Problem 15 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Formation of ozone from oxygen is an endothermic process. In the upper atmosphere, ultraviolet is the source of energy that drives the reaction. Assuming that both the reactions and the products of the reaction are in standard states, the standard enthalpy of formation of ozone from the following information: \(3 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{O}_{3}(\mathrm{~g}), \Delta H^{\circ}=286 \mathrm{~kJ}\), is (a) \(+143 \mathrm{~kJ} / \mathrm{mol}\) (b) \(-143 \mathrm{~kJ} / \mathrm{mol}\) (c) \(+286 \mathrm{~kJ} / \mathrm{mol}\) (d) \(-286 \mathrm{~kJ} / \mathrm{mol}\)

Step-by-Step Solution

Answer

+143 kJ/mol

Step 1: Understand the Given Data

We are given the reaction where 3 moles of dioxygen (O2) form 2 moles of ozone (O3) and the reaction absorbs 286 kJ of energy, indicating it is endothermic. The reaction is: \(3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{O}_{3}(\mathrm{g})\), with \(\Delta H^{\textdegree}=286 \mathrm{kJ}\).

Step 2: Calculate the Standard Enthalpy of Formation per Mole of Ozone

To find the standard enthalpy of formation of ozone per mole, we divide the total enthalpy change by the number of moles of ozone formed. The amount of energy absorbed is 286 kJ for the formation of 2 moles of ozone. Thus, the standard enthalpy of formation per mole of ozone is \(\frac{286 \mathrm{~kJ}}{2 \mathrm{moles}} = 143 \mathrm{kJ/mole}\).

Step 3: Determine the Correct Sign for the Enthalpy of Formation

Since the formation of ozone from oxygen is an endothermic process, the standard enthalpy of formation should be positive. Therefore, the sign of the standard enthalpy of formation per mole of ozone is positive.

Key Concepts

Standard Enthalpy Change

The standard enthalpy change, often represented by \( \Delta H^\circ \), is a critical concept in thermochemistry. It refers to the heat change that occurs when a reaction takes place under standard conditions, which include a pressure of 1 atmosphere and a temperature of 298.15 K (25°C). In essence, it is the quantity of heat released or absorbed during a chemical reaction for one mole of substance.

When we look at the formation of ozone from oxygen, the \( \Delta H^\circ \) value provides us with direct insight into the energetic aspects of the reaction. If the value of \( \Delta H^\circ \) is positive, like in our given reaction where it is 286 kJ, it indicates that the reaction requires energy input to proceed. This endothermic nature reflects the need for external energy, such as ultraviolet light in the atmosphere, to drive the formation of ozone from oxygen.

To further understand \( \Delta H^\circ \) in the context of this problem, one must consider the stoichiometry of the reaction. The given value relates to the entire process, not just the formation of one mole of product, which is why it's important to accurately calculate the per mole energy change when solving physical chemistry problems.

Endothermic Reactions

Endothermic reactions are chemical processes that absorb heat from their surroundings. As opposed to exothermic reactions, which release energy, endothermic reactions require a net input of energy to proceed. This energy is often supplied in the form of heat or light.

In the case of the formation of ozone, ultraviolet light provides the necessary energy for the diatomic oxygen molecules to reconfigure into triatomic ozone molecules. It's this energy absorption that is indicated by the positive enthalpy change of the reaction (\( \Delta H^\circ > 0 \)).

Energy Requirement and Stability

Typically, endothermic reactions lead to the production of substances that are less stable than the reactants because energy must be stored within the chemical bonds of the products. This contrasts with exothermic reactions, where products are generally more stable than the reactants due to the release of energy.

Thermochemistry

Thermochemistry is the branch of chemistry concerned with the heat changes that occur during chemical reactions. It is a sub-discipline of thermodynamics, which is the science of the relationship between heat, work, temperature, and energy. Thermochemistry focuses on the calculation of heat changes using the concept of enthalpy, entropy, and free energy, among other quantities.

Understanding thermochemistry is essential when analyzing reactions like the formation of ozone. It allows us to quantify the energy changes involved and predict the feasibility and direction of a reaction under certain conditions. The endothermic nature of the ozone formation process, as discussed earlier, is an example of a thermochemical investigation.

In educational contexts, physical chemistry problems involving thermochemistry not only require knowledge of chemical principles but also the application of mathematical skills to solve for various heat-related quantities. These problems can offer insights into the energy profiles of reactions and the interplay between kinetic and potential energy in chemical processes.

Physical Chemistry Problems

Physical chemistry problems often involve the application of mathematical concepts to chemical phenomena. They require a strong understanding of both disciplines to accurately describe and predict the behavior of chemical systems. Problems in this field, like determining the enthalpy of formation for a particular substance, involve the use of equations, stoichiometry, and a deep understanding of chemical principles.

For students tackling such problems, grasping the stoichiometry is crucial, as is the ability to interpret and apply thermodynamic data. These problems serve as an excellent bridge between theoretical knowledge and practical application, giving students a fuller understanding of the underlying processes that govern chemical reactions.

When solving problems, such as calculating the standard enthalpy of formation, it is also important for students to pay attention to the units and ensure that they're consistent throughout their calculations. This precision is critical in obtaining a correct and meaningful answer, as seen in the calculation of the standard enthalpy of formation of ozone from oxygen.