Half life method?

Question

I was wondering how you could use the half life method to prove a reaction was first order?

Answer 1

If the half-life (time from 100% to 50%, time from 50% to 25%, and so on) is constant, the reaction must be first order. Otherwise, it's not.

A more precise way of using the same idea is to plot the log of the amount against time. If the reaction is first order, you will get a straight line. That way, you are using all your information, and not just a few special points.

Why are these two ways of looking at it the same? because if the half life is constant, every half life the log of the amount goes down by log 2, so the plot has got to have constant slope, which means it's a straight line.