How do I calculate rate coefficient units?

For any rate equation, the units have to be equal on either side of the equation. The rate of reaction always has the units mol dm^-3 s^-1, and the concentration species in the equation typically have units of mol dm^-3, from this any rate coefficient unit can be determined. For example, a first order reaction; r = k[A]For the units to be equal on either side of the equation, mol dm^-3 s^-1 = k [mol dm^-3], the rate coefficient, k has to have units of s^-1An another example can be a second order reaction; r = k[A]²Here, the units of species A is a little different. As there is two A for each reaction, the units work out to be mol² dm^-6. Therefore to make the units equal, k has to have units of mol^-1 dm^-3 s^-1
In every reaction rate, the units of k can be worked out through simple calculations, you don't even have to memorise the answer for each type of reaction.