Learning Objectives:

• Learn the Arrhenius equation and how it relates the rate constant (k) of a chemical reaction to temperature, activation energy, and the gas constant.

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The Arrhenius Equation

Molecules only react if they collide with each other in the correct orientation. Increasing the temperature increases the energy and frequency of molecular collisions. The Arrhenius equation relates the rate constant k to all of these factors.

Formulation: The Arrhenius equation is given by: \[k=A⋅e^{−\dfrac{E_a}{RT}} \] where:
k is the reaction rate constant.
A is the pre-exponential factor or frequency factor.
E$_a$ is the activation energy.
R is the universal gas constant.
T is the absolute temperature.

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Solved Example: 9282-01

The rate constant for the reaction, A₂ B₄O → AB₄+ AO, is described as,

log k = 14.1 - \(\frac{{10000K}}{T}\)

The activation energy for this reaction (in kJ mol^-1) is closest to

A. 191.4

B. 83.14

C. 382.8

D. 166.28

Correct Answer: A

Solved Example: 9282-02

For a reaction, raising the temperature from 200 K to 300 K results in the increase of rate constant by a factor of 2. The activation energy for this reaction in kJ mol^-1  is closest to

(In 2 = 0.69)

A. 7.0

B. 3.5

C. 14.0

D. 0.83

Correct Answer: B