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Chapter 5: Problem 71

Using values from Appendix \(C\), calculate the standard enthalpy change for each of the following reactions: (a) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (b) \(\mathrm{Mg}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{SiCl}_{4}(l)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(g)\)

Short Answer

Expert verified
The standard enthalpy changes for the given reactions are: (a) \(螖H掳 = -197.78\ kJ\) (b) \(螖H掳 = 37.14\ kJ\) (c) \(螖H掳 = -961.92\ kJ\) (d) \(螖H掳 = -144.32\ kJ\)

Step by step solution

01

(a) Calculating standard enthalpy change for the reaction: \(2 SO_{2}(g) + O_{2}(g) \longrightarrow 2 SO_{3}(g)\)

To find the enthalpy change for this reaction, we first look for the standard enthalpies of formation (\(螖H_f掳\)) for the reactants and products from the Appendix C. For \(SO_{2}(g)\), the standard enthalpy of formation is: \(螖H_f掳[SO_{2}(g)] = -296.83\ kJ/mol\) For \(O_{2}(g)\), the standard enthalpy of formation is: \(螖H_f掳[O_{2}(g)] = 0\ kJ/mol\) (since elemental oxygen is in its standard state) For \(SO_{3}(g)\), the standard enthalpy of formation is: \(螖H_f掳[SO_{3}(g)] = -395.72\ kJ/mol\). Now we calculate the enthalpy change (\(螖H掳\)) for this reaction using the formula: \[螖H掳 = 危n\cdot 螖H_f掳(products) - 危n\cdot 螖H_f掳(reactants)\] Plugging in the values: \(螖H掳 = [2 \cdot (-395.72)] - [2 \cdot (-296.83) + 0] = -197.78\ kJ\)
02

(b) Calculating standard enthalpy change for the reaction: \(Mg(OH)_{2}(s) \longrightarrow MgO(s) + H_{2}O(l)\)

First, find the standard enthalpies of formation for the reactants and products from Appendix C. For \(Mg(OH)_{2}(s)\), the standard enthalpy of formation is: \(螖H_f掳[Mg(OH)_{2}(s)] = -924.50\ kJ/mol\) For \(MgO(s)\), the standard enthalpy of formation is: \(螖H_f掳[MgO(s)] = -601.53\ kJ/mol\). For \(H_{2}O(l)\), the standard enthalpy of formation is: \(螖H_f掳[H_{2}O(l)] = -285.83\ kJ/mol\). Calculate the enthalpy change (\(螖H掳\)) using the formula: \(螖H掳 = [(-601.53) + (-285.83)] - [(-924.50)]= 37.14\ kJ\)
03

(c) Calculating standard enthalpy change for the reaction: \(N_{2}O_{4}(g) + 4 H_{2}(g) \longrightarrow N_{2}(g) + 4 H_{2}O(g)\)

Find the standard enthalpies of formation for the reactants and products from Appendix C. For \(N_{2}O_{4}(g)\), the standard enthalpy of formation is: \(螖H_f掳[N_{2}O_{4}(g)] = 9.66\ kJ/mol\) For \(H_{2}(g)\), the standard enthalpy of formation is: \(螖H_f掳[H_{2}(g)] = 0\ kJ/mol\) (since elemental hydrogen is in its standard state) For \(N_{2}(g)\), the standard enthalpy of formation is: \(螖H_f掳[N_{2}(g)] = 0\ kJ/mol\) (since elemental nitrogen is in its standard state) For \(H_{2}O(g)\), the standard enthalpy of formation is: \(螖H_f掳[H_{2}O(g)] = -241.82\ kJ/mol\). Calculate the enthalpy change (\(螖H掳\)) using the formula: \(螖H掳 = [0 + 4 \cdot (-241.82)] - [9.66 + 4 \cdot 0] = -961.92\ kJ\)
04

(d) Calculating standard enthalpy change for the reaction: \(SiCl_{4}(l) + 2 H_{2}O(l) \longrightarrow SiO_{2}(s) + 4 HCl(g)\)

