Determine The Order of A Reaction-First Order or Second Order and Calculate Its Rate Constant

May 30th, 2008

If we have a problem that we must determine the rate law of the reaction and we just given by a particular data, the easy step to solve the problem is by taking a plot of ln[reactant] versus time and 1/[reactant] versus time too. If we have a straight line between one of the two of the plots, thus the plot with the straight line is determined the order of the reaction. If the straight line is the plot which ln[reactant] versus time thus the reaction is first order, and the reverse is the second order. Take a look to the sample below:

A student has studied the decomposition of hydrogen peroxide, and he obtained the following data at a given temperature

[H2O2] M	Time (s)
1.00	0
0.91	120
0.78	300
0.59	600
0.37	1200
0.22	1800
0.13	2400
0.082	3000
0.050	3600

Is this reaction first order or second order?
Determine the rate law and the integrated law
What is the value of the rate constant for the reaction
What is the half-life for the reaction under the condition of the experiment

To find whether the rate law of this reaction is fisrt order or second order, we should have to make a plot of ln[H2O2] versus time and 1/[H2O2] versus time. If the first graph is a straight line thus the reaction should be fisrt order. If the second graph is a straight line thus the reaction is second order. The data necessary to make these plots are as follows:

Time (s)	1/[H2O2]	ln [H2O2]
0	1	0
120	1.094	-0.094
300	1.282	-0.248
600	1.695	-0.528
1200	2.703	-0.994
1800	4.545	-1.514
2400	7.692	-2.040
3000	12.195	-2.501
3600	20	-2.995

the resulting plots are shown in the figures below:

first order plot

second order reaction formula

from the figures above we know that ln[H2O2] versus time is a straight line but 1/[H2O2] versus time is not a straight line. Thus the decomposition of H2O2 is a fisrt order reaction and we can write the rate law as:

rate = k[H2O2]

and the integrated rate law as

ln[H2O2] = -kt + ln[H2O2]o

Since the reaction is first order, the slope of the line equals -k where

slope = Change in y / cahnge in x
slope = -2.995 - (-2.501) / (3600-3000)
slope = -8.233×10^-4 s^-

k = -(slope) = 8.233×10^-4 s^-

The half life of the fisrt order reaction difined as

half life first order formula