Give the units for the rate constants for the following rate law

Question

Give the units for the rate constants for the following rate law:
Rate = k[A]/[B].
Taking into account that sometimes the other concentration units may be used (e.g. NIST Chemical Kinetics Database uses both mol/L and molecule/cm3) express your results in terms of both cases.
(The units of k may be found by dimensional analysis)
1) Enter your answer for the concentration expressed in mol/L
2) Enter your answer for the concentration expressed in molecule/cm3. Round the numeric value to 3 significant figures if present.

I thought since the rate law is rate = k[A]/[B], k = (rate*[B])/[A] = (M/s)(M)/M = M/s and then I just have to convert it to the units. But the answers turned out to be 1) L^-1* mol^-1* s^-1 and 2) 6.02*10^20 molecule* cm^-3* s^-1.
I am so confused please help...

Answer 1

Not sure I've ever seen a rate equation where concentrations are divided.  Are you sure it isn't rate = k[A][B]?

If that were the case, then k = rate/[A][B] = M/s /M²

This converts to k =1/Ms = M^-1s^-1 which is the same as L^-1mol^-1s^-1 as reported in the correct answer.  So, I'm pretty sure the original rate equation is incorrectly written as rate = k[A]/[B].  No wonder you are confused.