The rate constants for the first-order decomposition of an organic compound in solution are measured at several temperatures:
Determine graphically the activation energy and frequency factor for the reaction.
Interpretation:
The activation energy and frequency factor for the given reaction has to be determined graphically.
Concept introduction:
Arrhenius equation:
Arrhenius equation is a formula that represents the temperature dependence of reaction rates
The Arrhenius equation has to be represented as follows
R represents the universal gas constant and it has the value of 8.314 J/K.mol
T represents the absolute temperature
A is the frequency factor
Activation energy can be determined through graphical method,
In the graph of
Answer to Problem 13.135QP
The activation energy and frequency factor for the given reaction are
Explanation of Solution
Given,
Rate constants for the first order decomposition of an organic compound in solution are measured at several temperatures, and they are listed below,
To draw the graph, we need
Form the given data we can draw the graph by plotting
Fig (1)
According to the straight-line equation in mathematics,
Herein,
The slope of the line is
Now, the activation energy for the given reaction can be calculated as follows,
The y-intercept equals the natural logarithm of the frequency factor (A).
Therefore,
The activation energy and frequency factor for the given reaction were graphically determined.
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Chapter 13 Solutions
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