Question

The following data are obtained from the decomposition of a gaseous compound Initial pressure in arm \(\quad 1.6 \quad 0.8 \quad 0.4\) Time for \(50 \%\) reaction in min \(80 \quad 113 \quad 160\) The order of the reaction is (a) \(0.5\) (b) \(1.0\) (c) \(1.5\) (d) \(2.0\)

Short answer

The reaction is second-order, option (d) 2.0.

Step-by-step solution

Understand the Problem

You have pressure and time data for the decomposition of a gas and need to determine the reaction order. Given is the initial pressure and the time to reach 50% reaction completion. The options for order are 0.5, 1.0, 1.5, and 2.0.

Understand Reaction Order Dependence

In kinetics, the reaction order affects how changes in concentration affect reaction rates. Use the formula for half-life for different reaction orders to relate given quantities.

Use Half-Life Formulas

For different reaction orders, half-life is dependent on concentration. For example, for zero-order, half-life is directly proportional to the initial concentration; for first-order, half-life is constant; for second-order, half-life is inversely proportional to the initial concentration.

Simplify Given Data Using Formulas

Given: Initial pressure data is similar to concentration data and time for 50% completion corresponds to half-life. Compare given data against expected patterns: - Check if half-life remains constant for different initial pressures (a sign of first-order reaction). - Check if half-life doubles for a halving of initial pressure (a sign of second-order reaction).

Analyze the Trends

Examine the pattern: - Pressure 1.6 gives 80 min, pressure 0.8 gives 113 min, and pressure 0.4 gives 160 min. - If time increased proportionally to pressure changes directly or inverse quadratic, this finding helps find order.

Conclude Based on Data Analysis

For the first-order reaction, half-life remains the same across changing initial concentrations, which is not the case here. For the second-order reaction, half-life should double when initial pressure is halved, closely matching the pattern presented.

Key concepts

Reaction Order

In chemical kinetics, understanding the concept of reaction order is crucial for predicting how changes in concentration affect the reaction rate. The reaction order is a classification that represents how the rate of a reaction depends on the concentration of reactants.
Understanding this can help us determine how a reaction proceeds over time. Reaction order can be an integer, zero, fractional, or even negative, reflecting complex interactions between molecules.

• A **zero-order** reaction means the rate is independent of the concentration of the reactants. Here, the reaction progresses linearly with time.
• A **first-order** reaction implies the rate is directly proportional to the concentration of one reactant.
• In a **second-order** reaction, the rate depends on the square of the concentration of one reactant or the product of the concentrations of two reactants.
• Fractional orders, like **1.5**, indicate complex or multi-step reaction mechanisms.

Grasping reaction order is essential as it helps in determining the kinetics, predicting how much time a reaction needs to go to completion, and scaling up reactions in industrial processes.

Half-Life

Half-life is a fascinating concept in chemical kinetics. It refers to the time required for half of the reactant to be consumed in a reaction. This measure helps us understand reaction dynamics and is particularly useful for analyzing unstable compounds.
The half-life (\( t_{1/2} \)) of a reaction can vary greatly depending on the reaction order:

• For a **zero-order** reaction, the half-life decreases as the concentration of reactants decreases. The formula \(t_{1/2} = \frac{[A]_0}{2k}\), directly links initial concentration \([A]_0\) to the half-life.
• In a **first-order** reaction, the half-life is constant and not influenced by changes in initial concentration. It is calculated using the formula \(t_{1/2} = \frac{0.693}{k}\).
• For a **second-order** reaction, the half-life increases as the concentration of reactants decreases. Here, \(t_{1/2} = \frac{1}{k[A]_0}\).

Knowing the half-life allows us to predict how a reactant's concentration diminishes over time, crucial for both laboratory and industrial applications.

Decomposition Reaction

Decomposition reactions are a fundamental type of chemical reaction where a single compound breaks down into simpler substances. These reactions are critical in fields like pharmaceuticals, materials science, and environmental science.
A decomposition reaction can be represented generally as:\[ \text{AB} \rightarrow \text{A} + \text{B} \] Here are a few important takeaways:

• Decomposition requires energy, often in the form of heat, light, or electricity, to break chemical bonds.
• This type of reaction is generally endothermic, meaning it absorbs energy from its surroundings.
• Chemical kinetics of decomposition reactions can vary significantly. For gaseous compounds, changes in pressure give valuable insight into reaction dynamics.
• Understanding the kinetics of decomposition reactions helps in developing safety measures for handling reactive or explosive materials.

By examining kinetic data such as changes in pressure over time, we can better understand and predict the behavior of decomposing compounds. This is particularly useful when trying to manage or mitigate potential hazards.