The integrated rate law allows chemists to predict the reactant concentration af

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]0ekt

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 certain first-order reaction has a rate constant of 1.70×103 s1. How long will it take for the reactant concentration to drop to 18 of its initial value?

Express your answer with the appropriate units.

Explanation / Answer

rate constant = 1.70×103 s^1

time = t = ?

initial concentration = Ao = 100

after some time reamining = 18

formula : t = 1/k * ln (Ao / At)

t = 1/1.70 x 10^-3 * ln (100 / 18)

t = 1009 sec

t = 16.8 min

time = 16.8 min

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.