Find the standard enthalpies of formation for the reactants and products from Appendix C. For \(SiCl_{4}(l)\), the standard enthalpy of formation is: \(螖H_f掳[SiCl_{4}(l)] = -640.10\ kJ/mol\) For \(H_{2}O(l)\), the standard enthalpy of formation is: \(螖H_f掳[H_{2}O(l)] = -285.83\ kJ/mol\). For \(SiO_{2}(s)\), the standard enthalpy of formation is: \(螖H_f掳[SiO_{2}(s)] = -910.75\ kJ/mol\). For \(HCl(g)\), the standard enthalpy of formation is: \(螖H_f掳[HCl(g)] = -92.30\ kJ/mol\). Calculate the enthalpy change (\(螖H掳\)) using the formula: \(螖H掳 = [(-910.75) + 4 \cdot (-92.30)] - [(-640.10) + 2 \cdot (-285.83)] = -144.32\ kJ\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Standard Enthalpies of Formation
Understanding the standard enthalpies of formation is crucial when it comes to studying chemical reactions and energetics. The standard enthalpy of formation, represented by \( \Delta H_f^\circ \), is the heat change that occurs when one mole of a compound is formed from its elements in their standard states. For instance, the formation of water from hydrogen and oxygen gases would have a distinct \( \Delta H_f^\circ \). A crucial point to note is that the standard enthalpy of formation for a pure element in its stable form, such as \( O_2(g) \) or \( H_2(g) \) is defined as zero.When calculating the enthalpy change for a reaction, we subtract the sum of the standard enthalpies of formation of the reactants from the sum of the standard enthalpies of formation of the products. Through this approach, we capture the overall enthalpic evolution or consumption for the reaction under standard conditions, which typically include a pressure of 1 bar and a temperature of 298 K (25掳C).
Thermochemistry
Thermochemistry is the study of the energy and heat associated with chemical reactions and physical transformations. It is a branch of thermodynamics that gives us insights into the energy changes, particularly heat transfer, involved in chemical processes. For understanding and quantifying energy changes, thermochemistry employs concepts such as enthalpy (\( H \)), entropy (\( S \)), and Gibbs free energy (\( G \)), along with the principle that energy is conserved in chemical reactions.
The enthalpy change of a reaction hints at whether the process is exothermic (releases heat) or endothermic (absorbs heat), and it is a key parameter for predicting the spontaneity and feasibility of chemical reactions. Calculating the enthalpy change for reactions using standard enthalpies of formation is a fundamental application of thermochemistry. For processes occurring at constant pressure, the change in enthalpy equals the energy flow as heat.
Chemical Reactions
Chemical reactions are processes where reactants transform into products, involving the breaking and making of chemical bonds. These changes carry associated energy changes, which are often observed as heat released or absorbed. The enthalpy change of a chemical reaction provides a measure of this heat under constant pressure and helps in predicting the reaction's direction and the energy required to sustain it.
The signs of the enthalpy change also convey the nature of the chemical process: a negative \(\Delta H^\circ\) value denotes an exothermic reaction, where energy is released to the surroundings, while a positive value indicates an endothermic reaction, where energy is absorbed from the surroundings. This insight is essential for the development of industrial processes, safety assessments, and energy management strategies involving chemical reactions. Students need to grasp how the combination of different substances and the rearrangement of atoms in a chemical reaction are closely related to energy changes, for a deeper understanding of chemistry.
Hess's Law
Hess's Law is a powerful tool in thermochemistry that states the total enthalpy change for a reaction is the same, no matter how it occurs, as long as the initial and final conditions are the same. This principle derives from the law of energy conservation and allows us to calculate the enthalpy change of a complex reaction by breaking it down into simpler steps with known enthalpy changes.
For instance, if you cannot directly measure the enthalpy change of a reaction, you can find it by using known enthalpies of formation for the reactants and products or by combining other reactions that add up to your target reaction, both of which are applications of Hess's Law. This approach is particularly helpful when direct measurement is difficult or impossible. Thus, Hess's Law provides an essential method for predicting reaction energetics, which can be foundational in both theoretical and applied chemistry.

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Most popular questions from this chapter

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