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# Integrated Rate Law Concept 2

by Jules Bruno
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for reactions with first order mechanics, we're gonna say we use the following equation which is Ln of A. T equals negative Katie plus Ln of a. Oh Now here again, 80 is our initial, is our final concentration of your reactant. A. O. Is the initial concentration of your reactant. Que here is your rate constant and remember units for K is M to the negative N. N. Being the order of the reaction. Which in this case would be one plus one times time and verse here, let's just use seconds. Because a lot of the times, time and verses in seconds. So negative one plus one comes out to zero. 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 and verse. Okay, 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 of A T is equal to Y, your k, negative K. Is equal to M. Which is your slope T. Is equal to X. And then allen A. L is equal to be. Now, anytime we see a plot of Ln of reacting concentration versus time, that's a dead giveaway that it's first order because remember a plot is always of Y versus X. So here are why is L N A N R X is R T. So here is our Y axis with the L of the reacting concentration. Here's our X. Which is time. L N 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 reacting concentration over change in time. Now, lastly, what's important to remember is that all first order process radioactive processes um follow a first order mechanism of first order rate law. Okay, 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 the question is talking about a radioactive isotope. If a question says the word radioactive, that's a dead giveaway that you're dealing with the 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.