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## Q. 13.5

The Second-Order Integrated Rate Law: using Graphical analysis of Reaction Data
Consider the equation for the decomposition of NO$_{2}$.
NO$_{2}$(g) → NO(g) + O(g)
The concentration of NO$_{2}$ is monitored at a fixed temperature as a function of time dur-ing the decomposition reaction, and the data are tabulated in the margin. Show by graphical analysis that the reaction is not first order and that it is second order. Determine the rate constant for the reaction

## Verified Solution

To show that the reaction is not first order, prepare a graph of ln [NO$_{2}$] versus time.
The plot is not linear (the straight line does not fit the data points), confirm-ing that the reaction is not first order. In order to show that the reaction is second order, prepare a graph of 1/[NO$_{2}$] versus time.
This graph is linear (the data points fit well to a straight line), confirming that the reaction is indeed second order. To obtain the rate constant, determine the slope of the best fitting line. The slope is 0.255 M$^{-1} . s^{-1}$; therefore, the rate constant is 0.255 M$^{-1} . s^{-1}$.