Problem 14 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

At \(518{ }^{\circ} \mathrm{C}\), the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 Torr, was \(1.00\) Torr \(\mathrm{s}^{-1}\) when \(5 \%\) had reacted and \(0.5\) Torr \(\mathrm{s}^{-1}\) when \(33 \%\) had reacted. The order of the reaction is : [Main 2018] (a) 2 (b) 3 (c) 1 (d) 0

Step-by-Step Solution

Answer

The reaction order is 2.

Step 1: Understand the Problem

We need to determine the order of reaction of gaseous acetaldehyde based on the rate of decomposition at two different conversion percentages.

Step 2: Define Reaction Order

The order of a reaction determines how the rate is affected by the concentration of the reactant. For a rate law \( r = k [A]^n \), \( n \) is the order.

Step 3: Calculate Initial Reactant Pressures

The initial pressure is 363 Torr. When 5% reacts, the pressure of unreacted acetaldehyde is \( 363 \times 0.95 = 344.85 \) Torr. At 33% reacted, it is \( 363 \times 0.67 = 243.21 \) Torr.

Step 4: Use Rate Law at 5% Reaction

Given the rate of 1.00 Torr/s when 5% reacted, use the rate law: \( r_1 = k [343.85]^n = 1.00 \) Torr/s.

Step 5: Use Rate Law at 33% Reaction

Given the rate of 0.5 Torr/s when 33% reacted, use the rate law: \( r_2 = k [243.21]^n = 0.5 \) Torr/s.

Step 6: Formulate Ratios

By dividing the second rate equation by the first, we get:\[ \frac{r_2}{r_1} = \left( \frac{[243.21]}{[344.85]} \right)^n = \frac{0.5}{1.00} = 0.5 \]

Step 7: Solve for Reaction Order \( n \)

\[ \left( \frac{243.21}{344.85} \right)^n = 0.5 \] Solve for \( n \): Taking logarithms, \( n = \frac{\log(0.5)}{\log(243.21/344.85)} \) = \( 2 \).

Step 8: Conclusion

The reaction order based on the calculations is 2. Thus, the reaction is a second-order reaction.

Key Concepts

Rate of Reaction

The rate of reaction is a fundamental concept in chemistry that describes how fast or slow a chemical process occurs. In this context, it refers to the speed at which acetaldehyde decomposes at a particular temperature and pressure. To understand the rate of reaction, consider that it measures the change in concentration of reactants or products over time. This is often expressed in units like Torr/s, as seen in the exercise.

Key factors influencing reaction rates include:

• Concentration of reactants: Higher concentrations generally increase the rate as more reactant particles are available to collide and react.
• Temperature: An increase typically speeds up reactions because particles have more energy to overcome activation barriers.
• Catalysts: These substances lower the activation energy required, thereby increasing the rate without being consumed in the process.

By calculating how the decomposition rate changes with varying amounts of acetaldehyde, you determine the reaction order, which shows dependence on the reactant's concentration.

Chemical Kinetics

Chemical kinetics is the field of study that examines the rates of chemical processes. It provides insights into the speed of reactions and the step-by-step pathways that reactions follow. When analyzing chemical kinetics, key focus areas include reaction rates, mechanisms, and the factors that influence these aspects.

Understanding the order of a reaction is an essential part of chemical kinetics. The reaction order provides insight into how the rate is influenced by the concentration of reactants. The general rate law is given by \(r = k [A]^n\), where \(r\) is the reaction rate, \(k\) is the rate constant, \([A]\) is the concentration of the reactant, and \(n\) is the reaction order. The rate constant, \(k\), is influenced by factors such as temperature and presence of catalysts but not by concentration changes.

In the presented exercise, it demonstrates how to find the reaction order by comparing reaction rates at different stages of decomposition. By mathematically calculating the changes in rates, students learn to deduce the order, which in turn helps them understand the underlying reaction mechanism.

Gaseous Acetaldehyde Decomposition

Gaseous acetaldehyde decomposition is a specific chemical reaction where acetaldehyde (CH₃CHO) breaks down into simpler substances. This reaction is significant in various industrial and environmental processes. At high temperatures, such as the 518°C mentioned in the exercise, acetaldehyde molecules gain enough energy to dissociate.

In the given scenario, acetaldehyde starts at a pressure of 363 Torr. As the reaction proceeds, a portion of the acetaldehyde reacts, lowering the pressure. For instance, when 5% has reacted, the pressure adjusts to 344.85 Torr, and further decreases to 243.21 Torr when 33% has reacted. Observing these pressure changes provides valuable data on how quickly the decomposition happens under certain conditions, leading us to determine the reaction order as second order.

This example not only underscores the practical implications of chemical kinetics and reaction order determination but also enhances understanding of gaseous reactions. Learning how to calculate such changes is crucial for students focusing on physical chemistry and industrial applications of chemical reactions.