A certain first-order reaction a → b is 25% complete in 42 min at 25°c. What is the half-life of the reaction?

First-order reaction is defined as the reaction in which the rate of the reaction is dependent on the concentration of only one reactant.

The half-life of the reaction is 101.6 minutes.

The rate constant for the first-order reaction can be determined by:

In which:

x= amount of reactant decomposed in time t

k= rate constant  

a-x= amount of reactant left after time t

t= time required for a reaction

a= initial concentration

The initial concentration of the reaction is 100.

Now, given:

x = 25

a - x = 75

t = 42

Putting the values in the above equation, we get:

k = 6.85 x 10 ⁻³

The half-life will be:

minutes.

Therefore, the half-life of the reaction is 101.6 minutes.

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minutes

Explanation:

For a First order reaction, the rate constant is determined by

Where

k= rate constant

t= time required for a reaction

a= initial concentration

x= amount of reactant decomposed in time t

a-x= amount of reactant left after time t

Let the initial concentration be

Then

Substituting the given values in above equation, we get -

Also,

minutes

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explanation: