The rate of formation of a product depends on the the concentrations of the reactants.
If products A and B produce product C, a general equation for the formation of C is of the kind rate = k*[A]^a * [B]^b
[ ] is used for the concentration of each compound.
When k, m and n are unknown, chemists run lab trials to calculate them..
You have these data from 3 trials
Trial [A] [B] Rate
(M) (M) (M/s)
1 0.50 0.010 3.0×10−3
2 0.50 0.020 6.0×10−3
3 1.00 0.010 1.2×10−2
Trials 1 and 2 are run at constant [A] which permits to calculate the exponent b, in this way
rate 1 = 3.0 * 10^ -3 = k [A1]^a * [B1]^b
rate 2 = 6.0*10^-3 = k [A2]^a * [B2]^b
divide rate / rate 1 => 2 = [B1]^nb/ [B2]^b
[B1] = 0.010 and [B2] = 0.020 =>
6.0 / 3.0 =( 0.020 / 0.010)^b => 2 = 2^b => b = 1
In the same way trials 1 and 3, which were run at constan [B], are used to calculate a
rate 3 / rate 1 = 12 / 3.0 = (1.0)^a / (0.5)^a => 4 = 2^a => 2^2 = 2^a => 2 = a
Now use any of the data to find k
With the second trial: rate = 6*10^-3 m/s = k (0.5)^2 * (0.02) =>
k = 6.0*10^-3 M/s / (0.05 M^3) = 0.12 M^-2 s^-1
With the calcualted values of k, a and b you use the formula of the rate with the concentrations given
rate = k[A]^2*[B] = 0.12 M^-2 s^-1 * (0.50M)^2 * (0.075M) = 0.0045 M/s = 4.5*10^=3 M/s
Answer: 4.5 * 10^-3 M/s