Interpretation:
Half-life of the first-order reaction has to be calculated if the reactant concentration is
Answer to Problem 13.56QE
Half-life of the reactant is
Explanation of Solution
Integrated rate law for the first order reaction is given as follows;
Where,
For the concentration of the reactant of
The integrated rate law can be given as shown below;
Substituting the values in the equation as shown below;
For the concentration of the reactant of
The integrated rate law can be given as shown below;
Substituting the values in the equation as shown below;
Considering the equations (1), and (2), it is found that the left side is equal. Therefore, equating the right side of both equations, the rate constant can be calculated as shown below;
Therefore, the rate constant of the reaction is
The relationship between half-life and the rate constant of first order reaction is given as follows;
Thus, half-life of the reactant is calculated as
Initial concentration can be calculated by substituting the rate constant value in equation (1) as follows;
Therefore, the initial concentration of the reactant is
Time taken for the reactant concentration to decrease from
Therefore, the time taken for the reactant concentration to decrease to
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Chapter 13 Solutions
Chemistry: Principles and Practice
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