Rate Constant Units: Study with Video Lessons, Practice Problems & Examples

The units of the rate constant (k) vary based on the reaction order. For zero-order reactions, k is expressed as molarity per second (M/s). First-order reactions have k as inverse seconds (s^-1), while second-order reactions use k as inverse molarity times seconds (M^-1s^-1). Notably, all units include inverse seconds, reflecting the reaction's kinetics. Understanding these units aids in applying concepts to reaction mechanisms and enhances comprehension of reaction rates and their implications in biochemical processes.

Rate Constant Units

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 Example 1

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.

Alright. So this practice problem wants us to determine the units for each of the three rate constants below in the enzyme-catalyzed reaction shown here. And so recall from our previous lesson videos that initially, at the very beginning of an enzyme-catalyzed reaction, there are only three relevant rate constants, and those are k1, k-1, and k2. And so this practice problem just wants us to determine the units for each of these three rate constants. Now, we know from our previous lesson video that regardless of if the rate constant is for a zero order, a first order, or a second order reaction, we know that the rate constant units are going to include the inverse seconds in one way or another. And so for that reason, we can go ahead and include inverse seconds for each of these rate constants. But, if we want to determine the complete units for each of these rate constants, we're going to need to determine the overall reaction order for each of these three reactions that these rate constants are a part of. And if we want to determine the overall reaction order, then we're going to need to determine the rate law for each of these three reactions, and that's exactly what we're going to do next is determine the rate laws for each of these three reactions. There are three rate laws for each of these three reactions and for the first rate law that we're going to consider is the rate law for the enzyme substrate complex formation. Now notice up above in this expression of the enzyme-catalyzed reaction, the enzyme substrate complex can only be formed in one way, and that is through this rate constant k1, which takes the free enzyme and the free substrate and forms the enzyme substrate complex. And so, recall from our previous lesson videos that the rate law is just another way to express the reaction velocity v, and it says that the reaction velocity v is equal to the rate constant k, which is k1 for this rate law, times the concentration of the reactants, and notice that there are actually two reactants here for this reaction that forms the enzyme substrate complex. The two reactants are the free enzyme and the free substrate. So, we're going to include both of those in our rate law, the free enzyme and the free substrate. And, of course, because both of their coefficients here are 1, and we're going to assume that these are elementary reactions. And of course, if we want to determine the overall reaction order from this rate law, all we need to do is take the sum of each of these individual reaction orders. So 1 plus 1 is 2, which tells us that this is a second order reaction, the overall reaction order. And of course, we know from our last lesson video, if we're trying to determine the units for this rate constant k1, which we now determined is a second order rate constant, we know that the sum of the exponents in the units are going to reveal the reaction order. And so what that means is that we're going to need to have molarity inverse molarity here, so that we have negative one minus 1, gives us negative 2, and that two in there tells us that these are units for second order rate constants. And so now that we've determined the units for k1, we can go ahead and move on to our next rate law. The next rate law here is the rate law for the enzyme substrate complex breakdown backward. And so notice that the enzyme substrate complex can break down in actually two ways. It can break down backward via k-1, or it could break down forward via k2. And so here, we're focused specifically on the breakdown backward, and so we're focused on k-1. And so notice that, the rate law again is going to be the reaction velocity, which is equal to the rate constant k, which is going to be k-1 for this backward breakdown, times the concentration of the reactant, which for this backward reaction here, the reactant is going to be the enzyme substrate complex. And then, of course, the coefficient in front of the enzyme substrate complex is 1, which tells us that the reaction order for this reactant is 1. And since there's only one reactant that's part of this rate law, and its reaction order is 1, that tells us that the overall reaction order is first order. And so what this means is that the for first order reactions, the units of the rate constant, are, the sum of the exponents in the units have to total up to 1 for first order. And so notice here that we already have, inverse seconds, and so this inverse seconds here, the exponent already totals to a value of 1. And so this is the appropriate units, inverse seconds is the appropriate units for our k-1 rate constant. So now moving on to our final rate constant here, we're going to look at the rate law for the enzyme substrate complex breakdown forward this time via k2. And so the rate law is going to be the reaction velocity, which is equal to the rate constant k2 times the concentration of the reactant, which is the enzyme substrate complex again. And of course, the reaction order is going to be 1. And so notice that this is also a first order reaction, just like the backward breakdown, which means that the units are going to be exactly the same for the k2 rate constant. And so, these are the appropriate units for each of these rate constants here. And that concludes this practice problem, so I'll see you guys in our next video.

Here’s what students ask on this topic:

What are the units of the rate constant for a zero-order reaction?

The units of the rate constant (k) for a zero-order reaction are molarity per second (M/s). This can also be expressed as molarity times inverse seconds (M·s^-1). In a zero-order reaction, the rate of reaction is independent of the concentration of the reactants, which is why the units of k include only the concentration term (molarity) and time (seconds). Understanding these units helps in analyzing reaction kinetics and determining how the reaction rate changes over time.

How do the units of the rate constant differ for first-order and second-order reactions?

For first-order reactions, the units of the rate constant (k) are inverse seconds (s^-1). This indicates that the reaction rate is directly proportional to the concentration of one reactant. For second-order reactions, the units of k are inverse molarity times seconds (M^-1s^-1). This reflects that the reaction rate is proportional to the product of the concentrations of two reactants or the square of the concentration of a single reactant. These differences in units help in identifying the reaction order and understanding the kinetics involved.

Why do all units of the rate constant include inverse seconds?

All units of the rate constant (k) include inverse seconds (s^-1) because the rate of a chemical reaction is typically expressed as a change in concentration over time. The inverse seconds term reflects the time dependency of the reaction rate. For zero-order reactions, the units are M/s; for first-order reactions, they are s^-1; and for second-order reactions, they are M^-1s^-1. This commonality helps in understanding the temporal aspect of reaction kinetics across different reaction orders.

How can you determine the reaction order from the units of the rate constant?

You can determine the reaction order by analyzing the units of the rate constant (k). For zero-order reactions, k has units of molarity per second (M/s). For first-order reactions, k has units of inverse seconds (s^-1). For second-order reactions, k has units of inverse molarity times seconds (M^-1s^-1). By summing the exponents of the units, you can identify the reaction order. For example, M¹s^-1 (0 order), s^-1 (1st order), and M^-1s^-1 (2nd order) indicate the respective reaction orders.

What is the significance of understanding the units of the rate constant in biochemical processes?

Understanding the units of the rate constant (k) in biochemical processes is crucial for analyzing reaction kinetics and mechanisms. The units help determine the reaction order, which indicates how the concentration of reactants affects the reaction rate. This knowledge is essential for designing experiments, optimizing reaction conditions, and interpreting data in biochemical research. For example, knowing that a reaction is first-order (units of k: s^-1) helps predict how changes in reactant concentration will impact the reaction rate, aiding in the development of efficient biochemical pathways and drug formulations.