Question

Write a pair of chain propagation steps for the radical bromination of propane to give 1-bromopropane. Then calculate \(\Delta H^{0}\) for each propagation step and for the overall reaction.

Short answer

Based on the given step-by-step solution, provide a short answer for the radical bromination of propane to give 1-bromopropane: The chain propagation steps for the radical bromination of propane to give 1-bromopropane are as follows: Step 1: R• + Br₂ → 1-Bromopropane + Br• Step 2: Br• + Propane → R• + HBr To calculate the standard enthalpy changes for each step, we use the enthalpies of formation. We then sum the enthalpy changes for both propagation steps to find the standard enthalpy change for the overall reaction, ΔH⁰(overall).

Step-by-step solution

Write the chain propagation steps for radical bromination of propane to form 1-bromopropane

The chain propagation steps for the radical bromination of propane to give 1-bromopropane are as follows: Propagation Step 1: Propane radical (R•) reacts with a Br2 molecule, leading to the formation of 1-bromopropane and a bromine radical (Br•). \(\text{R}• + \text{Br}_2 \rightarrow \text{1-Bromopropane} + \text{Br}•\) Propagation Step 2: The bromine radical (Br•) generated in the previous step can react with another propane molecule to form a new propane radical (R•) and a molecule of HBr, continuing the chain reaction. \(\text{Br}• + \text{Propane} \rightarrow \text{R}• + \text{HBr}\)

Calculate the standard enthalpy change for each propagation step

We can use the standard enthalpies of formation to calculate the enthalpy change for each propagation step: \(\Delta H^{0}_{step\,1}= (\Delta H_f(\text{1-Bromopropane}) + \Delta H_f(\text{Br}•)) - (\Delta H_f(\text{R}•) + \Delta H_f(\text{Br}_2)) \) \(\Delta H^{0}_{step\,2}= (\Delta H_f(\text{R}•) + \Delta H_f(\text{HBr})) - (\Delta H_f(\text{Br}•) + \Delta H_f(\text{Propane})) \) Use the known enthalpies of formation to find the values of \(\Delta H^{0}_{step\,1}\) and \(\Delta H^{0}_{step\,2}\).

Calculate the standard enthalpy change for the overall reaction

To calculate the standard enthalpy change for the overall reaction, sum the enthalpy changes for both propagation steps: \(\Delta H^{0}_{overall} = \Delta H^{0}_{step\,1} + \Delta H^{0}_{step\,2}\) With the enthalpy changes for both steps determined, you can now find the value of \(\Delta H^{0}_{overall}\).

Key concepts

Chain Propagation Steps

Understanding the mechanism of radical bromination is essential in organic chemistry. The process involves a series of chain propagation steps that allow the reaction to continue once it has been initiated. In the context of the exercise, the radical bromination of propane leading to 1-bromopropane includes two key propagation steps.

In the first step, a propane radical, often represented as R•, reacts with a molecule of bromine (Br2). This reaction yields 1-bromopropane and a bromine radical (Br•). The newly-formed Br• is highly reactive and proceeds to the second step, where it reacts with another propane molecule. This produces another propane radical, R•, which can now continue the chain process, and a molecule of hydrobromic acid (HBr). This continuous cycle of radical generation and consumption propagates the chain reaction, leading to the production of a significant amount of the bromination product.

It is crucial for students to know that these chain propagation steps are integral to the sustained reaction and product formation. This understanding not only assists in visualizing the chemical process but is also foundational in predicting reaction outcomes in similar radical-based reactions.

Standard Enthalpy Change

Enthalpy change, denoted as \(\Delta H^{0}\), is a measure of heat released or absorbed during a chemical reaction under standard conditions. In the exercise, we calculate the standard enthalpy change for each propagation step to understand the energy dynamics of the reaction. This involves using the standard enthalpies of formation of the reactants and products involved in each step.

For example, the calculation for the first propagation step takes the enthalpy of formation of 1-bromopropane and the bromine radical and subtracts the enthalpy of formation of the propane radical and molecular bromine. A similar approach is applied for the second step, involving the formation of hydrobromic acid. These calculations allow students to assess the energetics of each step and determine whether they are endothermic or exothermic. The sum of the enthalpy changes for both steps yields the overall enthalpy change of the reaction, providing insight into the total energy change for the process. By understanding the standard enthalpy change, students gain insights into the feasibility and spontaneity of chemical reactions.

Enthalpies of Formation

The enthalpies of formation, represented by \(\Delta H_f\), are central to thermochemistry and are defined as the heat change that occurs when one mole of a compound is formed from its elements at standard conditions. These values are crucial when calculating the standard enthalpy change of a reaction.

Enthalpies of formation are reference points for gauging the stability of compounds and the energy involved in their creation. When solving the problem, we look for the enthalpies of formation for each species involved in the reaction—propane, bromine, 1-bromopropane, and hydrobromic acid. These values are often sourced from tables in textbooks or reliable databases. Knowing them enables students to calculate the enthalpy changes for the chain propagation steps and the overall reaction. In teaching about enthalpies of formation, it's beneficial to emphasize their role in determining reaction energetics and as a foundational concept for understanding chemical bonding and reaction thermodynamics.