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A second-order reaction is one where the rate depends on the concentration of
the species to the second power. For a general unimolecular reaction,
- A -> products
the reaction rate expression for a second order
reaction is
- rate = k[A]0 = k[A]2
The
integrated
rate law for a 2nd order reaction can be easily
shown to be
- 1/[A] - 1/[A]0 = kt
Example: Butadiene dimerizes to form C8H12. This
reaction is 2nd order in butadiene. If the rate constant for the reaction is
0.84 L/mol min, how long will it take for a 0.500 M sample of butadiene to
dimerize until the butadiene concentration is 0.200 M?
Solution: Use the integrated rate law above
- 1/[C4H6] -
1/[C4H6]0 = kt
The intial
concentration is 0.500 M, and the final concentration is 0.200 M. K is 0.84
L/mol min, so
- 1/0.200 mol/L - 1/0.500 mol/L = 0.84 L/mol min * t
-
- t = 3.6 minutes
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