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Oxidized buckminsterfullerene absorbance during thermal decomposition at 23°c
time (minutes) C 60 O 3 absorbance
3 0.04241
9 0.03634
15 0.03121
21 0.02680
27 0.02311
33 0.01992
39 0.01721
45 0.01484
51 0.01286
57 0.01106
63 0.00955
69 0.00827
75 0.00710
81 0.00616
87 0.00534
93 0.00461
99 0.00395

Oxidized buckminsterfullerene absorbance

The rate at which the decomposition reaction is occurring is clearly related to the rate of change of theconcentration [ C 60 O 3 ] , which is proportional to the slope of the graph in . Therefore, we define the rate of this reaction as

Rate t [ C 60 O 3 ] Δ [ C 60 O 3 ] Δ t
We want the rate of reaction to be positive, since the reaction is proceeding forward. However, because we aremeasuring the rate of disappearance of the reactant in this case, that rate is negative. We include a negative sign in thisdefinition of rate so that the rate in is a positive number. Note also that the slope of the graph in should be taken as the derivative of the graph, since the graph is not a straight line. We will approximate that derivative byestimating the slope at each time in the data, taking the change in the absorbance of the C 60 O 3 divided by the change in time at each time step. The rate, calculated in this way, is plotted as a function of time in .

Rate of decomposition

It is clear that the slope of the graph in changes over the course of time. Correspondingly, shows that the rate of the reaction decreases as the reaction proceeds. The reaction is at first very fast but then slowsconsiderably as the reactant C 60 O 3 is depleted.

The shape of the graph for rate versus time ( ) is very similar to the shape of the graph for concentration versus time ( ). This suggests that the rate of the reaction is related to the concentration of C 60 O 3 at each time. Therefore, in , we plot the rate of the reaction, defined in and shown in , versus the absorbance of the C 60 O 3 .

Rate versus concentration

We find that there is a very simple proportional relationship between the rate of the reaction and theconcentration of the reactant. Therefore, we can write

Rate t [ C 60 O 3 ] k [ C 60 O 3 ]
where k is a proportionality constant. This equation shows that, early in thereaction when [ C 60 O 3 ] is large, the reaction proceeds rapidly, and that as C 60 O 3 is consumed, the reaction slows down. is an example of a rate law , expressing the relationship between the rate of a reaction and the concentrations of the reactant or reactants.Rate laws are expressions of the relationship between experimentally observed rates and concentrations.

As a second example of a reaction rate, we consider the dimerization reaction of butadiene gas, C H 2 = C H - C H = C H 2 . Two butadiene molecules can combine to form vinylcyclohexene, shownin .

Dimerization of butadiene to vinylcyclohexene

provides experimental data on the gas phase concentration of butadiene [ C 4 H 6 ] as a function of time at T 250 ° C .

Dimerization of butadiene at 250°c
Time (s) [ C 4 H 6 ] (M) Rate (M/s) Rate [ C 4 H 6 ] Rate [ C 4 H 6 ] 2
0 0.0917 9.48 -6 1.03 -4 1.13 -3
500 0.0870 8.55 -6 9.84 -5 1.13 -3
1000 0.0827 7.75 -6 9.37 -5 1.13 -3
1500 0.0788 7.05 -6 8.95 -5 1.14 -3
2000 0.0753 6.45 -6 8.57 -5 1.14 -3
2500 0.0720 5.92 -6 8.22 -5 1.14 -3
3000 0.0691 5.45 -6 7.90 -5 1.14 -3
3500 0.0664 5.04 -6 7.60 -5 1.14 -3
4000 0.0638 4.67 -6 7.32 -5 1.15 -3

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Source:  OpenStax, Concept development studies in chemistry. OpenStax CNX. Dec 06, 2007 Download for free at http://cnx.org/content/col10264/1.5
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