Reaction orders and rate constants

Question

In each of the following situations where the rate law and units used are described, suggest units for the rate constant (k).

a. A third-order reaction where the rate is measured in mol L^-1 s ^-1 and the concentrations of all reactants are measured in mol L^-1

b. A rate law that has the concentration of the two reactants measured in M (each is first-order) and a rate that is measured in mol L^-1 min ^-1

Answer 1

When finding units for the rate constant (k), just take the order of the reaction and plug in the units and then cancel as needed. So, this works in the following way:

a) A third order reaction:

rate = k [M]³

units of rate = mol L^-1s^-1

units of concentration = mol L^-1

plugging in the units and solving for k, we have...

mol L^-1s^-1 = k (mol L^-1)³

k = mol L^-1s^-1 / (mol L^-1)³

k = M^-2s^-1 (I simply changed ML^-1 to M). This can also be written as 1/M²s

b) rate = [A]¹[B]¹

rate is in mol L^-1 min^-1 (which I'll change to M/min or Mmin^-1, because ML^-1 is the same as M)

concentrations are in M

rate = k[A][B]

M/min = k(M)(M)

k = M/min / M²

k = 1/Mmin = M^-1min^-1