Question

The integrated rate law allows chemists to predict the reactant concentration after a certain amount of time, or the time it would take for a certain concentration to be reached.

The integrated rate law for a first-order reaction is:
[A]=[A]0e−kt

Now say we are particularly interested in the time it would take for the concentration to become one-half of its initial value. Then we could substitute [A]02 for [A] and rearrange the equation to:
t1/2=0.693k  
This equation calculates the time required for the reactant concentration to drop to half its initial value. In other words, it calculates the half-life.

A)What is the half-life of a first-order reaction with a rate constant of 2.30×10⁻⁴  s−1

B)What is the rate constant of a first-order reaction that takes 188 seconds for the reactant concentration to drop to half of its initial value?

C)A certain first-order reaction has a rate constant of 3.90×10⁻³ s−1. How long will it take for the reactant concentration to drop to 18 of its initial value?

Answer 1

The answer of (A) and (B) has been given below in Image.

The solution of (C) has been given below in image.