Question

Draw a graph which is used to calculate the activation energy of a reaction. Give the appropriate expressions used to calculate the activation energy graphically.

Draw a graph which can be used to calculate the activation energy of a reaction.

Answer 1

The concept of activation can be understood with the help of Arrhenius equation, which is given as

\[\ce{k = Ae^{-E_a/(RT)}}\]

Where, k is rate constant of the reaction, 

A is pre-exponential factor,

E_a activation energy of the reaction, 

T is the temperature

R is the universal gas constant

By taking log of above equation, we can reduce it as,

⇒ \[\ce{ln k = ln(Ae^{-E_a/(RT)})}\]

⇒ \[\ce{ln k = ln A + ln (e^{-E_a/(RT)})}\]

⇒ \[\ce{ln k = ln (A) + \frac{-E_a}{RT} ln (e)}\]

⇒ \[\ce{ln k = \frac{-E_a}{R} (\frac{1}{T}) + ln (A)}\]

On comparing above equation with

y = mx + c

we get that,

\[\ce{m = \frac{-E_a}{R}}\], with X- axis as \[\ce{\frac{1}{T}}\] along the Y-axis as ln k and a constant of ln(A). Therefore, we can plot the graph as:

Also, the graph between the energy of reaction and progress of reaction can be plotted as: