Determine order of reaction. Thank you!

Question

Use the data below to determine the order of the reaction based on the first two half-life cycles.

Time (s)	[X] (M)
0	10.00
100	7.45
180	5.00
220	4.10
360	2.50
410	1.85

Answer 1

Ask yourself "how is the concentration of [X] changing with time?" Or, ask yourself "how long does it take for the concentration of [X] to be cut in half?"

You can see that it takes 180 seconds for the [X] to go from 10.00 M to 5.00 M (i.e. cut in half). Then to go from 5.00 M to 2.50 M (cut in half again), it takes another 180 seconds. So, apparently, the half life for this reaction is 180 seconds. This means that every 180 seconds, the [X] is cut in half.

If you learn about reaction kinetics, you will learn that a first order reaction has a constant half life, i.e it doesn't change as the concentration changes. In a second order reaction, the half life becomes longer and longer as the [X] decreases and for a zero order reaction the half life becomes shorter and shorter as the [X] decreases.

There is a significant amount of math that goes into determining these factors, but if you simply remember these facts, that should help you.

So, in summary, the reaction described in the present problem is FIRST ORDER.