Question

Suppose you want to determine the rate law that governs the kinetics of the reaction A+Bà products, carried out in the presence of catalyst C. you perform measurements of initial reaction velocities on four different mixtures of starting materials and obtain the following results:

Expt. #    [A]₀    [B]₀    [C]₀    v₀

1              0.4    0.3      0.6      0.6

2              1.2      0.3      0.6      1.79   

3              0.4      0.3      1.8      5.41

4              1.2      0.9      0.6      1.79

where the initial concentrations are expressed mold m^-3, the initial reaction velocities are expressed in mol dm^-3s^-1 and the v₀ data was obtained at 298K. Use these results to determine the differential rate law for the kinetics of the reaction and also evaluate the relevant rate constant.

Answer 1

A   +   B      Product

Suppose the rate law is expressed as

r = k [A]ⁿ [B]^m

Considering expt. 1 and 2; Keeping the concentration [B]₀ same and increasing the concentration of [A]₀ by three times, the rate (v₀) increases by 3 times.

So, the rate law is expressed as

3r = k [3A]ⁿ [B]^m

3r = 3ⁿ k [A]ⁿ [B]^m

3 = 3ⁿ

So, n = 1

Considering expt. 2 and 4; Keeping the concentration [A]₀ same and increasing the concentration of [A]₀ by three times, the rate (v₀) remains same.

So, the rate law is expressed as

r = k [A]ⁿ [3B]^m

r = 3^m k [A]ⁿ [B]^m

1 = 3^m

So, m = 0

Hence, the rate law is

r = k [A]¹ [B]⁰

r = k [A]¹

Now, considering the values in experiment 1 and substituing the values in rate law, we get;

0.6 mol dm^-3 s^-1 = k (0.4 mol dm^-3)¹

0.6 mol dm^-3 s^-1 = k (0.4 mol dm^-3)

k = 0.6 s^-1 / (0.4)

k = 1.5 s^-1