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# STATE AND EXPLAIN THE ACTIVATION ENERGY EQUATION

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## STATE AND EXPLAIN THE ACTIVATION ENERGY EQUATION

This page features two equations that can be used to calculate the activation energy of a chemical equation. But first, let’s have a quick recap of what activation energy really is.

### WHAT IS ACTIVATION ENERGY?

To put it in simple terms, activation energy is the quantity of energy that must be supplied to reactants in order to initiate a reaction.

If two or more reactants come together, there is a certain amount of energy that must be made available for a real chemical reaction to start.

If the amount of energy made available to the reactants is less than the activation energy, the chemical reaction will not commence. The energy available must be greater than the activation energy before a chemical reaction will occur. This is why another name for activation energy is ‘ENERGY BARRIER’.

Thus, activation energy is an energy threshold that must be exceeded for reactants to start forming products.

Graphically, activation energy can be represented in both exothermic and endothermic reactions as follows:

### FOR EXOTHERMIC REACTION

Here, enthalpy change = H = H – H = -ve [since H is less than H]

E = activation energy.

### FOR ENDOTHERMIC REACTION

Here, enthalpy change = H = H – H = +ve [since H is greater than H]

E = activation energy.

Ht = threshold energy.

Thus, the two equations one can use to calculate the activation energy of a chemical equation are as follows:

## CALCULATING ACTIVATION ENERGY FROM THE REACTION PROCESS GRAPH

Thus, if we plot the chemical process in a graph, as shown above, we can easily deduce the activation energy using the relation:

Activation energy = threshold energy – the heat of reactants

E = Ht – H

## CALCULATING ACTIVATION ENERGY FROM ARRHENIUS LAW

Arrhenius’s law can be stated thus:

Where: k = reaction rate

A = exponential factor

E = activation energy

R = gas constant = 8.3145 J/K.mol

T = temperature in kelvin

Resolving the equation further, we have:

RT In k = – E + RT In A

E = RT In A – RT In k

E = RT[In A – In k]

E = RT [In A/k]

Thus, the activation energy equation is given as:

E = RT [In A/k]

You can also calculate activation energy from the graph of In k against 1/T. the slope of this graph equals – E/R

Thus, activation energy can be calculated from the slope of the graph by doing:

Slope = -E/R

Eₐ = – R × slope