Concept explainers
Chemical Reactions A self-catalytic chemical reaction results in the formation of a compound that causes the formation ratio to increase. If the reaction rate is modeled by
where is a positive constant, is the initial amount of the compound, and is the variable amount of the compound, for what value of is the reaction rate a maximum?
To calculate: The value of so that the reaction rate is maximum.
Answer to Problem 19AYU
The reaction rate is maximum when .
Explanation of Solution
Given:
The reaction rate of the self catalyst is
where is the initial amount of the compound, is the variable amount of the compound and is a positive constant.
Formula used:
Calculation:
We have the reaction rate
We can see that the reaction rate is a quadratic equation with .
Since, is negative, the vertex is the point of maximum value.
Thus, the maximum reaction occurs at
Thus, the reaction rate is maximum when .
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