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Question

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6. The data below were collected for the reaction: B ro; +5 Br-+ H()' 3B, +9H20 Initial Rate, 1,O 0.10 0.10 0.10 0.15 Experiment Bro 0.10 0.20 0.10 0.20 0.10 0.10 0.30 0.10 1.2 2.4 3.6 5.4 a) Determine the rate law for this reaction b) Calculate the value of k for this reaction and express it with the correct units 7. The rate law for the reaction 2NO(g)2NO(g)+O2(g) is rate-k[Nor a) What would the integrated rate law equation look like for this reaction? b) How would a graph of this equation look? c) How would you find the value of k from this graph?

Explanation / Answer

Let the rate law be

R = K[BrO3-]a [Br-]b[ H3O+]c , where K is rate constant

And a, b and c are orders of [BrO3-], [Br-] and [H3O+]respectively.

The purpose of the experiments is to determine value of a, b,c and rate constant.

From 1st experiment

K[ 0.1]a[0.1]b [0.1]c = 1.2    (1)

From 2nd experiment

K[ 0.2]a[0.1]b [0.1]c = 2.4    (2)

Eq.2/ Eq.1 gives (0.2/0.1)a= 2.4/1.2= 2

2a= 2, a =1      

From 3rd experiment

K[ 0.1]a[0.3]b [0.1]c = 3.6   (3)

Eq.3/Eq.1 gives 3b = 3.6/1.2= 3, b=1

From 4th experiment

K[ 0.2]a[0.1]b [0.15]c = 5.4    (4)

Eq.4/Eq.2 gives (0.15/0.1)c= 5.4/2.4= 2.25

Hence 1.5c= 2.25, c= 2

So the rate law becomes

R = K[BrO3-] [Br-][ H3O+]2 , where K is rate constant

From 1st experiment

1.2 = K[ 0.1] [0.1][0.1]2, K=12000/M3.sec

So the rate law becomes R= 12000[BrO3-] [Br-][ H3O+]2

2. rate law -d[NO2]/dt= K[NO2]2, K is rate constant

at t=0, let [NO2] =[NO2]o ( initial concentration) at t=t [NO2] =[NO2] ( concentration at any time, t

-d[NO2]/[NO2]2= Kt

when integrated between t=0 and t= t

1/[NO2] = 1/[NO2]0+ Kt

so a plot of 1/[NO2] vs time gives straight line whose slope is K.