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# Units of the rate constant

AP.Chem:
TRA‑3 (EU)
,
TRA‑3.B (LO)
,
TRA‑3.B.4 (EK)

## Video transcript

in this video we're going to be talking about how you can find the units for your rate constant K so the two things that you should know before we get started are that one rate constant K has units so this is an always true of constants in chemistry but it is true of K the second thing to remember is that your rate constant the units of K depend on your on your rate law and so we're going to use this second point to use the rate law to derive the units of K and this is really handy because that means you don't have to memorize what the units of K are for different orders of reactions so we're going to focus on the three most common rate laws that you see in chemistry class so we're going to talk about zeroth first and second order reactions and we will divide a we will derive their units so first let's look at zeroth order so zeroth order reactions have a rate law that look like this so the rate is equal to K times your concentration of your reactant a to the zeroth order and anything to the zeroth or sorry to the zeroth power and anything to the zeroth power is just 1 so our rate is equal to the rate constant K the units of rate are always going to be the same so the units of rate are always molar per second and you can also just think of units almost like numbers if you have an equal sign the units on both sides of your equal sign have to be the same and they have to match so here since we have rate equal decay that means K has to also have units of molar per second so this tells us that units for a zeroth order reaction are molar per second we can use that same idea to figure out the units of K for first and second order reactions too so for a second-order sorry for a first order reaction so for first order a first order reaction rate law is rate is equal to the our rate constant K times the concentration of our reactant raised to the first power units of rate our molar per second and the units of concentration are always going to be molar so now we know that the units of K times molar equals molar per second so we have molar on both sides so we don't have to worry about that but we're missing a 1 over a second term so that tells us that the units of K are 1 over seconds the other way we can try to figure out the unit's here if you're not comfortable with sort of back calculating what the units are is we can actually rearrange this rate law so if we just put K on on one side and everything else on the other side we get that K is equal to rate divided by the concentration of 8 so all I did was divide both sides here by the concentration of 8 and since we know that the unit's on both sides of the equal sign have to be the same then we can figure out the units of K by dividing the units of rate by the units of our concentration so that's just molar per second for the rate divide it by molar for the concentration and then the molar cancels out and we're left with 1 over seconds so that's an even more straightforward way to find the units of K but the idea is the same you can treat units the same way you treat numbers and you just have to make sure they match on both sides of your equal sign the last example we're going to go through is going to be for second-order reactions so second-order reactions or second-order rate laws have the form rate is equal to our rate constant K times the concentration of our reactant to the second power so on one side we have molar per second for the rate and on the other side now since our concentration is squared we have molar squared so molar squared times something is equal to molar per second we need to add a 1 / seconds in our units for K because we need to make sure when we multiply these we get the seconds on the bottom and we need to cancel out one of these concentration terms so we need to put molar in the denominator as well so the units of K for a second-order reaction are one over molar molar seconds so these are the three most common molecularity x' that you might see in a chemistry class and sometimes you have reactions I aren't zeroth first or second order and whenever that happens you can always use a rate law to find the units of the rate constant K
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