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914 Chapter 17 | Kinetics
In order to determine the slope of the line, we need two values of ln[H2O2] at different values of t (one near each end of the line is preferable). For example, the value of ln[H2O2] when t is 6.00 h is −0.693; the value when t = 12.00 h is −1.386:
Check Your Learning
Graph the following data to determine whether the reaction is first order.
Trial
Time (s)
[A]
1
4.0
0.220
2
8.0
0.144
3
12.0
0.110
4
16.0
0.088
5
20.0
0.074
Answer: The plot of ln[A] vs. t is not a straight line. The equation is not first order:
Second-Order Reactions
The equations that relate the concentrations of reactants and the rate constant of second-order reactions are fairly complicated. We will limit ourselves to the simplest second-order reactions, namely, those with rates that are dependent upon just one reactant’s concentration and described by the differential rate law:
For these second-order reactions, the integrated rate law is:
where the terms in the equation have their usual meanings as defined earlier.
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