Variation of the rate constant with temperature for the first-order reaction:
is given in the following table. Determine graphically the activation energy for the reaction.
T(K) |
k(s-1) |
298 |
|
308 |
|
318 |
|
328 |
|
338 |
|
Interpretation:
The activation energy of the given reaction is to be determined graphically.
Concept introduction:
Activation energy is the minimum energy required to initiate a reaction. It is calculated by Arrhenius equation. The higher the activation energy of the reaction, the more is the energy required for the initiation of the reaction, and slower is the rate of reaction.
Activation energy can be calculated by Arrhenius equation.
Here,
Slope of the graph is calculated by the expression given as:
Here,
According to Arrhenius equation, the slope is equal to the expression given as:
Here,
Answer to Problem 48QP
Solution:
Explanation of Solution
Given information:
The data corresponding to the reaction is given as follows:
Taking the natural log for each value of
The plot between
Slope of the graph is calculated by the expression given as follows:
Here,
Substitute the values of
According to Arrhenius equation, the slope is equal to the expression given as follows:
Here,
Rearrange the above equation for activation energy as,
The value of activation energy is
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