The initial concentration of a reactant in a first order reaction is 0.860 M. What will be its concentration after 4 half-lives have passed?

Answer 1

Because it is only 4 half lives in this problem, it isn't difficult to use 0.8600 goes to 0.4300 goes to 0.2150 goes to 0.1075 goes to 0.05375. But you may have a problem where the number of half lives isn't so simple, and in that case you'll want to use a very simple formula for 1st order decay. It goes like this...

Fraction remaining = 0.5ⁿ

n = number of half lives that have elapsed, which in this case = 4

0.5⁴ = 0.0625 which is the fraction remaining

amount remaining = 0.0625 x 0.860 = 0.0538 M (to 3 sig. figs.)

Answer 2

Hi Hunter!

Since we already know the initial concentration of the reactant and we know that there are 4 half-lives, we just need to halve the initial reactant concentration four separate times to get the final concentration:

0.8600 --> 0.4300 --> 0.2150 --> 0.1075 --> 0.05375 M