0.16 Reaction rates (Page 2/9)

Concept development studies in Page 2 / 9

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

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 [link] . Therefore, we define the rate of this reaction as

Rate t [C_{60} O_{3}] Δ [C_{60} O_{3}] Δ t

[link] is a positive number. Note also that the slope of the graph in [link] 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 theC 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 [link] .

It is clear that the slope of the graph in [link] changes over the course of time. Correspondingly, [link] 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 ( [link] ) is very similar to the shape of the graph for concentration versus time ( [link] ). This suggests that the rate of the reaction is related to the concentration ofC ₆₀ O ₃ at each time. Therefore, in [link] , we plot the rate of the reaction, defined in [link] and shown in [link] , versus the absorbance of theC ₆₀ O ₃ .

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 asC ₆₀ O ₃ is consumed, the reaction slows down. [link] 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,CH ₂ =CH-CH=CH ₂ . Two butadiene molecules can combine to form vinylcyclohexene, shownin [link] .

[link] 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	$4.67 -6$	$7.32 -5$	$1.15 -3$

We can estimate the rate of reaction at each time step as in [link] , and these data are presented in [link] as well. Again we see that the rate of reaction decreases as theconcentration of butadiene decreases. This suggests that the rate is given by an expression like [link] . To test this, we calculate $Rate [C_{4} H_{6}]$ in [link] for each time step. We note that this is not a constant, so [link] does not describe the relationship between the rate of reaction and the concentration of butadiene.Instead we calculate $Rate [C_{4} H_{6}] 2$ in [link] . We discover that this ratio is a constant throughout the reaction. Therefore, therelationship between the rate of the reaction and the concentration of the reactant in this case is given by

Rate t [C_{4} H_{6}] k [C_{4} H_{6}] 2

which is the rate law for the reaction in [link] . This is a very interesting result when compared to [link] . In both cases, the results demonstrate that the rate of reactiondepends on the concentration of the reactant. However, we now also know that the way in which the rate varies with the concentrationdepends on what the reaction is. Each reaction has its own rate law, observed experimentally.

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Source: OpenStax, Concept development studies in chemistry 2012. OpenStax CNX. Aug 16, 2012 Download for free at http://legacy.cnx.org/content/col11444/1.4

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0.16 Reaction rates (Page 2/9)

Oxidized buckminsterfullerene absorbance

Rate of decomposition

Rate versus concentration

Dimerization of butadiene to vinylcyclohexene

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