In this video, we're going to talk about the units of the rate constant. So as we already know from our previous lesson videos, the units of the rate constant k will actually differ depending on the overall reaction order. And so what we're saying here is that the units of the rate constant k will be different for 0 order, first order, and second order reactions. And so down below, we're going to focus specifically on the units of the rate constant, which are as follows, in the following table. And so notice in this table down below, in the first column here, what we have is the overall reaction order, and in the second column, what we have is the units of the rate constant k. And so for 0 order reactions, the units of the rate constant k turn out to be molarity per second. And, of course, molarity per second is the same thing as saying molarity times inverse seconds. And so this is the same exact thing as this. Now for first order reactions, the units of the rate constant k turn out to be 1 over seconds. And so, of course, this is the same thing as saying just inverse seconds. And so this is the same thing as this. And then, of course, last but not least, for second order reactions, the units of the rate constant k turn out to be 1 over molarity times seconds. And so this, of course, turns out to be inverse molarity times inverse seconds. And so again, this is the same thing as this. And so one thing to note about all of these units that they share in common is that they all contain inverse seconds as part of the units in one way or another. And so notice that for second order reactions, the units contain inverse seconds. For first order reactions, the rate constant units contain inverse seconds. and for 0 order reactions, the units also contain inverse seconds. And so that's definitely helpful to help us memorize these units. The exponents will actually indicate the overall reaction order. And so notice for 0 order reactions, if we sum all of the unit exponents, it would be 1 on the molarity, minus 1, and 1 minus 1 is of course 0, which tells us that this unit is specifically for 0 order reactions. Now, for first order reactions, notice that the units, the exponents here are just negative 1, or just 1 for that matter, which tells us that this is the units for first order reactions. And then, of course, last but not least, for second order reactions, if we sum the units here, negative one minus 1 is, of course, negative 2, so that reminds us that this is for second order reactions. And so keeping that in mind, we'll be able to apply these concepts here in our example problem. So I'll see you guys there.
Rate Constant Units - Video Tutorials & Practice Problems
Rate Constant Units
Video transcript
Rate Constant Units Example 1
Video transcript
Alright. So here we have an example problem that's asking, what are the rate constant units for the following rate law shown right here? And so recall from our previous lesson videos that the rate law is just another way to write or express the reaction velocity, v. And the rate law always says that the reaction velocity, v, is equal to the rate constant, k, times the initial concentration of the reactants raised to the reaction order. And so because we only have one initial concentration listed here in our rate law, that tells us that there's only one reactant here that affects the rate of this particular reaction. And so because it's raised to the power of 2, that tells us that the overall reaction order must be second order for this reaction. And so, what we need to recall from our previous lesson videos is that when it comes to the rate constant units, one thing that we know that they all have in common is that they all include inverse seconds in one way or another. And so for that reason, we can automatically eliminate option D here since it does not contain inverse seconds. Now, another thing that we need to recall from our previous lesson videos is that the sum of the exponents and the units will actually reveal the overall reaction order. And so we know that the overall reaction order is second order, so we know that the sum of the exponents somehow has to equal to either 2 or negative 2. And so that means that we're going to need molarity in here to help this reach either 2 or negative 2. Now, it could be molarity cubed, and so if it was molarity cubed, then that would get us to 2. But if you recall from our previous lesson videos, we never had a unit that had molarity cubed, so we know that can't be right. And so another option would be to have inverse molarity. And so negative one minus 1 here equals negative 2, which matches with second order, overall reaction. And so it turns out that this is actually the answer that we're looking for, which matches with option C. So this here concludes our example problem and we'll be able to get some practice in our next practice video. See you there.
Determine the units for each of the 3 rate constants below in the enzyme-catalyzed reaction.