The thermal decomposition of ammonia at high temperatures...

The thermal decomposition of ammonia at high temperatures was studied in the presence of inert gases. Data at $2000 . \mathrm{K}$ are given for a single experiment. $$ \begin{array}{cr} \mathrm{NH}_{3} \longrightarrow & \mathrm{NH}_{2}+\mathrm{H} \\ t \text { (hours) } & {\left[\mathrm{NH}_{3}\right](\mathrm{mol} / \mathrm{L})} \\ \hline 0 & 8.000 \times 10^{-7} \\ 25 & 6.75 \times 10^{-7} \\ 50 & 5.84 \times 10^{-7} \\ 75 & 5.15 \times 10^{-7} \\ \hline \end{array} $$ Plot the appropriate concentration expressions against time to find the order of the reaction. Find the rate constant of the reaction from the slope of the line. Use the given data and the appropriate integrated rate equation to check your answer.

The thermal decomposition of ammonia at high temperatures was studied in the presence of inert gases. Data at $2000 . \mathrm{K}$ are given for a single experiment.
$$ \begin{array}{cr} \mathrm{NH}_{3} \longrightarrow & \mathrm{NH}_{2}+\mathrm{H} \\ t \text { (hours) } & {\left[\mathrm{NH}_{3}\right](\mathrm{mol} / \mathrm{L})} \\ \hline 0 & 8.000 \times 10^{-7} \\ 25 & 6.75 \times 10^{-7} \\ 50 & 5.84 \times 10^{-7} \\ 75 & 5.15 \times 10^{-7} \\ \hline \end{array} $$
Plot the appropriate concentration expressions against time to find the order of the reaction. Find the rate constant of the reaction from the slope of the line. Use the given data and the appropriate integrated rate equation to check your answer.

Key Concepts

Reaction Order

This concept involves determining how the rate of a chemical reaction depends on the concentration of its reactants. By testing different forms of the integrated rate laws—such as plotting concentration, the logarithm of concentration, or the reciprocal of concentration against time—a straight line indicates the correct order. For instance, a linear plot of ln([A]) versus time signifies a first-order reaction, while a linear plot of 1/[A] versus time indicates a second-order reaction.

Integrated Rate Law

Integrated rate laws provide equations that relate the concentration of reactants to time based on the reaction order. They are essential for analyzing kinetic data as they allow one to determine the reaction order by rearranging the rate law into a form that, when plotted, produces a straight line. Each order has its own integrated form, which can be used to extract the rate constant from the slope of the linear plot.

Graphical Analysis

Graphical analysis is a method used to determine the reaction order by plotting concentration data using the integrated rate law frameworks. By converting the concentration data in various ways (e.g., taking the logarithm for first-order or the reciprocal for second-order reactions) and plotting against time, one can visually assess which plot produces a straight line. The linearity of a plot confirms the reaction order and provides a basis for further kinetic analysis.

Rate Constant Determination

After identifying the correct reaction order using the integrated rate law and corresponding plot, the rate constant (k) can be determined from the slope of the linear relationship. The rate constant is a fundamental parameter in chemical kinetics that quantifies the speed of a reaction under given conditions, and its value is derived directly from the slope of the best-fit line in the appropriately linearized graph.

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