If a solution containing 18.0 g of a substance reacts by first-order kinetics, how many grams remain after three half-lives?

Answer: 2.25 g

Explanation:

1) The half-life is the fime for which the initial concentration is decreased by half of the original concentration.

2) So, after every period of one half-life the concentration of the reactant will decrease by half.

3) In this case after 3 half-lives, the concentration will decrease by half 3 times which is 2^3 = 8

So, the amount that will remain will be 18.0 g / 8 = 2.25 g.

4) You can do it in 3 stages in this way:

One half-life = > 18.0g / 2 = 9.0 g

Two half-lives = > 9.0g / 2 = 4.5 g

Three half-lives = > 4.5 g / 2 = 2.25 g