΔH>0 |

k_{b} |

Since

Kc = | [C] ——– [A][B] |

increasing temperature shifts position of equilibrium to the right (previous section).

This increase [C] and decreases [A] and [B], thus Kc increases.

**Does this explanation sound convincing to you?**

Have you asked yourself why a change of concentrations of any reactants or products (eg. A, B or C in the reversible reaction in the above example) does not change the value of K?

**Alternative reason (thermodynamics perspective):**

In 1884, J.B van’t Hoff proposed a relationship between the equilibrium constant, K of a reversible reaction to the reaction temperature, T :

d (ln K) ——– dT |
= | ΔH ——– RT ^{2} |

How does the famous** van’t Hoff equation lead us to the same conclusion** as what our A level teachers have taught us, **but in a more convincing manner?**

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