For reactions with first order mechanics we're going to say we use the following equation which is ln⁡(AT)=−KT+ln⁡(AO). Now here again AT is our final concentration of your reactant. AO is the initial concentration of your reactant. K here is your rate constant. And remember units for K is M to the negative NN being the order of the reaction, which in this case would be 1 + 1 times time. Inverse.

Here let's just do seconds, because a lot of the times time inverses in seconds, so -1 + 1 comes out to 0. Anything to the zero power is equal to just one, so it drops out. So that would mean that K here is in units of time inverse. So here T again is time. And we're going to say here that our equation for first order processes follows the equation for straight line, which means that ln⁡(AT) is equal to Y. Your K negative K is equal to M which is your slope, T is equal to X and then ln⁡(AO) is equal to B.

Now anytime we see a plot of ln⁡(reactant) concentration versus time, that's a dead giveaway that it's first order because remember a plot is always AY versus X. So here are Y is ln⁡(A) and our X is RT. So here is our Y axis with the ln⁡(reactant) concentration. Here's our X which is time ln⁡(AO) is just our initial starting amount. And then remember slope is equal to change in Y over change in X, which is the same thing as change in reactant concentration over change in time.

Now lastly, what's important to remember is that all first order process all radioactive processes follow a first order mechanism of first order rate law. OK, so not all first order processes are radioactive, It's just that the ones that are radioactive happen to be first order, so that's a key giveaway. So if a question is talking about a radioactive isotope, if a question says the word radioactive, that's a dead giveaway that you're dealing with their first order process. So keep in mind these little tips in terms of identifying the order of any type of word problem, we have to determine if it's first order or not.