In the given chemical reaction, the rate law is expressed as rate = k [NO₂]² [Cl₂]¹. To determine the overall order of the reaction, you simply sum the exponents of the concentration terms. Here, the order with respect to NO₂ is 2, and the order with respect to Cl₂ is 1. Therefore, the overall order of the reaction is:

Overall Order = 2 + 1 = 3

Next, to find the units for the rate constant k, we use the relationship that relates the rate of the reaction to the concentration of the reactants. The general form for the units of k is:

Units of k = m^-n s^-1

In this case, since the overall order is 3, we substitute n with 3:

Units of k = m^-3 s^-1

Thus, the units for the rate constant k in this reaction are m^-2 s^-1, indicating that k has dimensions of concentration raised to the power of negative two per unit of time.