Problem: A first order reaction has a rate constant of 0.500 s–1. How long, in seconds, would it take for the concentration of A to decrease from 0.860 M to 0.310 M?

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We’re being asked to determine the time it would take for the concentration of A to decrease from 0.860 M to 0.310 M.

The integrated rate law for a first-order reaction is as follows:

ln [A]t=-kt+ln [A]0

where:

[A]t = concentration at time t 
k = rate constant
t = time
[A]0 = initial concentration


We’re given:

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Problem Details

A first order reaction has a rate constant of 0.500 s–1. How long, in seconds, would it take for the concentration of A to decrease from 0.860 M to 0.310 M?

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