Calculate the initial rate for the formation of C at 25 ∘C, if [A]=0.50M and [B]=0.075M.

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