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.