
Consider the first-order reaction A → B shown here. (a) What is the rate constant of the reaction? (b) How many A (yellow) and B (blue) molecules are present at t = 20 s and 30 s?
(a)

Interpretation:
Half-life and the rate constant for the given reaction have to be determined.
Concept introduction:
Rate of the reaction is the change in the concentration of reactant or a product with time.
Rate equation for the general reaction
Half-life is the time required for one half of a reactant to react.
Half-life for a first order reaction is
Explanation of Solution
The given first order reaction is,
For first order reaction,
In the given diagram A molecules (yellow spheres) are converted to B molecules (blue spheres)
Fig (1)
There are 16 A molecules at
Using the following equation the rate constant of this reaction can be calculated.
Half-life for a first order reaction is
(b)

Interpretation:
The number of molecules of A and B present at
Concept introduction:
Rate of the reaction is the change in the concentration of reactant or a product with time.
Rate equation for the general reaction
Half-life is the time required for one half of a reactant to react.
Half-life for a first order reaction is
Explanation of Solution
The given first order reaction is,
For first order reaction,
In the given diagram A molecules (yellow spheres) are converted to B molecules (blue spheres)
Fig (1)
There are 16 A molecules at
Therefore,
At
At
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