Half-lives of first order versus second order

[Shannon Wasley 2J]

For some of the homework problems in Chapter 15, the problem asked to find the time it would take for the concentration to get to 1/4 or 1/8 of its original value. For a first order reaction, I worked it out that if the half life was, for example, 100 seconds and this was the value for the initial concentration to become half of its value, then to find how much time it would take for the concentration to be 1/4 of its initial value then it would just be double the half life, so it would be 200 seconds. This is also what the solutions manual did and it was the correct answer. Why is this not a correct way to do things for a second order reaction? since I have tried it and I get the wrong answer when I do it this way

[Gwyneth Huynh 1J]

The half life of a first order reaction does not depend on the initial concentration (half life= ln2/k) while the half life of a second order reaction does depend on the initial concentration (half life = 1/(k[A]initial). So you can use that method for first order reactions because the half life is constant. However, for second order reactions, the half life changes depending on the initial concentration.