Question

Determine the enthalpy change for the gaseous reaction of sulfur dioxide with ozone to form sulfur trioxide given the following thermochemical data: $$ \begin{aligned} 2 \mathrm{SO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{2}(g) & \Delta H^{\circ}=-602.8 \mathrm{~kJ} / \mathrm{mol} \\ 3 \mathrm{SO}(g)+2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{SO}_{3}(g) & \\\ \Delta H_{\mathrm{rxn}}^{\circ}=-1485.03 \mathrm{~kJ} / \mathrm{mol} \\ \frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{O}_{3}(g) & \Delta H_{\mathrm{rxn}}^{\circ}=142.2 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$

Short answer

The enthalpy change for the reaction is \(-1095.53 \text{ kJ/mol}.\)

Step-by-step solution

Identify the Target Reaction

We need to determine the enthalpy change for the reaction \( ext{SO}_2(g) + ext{O}_3(g) \rightarrow ext{SO}_3(g)\). This is our target reaction for which we will calculate the enthalpy change.

Extract Given Reactions and Data

We have three given reactions: 1. \(2 ext{SO}(g)+ ext{O}_2(g) \rightarrow 2 ext{SO}_2(g) \) with \(\Delta H^{\circ}=-602.8 \text{ kJ/mol}\).2. \(3 ext{SO}(g)+2 ext{O}_3(g) \rightarrow 3 ext{SO}_3(g)\) with \(\Delta H^{\circ}=-1485.03 \text{ kJ/mol}\).3. \(\frac{3}{2} ext{O}_2(g) \rightarrow ext{O}_3(g)\) with \(\Delta H^{\circ}=142.2 \text{ kJ/mol}\).

Manipulate and Combine Reactions

We need to manipulate these reactions to form the target reaction:1. Reverse reaction 1 to form 2SO(g): \(2 ext{SO}_2(g) \rightarrow 2 ext{SO}(g)+ ext{O}_2(g)\), changing \(\Delta H\) to +602.8 kJ/mol.2. Use reaction 2 directly, unchanged.3. Use reaction 3 unchanged and multiply it by 2/3: \(\text{O}_3(g) \rightarrow \frac{3}{2} ext{O}_2(g)\), changing \(\Delta H\) to \(-\frac{3}{2} \times 142.2 = -213.3\) kJ/mol.

Add Reactions and Simplify

Add the manipulated reactions together:- From the reversed reaction 1, we get \(2 ext{SO}_2(g) \rightarrow 2 ext{SO}(g) + ext{O}_2(g)\).- From reaction 2, we use it directly.- From manipulated reaction 3, we reverse it and use it normally to generate ozone and oxygen conversion.Simplify to obtain the target reaction of \(\text{SO}_2(g) + ext{O}_3(g) \rightarrow ext{SO}_3(g)\) by cancelling out common terms across reactions.

Calculate Enthalpy Change for Target Reaction

Add the enthalpy changes from the manipulated reactions:- Add \(+602.8 \, \text{kJ/mol} \) from the reversed reaction 1.- Add \(-1485.03 \, \text{kJ/mol}\) from reaction 2.- Add \(-213.3 \, \text{kJ/mol} \) from the manipulated reaction 3.Total enthalpy change for the target reaction is:\[\Delta H^{\circ} = 602.8 - 1485.03 - 213.3 = -1095.53 \, \text{kJ/mol}.\]

Key concepts

Thermochemical Equations

Thermochemical equations are chemical equations that include the enthalpy change of the reaction. This additional information reveals the energy change that occurs during the reaction, which can be either absorbed or released.
Understanding thermochemical equations is crucial because it helps in predicting how heat will behave in a reaction. You will often see these equations written with the enthalpy change, \( \Delta H \), alongside the reactants and products.
In the exercise, the provided thermochemical equations help us understand the energy changes involved. These equations form the basis for calculating the overall enthalpy change of a desired reaction. Each given equation signifies a known transformation that contributes to the final reaction. By manipulating these equations, you can derive enthalpy changes for other reactions using Hess's Law.

Hess's Law

Hess's Law is a pivotal concept in thermochemistry that allows for the calculation of enthalpy changes for reactions that are difficult to measure directly. It states that the total enthalpy change for a reaction is the sum of all changes, regardless of the number of steps in the reaction pathway.
This law is extremely useful as it lets you break down a complex reaction into simpler known reactions, whose enthalpy changes have been measured. Then, by manipulating these reactions algebraically, you can find the enthalpy change for the overall reaction.
In our example, Hess's Law enabled us to manipulate the provided thermochemical equations to align them with the target reaction path. By reversing, adjusting, and summing these equations, we determined the target reaction's enthalpy change without needing to measure it directly.

Chemical Reaction Enthalpies

Enthalpies of chemical reactions, represented by \( \Delta H \), are essential for understanding how much energy is absorbed or released during a reaction. This unit of measurement is important for gauging whether a reaction is exothermic (releases heat) or endothermic (absorbs heat).
In this exercise, the enthalpy changes for each provided reaction denote the energy status under standard conditions. For instance, a negative \( \Delta H \) indicates an exothermic reaction, meaning energy is released, while a positive \( \Delta H \) indicates an endothermic reaction.
The given reactions in the exercise each have associated enthalpies that contribute to finding the enthalpy change of the desired target reaction. These values provide a puzzle-like framework where you fit different reactions together to conform to the desired outcome, thereby calculating the net enthalpy change efficiently.

Manipulation of Reactions

The manipulation of reactions involves a series of algebraic adjustments to align with the desired outcome. This involves reversing reactions, changing their coefficients, and consequently adjusting their enthalpies to construct the overall reaction pathway leading to the target reaction.
In the exercise, we reversed one of the provided reactions to change the direction, which requires changing the sign of the enthalpy change. Additionally, coefficients in the reactions were adjusted to ensure the balancing of molecules across reactions. This manipulation was crucial to simplify the combination of reactions.
By creatively combining these individual steps, you can piece together reactions to form the exact path that matches the desired transformation. This manipulation ensures that all intermediary steps contribute accurately to the enthalpy calculation using Hess's Law.