The isomerization of methyl isonitrile (CH 3 NC ) to acetonitrile (CH3 CN) was studied in the ga

step 1 this problem is making a graph i'm just going to show you like an example so on x -axis you have

The isomerization of methyl isonitrile (CH 3 NC ) to...

The isomerization of methyl isonitrile (CH $_{3} \mathrm{NC}$ ) to acetonitrile $\left(\mathrm{CH}_{3} \mathrm{CN}\right)$ was studied in the gas phase at $215^{\circ} \mathrm{C}$, and the following data were obtained: \begin{tabular}{ll} \hline Time (s) & {$\left[\mathrm{CH}_{3} \mathrm{NCl}(M)\right.$} \\ \hline 0 & $0.0165$ \\ 2,000 & $0.0110$ \\ 5,000 & $0.00591$ \\ 8,000 & $0.00314$ \\ 12,000 & $0.00137$ \\ 15,000 & $0.00074$ \\ \hline \end{tabular} (a) Calculate the average rate of reaction, in $M / \mathrm{s}$, for the time interval between each measurement. (b) Graph $\left[\mathrm{CH}_{3} \mathrm{NC}\right]$ versus time, and determine the instantaneous rates in $M / \mathrm{s}$ at $t=5000 \mathrm{~s}$ and $t=8000 \mathrm{~s}$.

The isomerization of methyl isonitrile (CH $_{3} \mathrm{NC}$ ) to acetonitrile $\left(\mathrm{CH}_{3} \mathrm{CN}\right)$ was studied in the gas phase at $215^{\circ} \mathrm{C}$, and the following data were obtained:
\begin{tabular}{ll}
\hline Time (s) & {$\left[\mathrm{CH}_{3} \mathrm{NCl}(M)\right.$} \\
\hline 0 & $0.0165$ \\
2,000 & $0.0110$ \\
5,000 & $0.00591$ \\
8,000 & $0.00314$ \\
12,000 & $0.00137$ \\
15,000 & $0.00074$ \\
\hline
\end{tabular}
(a) Calculate the average rate of reaction, in $M / \mathrm{s}$, for the time interval between each measurement. (b) Graph $\left[\mathrm{CH}_{3} \mathrm{NC}\right]$ versus time, and determine the instantaneous rates in $M / \mathrm{s}$ at $t=5000 \mathrm{~s}$ and $t=8000 \mathrm{~s}$.

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Key Concepts

Graphical Analysis of Kinetic Data

Graphical analysis involves plotting concentration versus time to visualize how the concentration changes during the reaction. This graph is an essential tool in kinetics because the slope of the curve at any point represents the instantaneous reaction rate. It facilitates the identification of reaction regimes and the application of numerical differentiation techniques when finer details of the rate behavior are required.

Instantaneous Reaction Rate

The instantaneous rate is the speed of the reaction at a specific moment in time. It is conceptually the derivative of the concentration with respect to time at that instant. Since experimental data are often collected at discrete intervals, numerical methods such as taking the slope of a tangent line or using neighboring data points are applied to estimate this rate.

Average Reaction Rate

This concept refers to the overall change in concentration of a reactant or product divided by the total elapsed time over a finite interval. It is calculated by finding the difference in concentration at the beginning and the end of the time period and then dividing by the length of the interval. This method provides an approximation of the reaction's speed over that interval and is useful when data is sampled at discrete time points.

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