Question

The isomerization of methyl isonitrile \(\left(\mathrm{CH}_{3} \mathrm{NC}\right)\) 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: $$ \begin{array}{ll} \hline \text { Time (s) } & \text { [CH }_{3} \text { NC] (M) } \\ \hline 0 & 0.0165 \\ 2,000 & 0.0110 \\ 5,000 & 0.00591 \\ 8,000 & 0.00314 \\ 12,000 & 0.00137 \\ 15,000 & 0.00074 \\ \hline \end{array} $$ (a) Calculate theaverage 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 \(\mathrm{M} / \mathrm{s}\) at \(t=5000 \mathrm{~s}\) and \(t=8000 \mathrm{~s}\).

Short answer

The average rates of reaction for each time interval are as follows: \\ (1) \(2.75\times10^{-6} M/s\) \\ (2) \(2.03\times10^{-6} M/s\) \\ (3) \(1.59\times10^{-6} M/s\) \\ (4) \(1.16\times10^{-6} M/s\) \\ (5) \(1.26\times10^{-6} M/s\). For part (b), after graphing the function and calculating the slope of the tangent lines, the instantaneous rates at t=5000 s and t=8000 s are approximately \(1.77\times10^{-6} M/s\) and \(1.35\times10^{-6} M/s\), respectively.

Step-by-step solution

Calculate the concentration difference in each interval

In order to calculate the average rate of reaction, first calculate the concentration difference of CH3NC during each time interval. Subtract the initial concentration from the final concentration.

Calculate the time difference in each interval

To determine the average rate, divide the concentration difference calculated in step 1 by the time difference in seconds between the initial and final times of each interval.

Calculate the average rate of reaction

The average rate of reaction in \(M/s\) for each time interval can be calculated by dividing the concentration difference calculated in step 1 by the time difference calculated in step 2. #Part (b): Graph [CH3NC] versus time and determine the instantaneous rates in M/s at \(t=5000\) s and \(t=8000\) s#

Create a graph

Plot [CH3NC] represented on the y-axis against time in seconds represented on the x-axis with the given data.

Draw a tangent line to the curve

At t=5000 s and t=8000 s, draw a tangent line to the curve. This line describes the instantaneous rate of the reaction at that specific time.

Determine the slope of the tangent line

Calculate the slope of the tangent lines drawn in step 2. This can be done using the method of selecting two points on the line and calculating the difference in y divided by the difference in x. The slope of the tangent line is equal to the instantaneous rate of the reaction at the specified time.

Calculate the instantaneous rates at t=5000 s and t=8000 s

The instantaneous rates at t=5000 s and t=8000 s are equal to the slope of the tangent lines drawn in step 2. The results obtained are the desired instantaneous rates in \(M/s\).

Key concepts

Isomerization

Isomerization is a fascinating process where a molecule rearranges its structure to form a different isomer. This transformation often involves a structural reorganization but does not change the molecular formula. During isomerization, the atoms within the molecule move around to form a different arrangement, leading to a change in the molecule's properties.
In the case of methyl isonitrile, the isomerization process involves changing the linkage of the carbon and nitrogen atoms. The atoms undergo a reconfiguration to form acetonitrile. This process is significant in chemistry because it can alter the molecule's reactivity, stability, and interaction with other substances.
Isomerization reactions like this often require specific conditions, such as heat or catalysts, to proceed. Understanding the mechanism and conditions of isomerization helps in predicting and controlling the pathways of chemical reactions.

Average Rate of Reaction

The average rate of reaction gives us an idea of how fast or slow a reaction occurs over a specified time period. It is defined as the change in concentration of a reactant or product divided by the time interval over which the change occurs.
To calculate the average rate of reaction, you first need to determine the change in concentration of a substance. In the methyl isonitrile case, we look at how its concentration decreases over specified time intervals.

• Subtract the initial concentration from the final concentration for each time interval.
• Divide this concentration change by the time period during which the change occurred.

By calculating these rates for different intervals, we can compare the rates and understand how the reaction progresses over time.

Instantaneous Rate of Reaction

The instantaneous rate of reaction is a snapshot of the reaction rate at a specific moment in time. Unlike the average rate, which considers the entire time interval, the instantaneous rate is much more precise.
To find this rate, we typically use a graph of concentration versus time. When you draw a tangent line to the curve at the specific time of interest, the slope of this line represents the instantaneous rate.

• At any point on the concentration-time graph, observe the steepness of the curve. This steepness is the slope.
• The slope calculation is done by picking two points on the tangent line, intersecting at the point of interest.
• Calculate the slope by taking the difference in concentration (y-values) divided by the difference in time (x-values).

This technique provides a precise measurement of how quickly the reactants are converting into products at a specific time.

Methyl Isonitrile

Methyl isonitrile, with the chemical formula CH₃NC, is an organic molecule known for its ability to undergo isomerization. It has a unique structure where the nitrogen atom is connected to the carbon through a triple bond.
This compound is reactive and tends to reorganize into acetonitrile, particularly under increased temperature conditions. In the gas phase and at elevated temperatures, methyl isonitrile is prone to convert to its isomer, acetonitrile, as the heat provides the energy required to overcome the activation barrier for isomerization.
Studying methyl isonitrile helps chemists understand the behavior of functional groups and the dynamics of chemical reactions involving nitrile groups. This knowledge is useful in various chemical synthesis processes and industrial applications.

Acetonitrile

Acetonitrile, also represented as CH₃CN, is the product formed from the isomerization of methyl isonitrile. It is a simple organic nitrile with a carbon-nitrogen triple bond but differs in the connectivity when compared to methyl isonitrile.
Acetonitrile is widely used in laboratories and industries due to its excellent solvency and ability to dissolve a wide range of compounds. It is particularly prevalent in the pharmaceutical and chromatography industries as a polar aprotic solvent.
Understanding how methyl isonitrile converts into acetonitrile is crucial. This conversion process highlights how minor structural changes can significantly alter the molecule's physical and chemical properties, impacting its utility and interactions in practical applications.