Half-life (kinetics) for First Order Reactions The integrated rate law for a fir

Question

Half-life (kinetics) for First Order Reactions

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 inital value. Then we could substitute [A]02 for [A] and rearrange the equation to:
t1/2=0.693k  
This equation caculates the time required for the reactant concentration to drop to half its initial value. In other words, it calculates the half-life.

Half-life equation for first-order reactions:
t1/2=0.693k
where t1/2 is the half-life in seconds (s), and k is the rate constant in inverse seconds (s1).

Part A

What is the half-life of a first-order reaction with a rate constant of 4.10×104  s1?

Part B

What is the rate constant of a first-order reaction that takes 8.70 minutes for the reactant concentration to drop to half of its initial value?

Part C

A certain first-order reaction has a rate constant of 3.60×103 s1. How long will it take for the reactant concentration to drop to 18 of its initial value?

Half-life (kinetics) for First Order Reactions

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 inital value. Then we could substitute [A]02 for [A] and rearrange the equation to:
t1/2=0.693k  
This equation caculates the time required for the reactant concentration to drop to half its initial value. In other words, it calculates the half-life.

Half-life equation for first-order reactions:
t1/2=0.693k
where t1/2 is the half-life in seconds (s), and k is the rate constant in inverse seconds (s1).

Part A

What is the half-life of a first-order reaction with a rate constant of 4.10×104  s1?

Part B

What is the rate constant of a first-order reaction that takes 8.70 minutes for the reactant concentration to drop to half of its initial value?

Part C

A certain first-order reaction has a rate constant of 3.60×103 s1. How long will it take for the reactant concentration to drop to 18 of its initial value?

Explanation / Answer

t1/2 = 0.693/K
t1/2 = 0.693/(4.1*10^-4)
t1/2 = 1690.243 sec

t1/2 = 0.693/K
K = 0.693/(8.7 * 60)
K = 1.327 * 10^-3

K = 2.303/t log (a/a-x)
3.6 * 10^-3 = 2.303/t log (x/(x/8))
t = 577.727 Sec

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