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.

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).

What is the half-life of a first-order reaction with a rate constant of 3.50×104 s1?

Explanation / Answer

Given

rate constant (k) = 3.50 * 10-4s-1

we know

t1/2 = 0.693 / k

= 0.693 / 3.50 * 10-4s-1

= 1980 seconds

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