Problem 1 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Azomethane, \(\mathrm{CH}_{3} \mathrm{NNCH}_{3}\), decomposes according to the following equation: \(\mathrm{CH}_{3}-\mathrm{N} \equiv \mathrm{N}-\mathrm{CH}_{3}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})+\mathrm{N}_{2}(\mathrm{~g})\) The initial concentration of azomethane was \(1.50 \times 10^{-2}\) M. After 10 min, the concentration decreased to \(1.29 \times 10^{-2} \mathrm{M}\). The average rate of reaction during this time interval is (a) \(3.5 \times 10^{-6} \mathrm{Ms}^{-1}\) (b) \(2.1 \times 10^{-4} \mathrm{Ms}^{-1}\) (c) \(3.5 \times 10^{-6} \mathrm{M} \mathrm{h}^{-1}\) (d) \(2.1 \times 10^{-3} \mathrm{Mmin}^{-1}\)

Step-by-Step Solution

Answer

The average rate of reaction is (2.1 × 10^-3 M/min), therefore the correct answer is (d) 2.1 × 10^-3 Mmin^-1.

Step 1 - Identify Given Information

From the reaction equation and given data, identify the initial concentration of azomethane as 1.50 × 10^-2 M. Also note the decreased concentration after 10 minutes which is 1.29 × 10^-2 M. The time taken for this concentration change is 10 minutes.

Step 2 - Calculate Change in Concentration

Find the change in concentration of azomethane by subtracting the final concentration from the initial concentration: Change in concentration = (Initial concentration) - (Final concentration) = (1.50 × 10^-2 M) - (1.29 × 10^-2 M).

Step 3 - Convert Time to Appropriate Units

Since the rates are given in seconds, minutes, and hours, convert 10 minutes into seconds for (a) and (b), and leave it as minutes for (d). 10 minutes is equal to 600 seconds.

Step 4 - Calculate the Average Rate of Reaction

Use the formula for average rate of reaction: Average rate = Change in concentration / Change in time. Use the calculated concentration change and time in seconds or minutes, depending on the option unit, to calculate the average rate for each unit.

Step 5 - Choose the Correct Option

Compute the average rate for each unit and compare with the given options to determine the correct answer.

Key Concepts

Chemical Kinetics

Chemical kinetics is a branch of chemistry that studies the rates at which chemical reactions occur and the factors that affect these rates. It's all about understanding how quickly reactants are converted into products under various conditions. A fundamental concept in chemical kinetics is the reaction rate, which indicates the speed of a chemical reaction.

Reaction rates can be affected by several factors, including the concentration of reactants, temperature, catalysts, and the surface area of reactants. For instance, an increase in the concentration of the reactants generally leads to an increase in the reaction rate because there are more molecules available to collide and react with each other. Similarly, higher temperatures can increase the rate of a reaction by providing the energy needed to overcome the activation energy barrier, leading to more frequent and effective collisions between molecules.

In the context of azomethane decomposition, understanding how the concentration of azomethane changes over time is crucial in determining the reaction rate and therefore analyzing the kinetics of the reaction.

Reaction Rate Calculation

To calculate the reaction rate, you should understand that it measures the speed at which the reactants convert to products over time. It's expressed in terms of change in concentration of a reactant or product per unit time. In our case study of azomethane, we're specifically focused on the disappearance of azomethane, a reactant.

The general formula for average rate of reaction is:
\[ \text{Average rate} = \frac{\text{Change in concentration}}{\text{Change in time}} \]

Let's break this down:

• Change in concentration is the difference in the molar concentration of the reactant over the observed time period.
• Change in time is the time interval during which the concentration change occurred.

In order to calculate the average rate correctly, it's important to use consistent units for concentration and time. If your final rate needs to be in \(\text{M s}^{-1}\), make sure to convert the time to seconds; for \(\text{M min}^{-1}\), use minutes. This detail is important to arrive at an accurate measure of the reaction rate that makes sense for the context in which the problem is presented.

Azomethane Decomposition

Azomethane, \(\mathrm{CH}_3 \mathrm{NNCH}_3\), decomposes into ethane, \(\mathrm{C}_2 \mathrm{H}_6\), and nitrogen gas, \(\mathrm{N}_2\), in a process that's interesting to study from a kinetics standpoint. The decomposition reaction provides a great opportunity to apply the principles of chemical kinetics and reaction rate calculations.

When solving problems involving azomethane decomposition, it's important to take accurate note of the initial and final concentrations of azomethane, as these are essential for computing the average rate of reaction. In the given exercise, the initial concentration of azomethane was \(1.50 \times 10^{-2}\) M, and after 10 minutes decreased to \(1.29 \times 10^{-2}\) M. By applying the formula for reaction rate calculation, these concentrations, along with the time elapsed, allow us to calculate the average rate of reaction during this interval.

Understanding the steps of the reaction, including the stoichiometry, can also be critical for more complex kinetics problems where the rate law must be determined or when assessing mechanisms. Therefore, a clear, thorough interpretation of experimental data, such as concentration changes over time, is fundamental in the analysis of azomethane decomposition.