7.0 Arrhenius Equation

  Chemical Kinetics

It is a mathematical expression to describe the effect of temperature on the velocity of a chemical reaction. The equation is commonly given in the form of exponential function i.e., $$k = A{e^{ - \frac{{{E_a}}}{{RT}}}}$$ Taking log $(ln)$ both sides, we get $$\begin{equation} \begin{aligned} \ln k = \ln \left( {A{e^{ - \frac{{{E_a}}}{{RT}}}}} \right) = \ln A + \ln {e^{ - \frac{{{E_a}}}{{RT}}}} \\ \ln k = \ln A - \frac{{ - {E_a}}}{{RT}} \\\end{aligned} \end{equation} $$

where,

$k$ - Rate constant

$A$ - Arrhenius constant (represents frequency at which atoms and molecules in a ways that leads to reaction)

${{E_a}}$ - Activation Energy

${e^{ - \frac{{{E_a}}}{{RT}}}}$ - Boltzman factor (represents fraction of molecules having energy greater than activation energy)

As we all know that, a chemical reaction takes place due to the collision among reactant molecules. Every collision does not bring a chemical change. The collision that actually convert the reactants to product are Effective Collisions.

For effective collision, molecules should clear two energy barriers:

1. Energy Barrier

2. Orientation Barrier

Threshold Energy: Minimum amount of energy which is required by colliding molecules to make chemical reaction to occur.

Activation Energy: The extra amount of energy which the reactant molecules must require so that their mutual collision may lead to breaking of bonds. It is denoted by ${E_a}$. Its Unit is $kJ/mol$.

$${E_a} = {\text{Threshold Energy}} - {\text{Actual Average Energy}}$$

From the graph,

$\sum {{H_R}} $ = Sum of enthalpies of reactant

$\sum {{H_P}} $ = Sum of enthalpies of product

$\Delta H$ = Change in enthalpy = $\sum {{H_P}} $ - $\sum {{H_R}} $ = ${E_{{a_1}}} - {E_{{a_2}}}$

${E_{{a_1}}}$ = Energy of activation of forward reaction

${E_{{a_2}}}$ = Energy of activation of backward reaction

For exothermic reaction, $\Delta H < 0$ i.e., $$\begin{equation} \begin{aligned} {E_{{a_1}}} - {E_{{a_2}}} < o \\ {E_{{a_1}}} < {E_{{a_2}}} \\\end{aligned} \end{equation} $$

From graph, we can conclude that the minimum activation energy required for the reactants to convert to products is $\Delta H$ i.e., change in enthalpy.

For endothermic reaction, $\Delta H > 0$ i.e., $$\begin{equation} \begin{aligned} {E_{{a_1}}} - {E_{{a_2}}} > o \\ {E_{{a_1}}} > {E_{{a_2}}} \\\end{aligned} \end{equation} $$

Then, the reaction will automatically takes place and minimum activation energy will be $0$.