Question

Determine the rate law (be sure to include the value for k) for the following reaction using the data provided.

NO2(g)+O3(g)->NO3(g)+O2(g)

[NO2] (M) [O3]i (M) initial rate

0.10 0.33 0.0223

0.10 0.66 0.01788

0.25 0.66 1.112

Please help with reasoning on how to find the order of the reactions when they are not first or 0 order and how to find k. Thank you!

Answer 1

Given reaction is : NO₂(g)+O₃(g)->NO₃(g)+O₂(g)

Let the rate law be , r = k[NO₂]^m [O₃]ⁿ ----(1)

Where k = rate constant

r = rate of the reaction

m , n = orders of the reaction with respect to NO₂ &O₃ respectively

Let us apply the above tabulated values to Equation (1) we get

1st values ===> 0.0223 = k[0.10]^m [0.33]ⁿ ----(2)

2nd values ===> 0.0223 = k[0.10]^m [0.66]ⁿ ----(3)

3rd values ===> 1.112 = k[0.25]^m [0.66]ⁿ ----(4)

(4)/(3) gives 49.86 = 2.5^m

log 49.86 = m log2.5

m = 4.3

(3) / (2) gives 1 = 2ⁿ

---> n = 0

So rate law is r = k[NO₂]^4.3[O₃]⁰   

OR r = k[NO₂]^4.3