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It is sometimes helpful to use a more explicit algebraic method, often referred to as the method of initial rates , to determine the orders in rate laws. To use this method, we select two sets of rate data that differ in the concentration of only one reactant and set up a ratio of the two rates and the two rate laws. After canceling terms that are equal, we are left with an equation that contains only one unknown, the coefficient of the concentration that varies. We then solve this equation for the coefficient.
This reaction has been studied in the laboratory, and the following rate data were determined at 25 °C.
Trial | [NO] (mol/L) | [O 3 ] (mol/L) | |
---|---|---|---|
1 | 1.00 10 −6 | 3.00 10 −6 | 6.60 10 −5 |
2 | 1.00 10 −6 | 6.00 10 −6 | 1.32 10 −4 |
3 | 1.00 10 −6 | 9.00 10 −6 | 1.98 10 −4 |
4 | 2.00 10 −6 | 9.00 10 −6 | 3.96 10 −4 |
5 | 3.00 10 −6 | 9.00 10 −6 | 5.94 10 −4 |
Determine the rate law and the rate constant for the reaction at 25 °C.
We can determine the values of m , n , and k from the experimental data using the following three-part process:
Determine the value of m from the data in which [NO] varies and [O 3 ] is constant. In the last three experiments, [NO] varies while [O 3 ] remains constant. When [NO]doubles from trial 3 to 4, the rate doubles, and when [NO] triples from trial 3 to 5, the rate also triples. Thus, the rate is also directly proportional to [NO], and m in the rate law is equal to 1.
Determine the value of n
from data in which [O
3 ] varies and [NO]is constant. In the first three experiments, [NO] is constant and [O
3 ] varies. The reaction rate changes in direct proportion to the change in [O
3 ]. When [O
3 ] doubles from trial 1 to 2, the rate doubles; when [O
3 ] triples from trial 1 to 3, the rate increases also triples. Thus, the rate is directly proportional to [O
3 ], and
n is equal to 1.The rate law is thus:
Determine the value of k
from one set of concentrations and the corresponding rate .
The large value of k tells us that this is a fast reaction that could play an important role in ozone depletion if [NO] is large enough.
Determine the rate law and the rate constant for the reaction from the following experimental data:
Trial | [CH 3 CHO] (mol/L) | |
---|---|---|
1 | 1.75 10 −3 | 2.06 10 −11 |
2 | 3.50 10 −3 | 8.24 10 −11 |
3 | 7.00 10 −3 | 3.30 10 −10 |
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