Question

KINETICS AND EQUILIBRIUM Deducing a rate law from initial reaction rate data Some measurements of the initial rate of a certain reaction are given in the table below. initia ate of reaction .15 M 0.37 20x101 M/s 0.15 M10045 MI 2.4-103 M/S 33x105 M/s 0.66 Ml 0.37 M I Use this information to write a rate law for this reaction, and calculate the value of the rate constant k. Be sure your value for the rate constant has the correct number of significant digits. Also be sure your answer has the correct unit symbol. rate-

Answer 1

ANSWER

Three initial rate s are given, lets label them as Rate 1 Rate 2 and Rate 3

Rate 1 = 2 X 10⁴ M/s = k [N₂]ⁿ[H₂]^m

n and m are orders w.r.t Nitrogen and hydrogen respectively .

2 X 10⁴ M/s = k [0.15]ⁿ[0.37]^m =======1)

Similarly

Rate 3 = 3.9 X 10⁵ M/s = k [0.66]ⁿ[0.37]^m =========2)

divide (2) by (1)

3.9 X 10⁵ M/s / 2 X 10⁴ M/s = k [0.66]ⁿ[0.37]^m / k [0.15]ⁿ[0.37]^m

19.5 = [0.66 / 0.15]ⁿ = [4.4]ⁿ

It implies n = 2

Hence order w.r.t. N₂ is 2

Again

Rate 2 = 2.4 X 10³ M/s = k [0.15]ⁿ[0.045]^m =======3)

Divide (1) by (3)

2 X 10⁴ M/s / 2.4 X 10³ M/s = k [0.15]ⁿ[0.37]^m / k [0.15]ⁿ[0.045]^m

8.3 = [0.37 / 0.045]^m = [8.3]^m

It implies m = 1

Hence order w.r.t H₂ is 1So the rate equation is

Rate =  k [N₂]² [H₂]¹

Rate constant:

Consider rate 1

2 X 10⁴ M/s = k [0.15]²[0.37]¹

K =  2 X 10⁴ M/s / [0.15]²[0.37]¹ = 2.4 X 10⁶ L³ M^-2 s^-1