The accompanying graph shows the concentration of a reactant...

Name: Problem 121, Chapter 15: Chemistry A Molecular Approach
Uploaded: 2021-06-23T13:55:50-08:00
Duration: 1 min 6 s
Channel: David Collins
Description: The accompanying graph shows the concentration of a reactant as a function of time for two different reactions. One of the re- actions is first order, and the other is second order. Which of the two reactions is first order? Second order? How would you change each plot to make it linear?

The accompanying graph shows the concentration of a reactant as a function of time for two different reactions. One of the re- actions is first order, and the other is second order. Which of the two reactions is first order? Second order? How would you change each plot to make it linear?

The accompanying graph shows the concentration of a reactant as a function of time for two different reactions. One of the re-
actions is first order, and the other is second order. Which of the two reactions is first order? Second order? How would you
change each plot to make it linear?

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Key Concepts

First-Order Kinetics

This concept describes reactions where the rate is directly proportional to the concentration of a single reactant. The integrated rate law for a first-order reaction is ln[A] = -kt + ln[A?], which means that a plot of the natural logarithm of the reactant concentration versus time will yield a straight line with a slope of -k, the reaction’s rate constant.

Second-Order Kinetics

In second-order kinetics, the reaction rate is proportional to either the square of the concentration of one reactant or the product of the concentrations of two reactants. The integrated rate law for such reactions is 1/[A] = kt + 1/[A?]. This indicates that plotting the inverse of reactant concentration against time produces a straight line, with the slope corresponding to the rate constant.

Graphical Linearization

Graphical linearization is a method used to transform the nonlinear behavior of reaction data into a linear form, which makes it easier to determine key kinetic parameters like the rate constant and reaction order. For first-order reactions, linearization is achieved by plotting ln[A] versus time, while for second-order reactions it is done by plotting 1/[A] versus time.

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