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

The accompanying graph shows the concentration of a reactant as
a function of time for two different reactions. One of the reactions
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?

Key Concepts

Reaction Order

Reaction order determines how the rate of a chemical reaction depends on the reagent concentrations. It is a critical parameter in the rate law which offers insights into the reaction mechanism and overall kinetics of the process.

First Order Kinetics

For a first order reaction, the rate is directly proportional to the concentration of one reactant. The integrated rate law is ln[reactant] = -kt + ln[initial concentration], implying that a plot of the natural log of the reactant concentration versus time will yield a straight line, making it easy to determine the rate constant from the slope.

Second Order Kinetics

In a second order reaction, the rate is proportional either to the square of a single reactant’s concentration or to the product of two reactant concentrations. The integrated rate law for a reaction with respect to a single reactant is 1/[reactant] = kt + 1/[initial concentration]. This means that plotting 1/[reactant] against time produces a straight line, which facilitates the calculation of the rate constant.

Graphical Linearization

Graphical linearization involves transforming experimental data so that the relationship between variables becomes linear, which simplifies analysis and interpretation. For first order reactions, applying a logarithmic transformation (ln[reactant]) makes the plot linear, while for second order reactions, plotting 1/[reactant] versus time accomplishes the same linearization.

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