Answer: c. M^-1s^-1
Step-by-step explanation:
The overall order of a reaction is determined by adding the individual orders of each reactant in the rate equation. In this case, the overall order of the reaction is 2, which means the rate equation can be written as:
Rate = k[A]^m[B]^n
Here, m and n are the individual orders of the reactants A and B, respectively. The overall order is the sum of these individual orders (m + n), which is equal to 2 in our case.
Now, let's look at the units of the rate constant (k) based on the given rate equation:
Rate = k[A]^m[B]^n
The units of rate are usually expressed as M/s (molarity per second) as the concentrations are given in molarity (M) and time in seconds (s).
Since the overall order is 2, we have:
m + n = 2
The units of k can be deduced by considering the units of rate and the concentrations:
Rate = k[A]^m[B]^n
Rate = (M/s) = k [(M)^m (M)^n]
For the units to be consistent on both sides of the equation, we need to have:
(M/s) = k (M)^(m + n)
Now, since m + n = 2, we have:
(M/s) = k (M)^2
To balance the units, the units of k must be M^-1s^-1, so the correct answer is:
c. M^-1s^-1