Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 16: Problem 38

Relating ldeas Given the entropy change for the first two reactions below, calculate the entropy change for the third reaction below. \(\mathrm{S}_{8}(s)+8 \mathrm{O}_{2}(s) \longrightarrow 8 \mathrm{SO}_{2}(g) \qquad \Delta S=89 \mathrm{J} / \mathrm{K}\) \(2 \mathrm{SO}_{2}(s)+\mathrm{O}_{2}(s) \longrightarrow 2 \mathrm{SO}_{3}(g) \qquad \Delta S=-188 \mathrm{J} / \mathrm{K}\) \(\mathrm{S}_{8}(s)+12 \mathrm{O}_{2}(s) \longrightarrow 8 \mathrm{SO}_{3}(g) \qquad \Delta S=?\)

Short Answer

Expert verified
The entropy change for the third reaction is -99 J/K.

Step by step solution

01

Write the Given Reactions

Identify and write down the given reactions and their respective entropy changes.
02

Express the Target Reaction in Terms of Given Reactions

Express the third reaction (target reaction) in terms of the first two reactions.
03

Combine the Reactions to Form the Target Reaction

Combine the given reactions such that they result in the target reaction.
04

Calculate the Entropy Change for the Target Reaction

Add up the entropy changes of the first two reactions to find the entropy change for the target reaction.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

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

Thermodynamics
Thermodynamics is a core concept in understanding chemical reactions and their properties. It involves the study of energy changes, particularly heat, during chemical reactions and physical transformations. The fundamental laws of thermodynamics explain how energy is transferred and conserved within a system. In the context of entropy change, we're interested in the second law of thermodynamics, which states that the entropy of an isolated system will tend to increase over time. This law helps us predict whether a reaction will proceed spontaneously. By understanding the basics of thermodynamics, we can better understand how entropy changes impact reactions.
Reaction Mechanisms
Reaction mechanisms detail the step-by-step process by which reactants transform into products. These steps help us understand the pathway of reactions, the energy changes, and the intermediates formed along the way. Breaking down complex reactions into simpler steps makes it easier to analyze the reaction's overall properties. Each step involves specific reactants, intermediates, and products, with its own energy and entropy changes. Knowing the mechanism allows us to more accurately predict the behavior of a reaction under different conditions.
Entropy Calculations
Entropy, symbolized by S, is a measure of the disorder or randomness in a system. In chemical reactions, the change in entropy \(\triangle S\) is calculated to determine how the disorder changes from reactants to products.
Here, we are given the entropy changes of two reactions and need to find the entropy change of a third reaction.
The given reactions are:
  • \(\text{S}_{8}(s) + 8 \text{O}_{2}(s) \rightarrow 8 \text{SO}_{2}(g) \) with \(\triangle S = 89 \text{ J/K} \)
  • \(\text{2 SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{SO}_{3}(g) \) with \(\triangle S = -188 \text{ J/K} \)
To find the entropy change for \(\text{S}_{8}(s) + 12 \text{O}_{2}(s) \rightarrow 8 \text{SO}_{3}(g) \), we rearrange these reactions and combine their entropy changes. By expressing the target reaction as a combination of the given reactions and summing the entropy changes, we achieve the desired outcome.
Stoichiometry
Stoichiometry involves the quantitative relationships between the amounts of reactants and products in a chemical reaction. It allows us to predict the quantities of substances consumed and produced.
In our problem, stoichiometry helps us balance the reactions correctly to combine them:
  • We have the reaction \(\text{S}_{8}(s) + 8 \text{O}_{2}(s) \rightarrow 8 \text{SO}_{2}(g) \)
  • We modify \(\text{2 SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{SO}_{3}(g) \) to make it fit by multiplying: \(\text{4 SO}_{2}(g) + 2 \text{O}_{2}(g) \rightarrow 4 \text{SO}_{3}(g) \)
  • This adjustment allows us to rearrange and sum the reactions properly. \(\text{S}_{8}(s) + 12 \text{O}_{2}(s) \rightarrow 8 \text{SO}_{3}(g) \) by simple addition.
  • The adjusted entropy change is the sum: \(\triangle S = 89 \text{ J/K} + 2*(-188 \text{ J/K}) = 89 \text{ J/K} - 376 \text{ J/K} = -287 \text{ J/K} \)
With correct stoichiometry, we ensure our reactions are balanced and our entropy calculations are accurate.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Interpreting Concepts Absolute enthalpy cannot be determined; only change in energy can be measured. However, absolute entropy can be determined. Explain why an absolute entropy can be determined.

The standard enthalpy of formation for sulfur dioxide gas is \(-296.8 \mathrm{kJ} / \mathrm{mol}\) . Calculate the amount of energy given off in \(\mathrm{kJ}\) when 30.0 \(\mathrm{g}\) of \(\mathrm{SO}_{2}(g)\) is formed from its elements.

The gas-phase reaction of \(\mathrm{H}_{2}\) with \(\mathrm{CO}_{2}\) to produce \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CO}\) has \(\Delta \mathrm{H}=11 \mathrm{kJ}\) and \(\Delta \mathrm{S}=41 / \mathrm{K} .\) Is the reaction spontaneous at 298.15 \(\mathrm{K} ?\) What is \(\Delta G ?\)

Rewrite each equation below with the ?H value included in either the reactants or products, and identify the reaction as endothermic or exothermic. a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) \(\Delta H=-197.8 \mathrm{kJ}\) b. \(2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) \(\Delta H=+114.2 \mathrm{kJ}\) c. \(C_{2} \mathrm{H}_{4}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) \(\Delta H=-1411.0 \mathrm{kJ}\)

a. Distinguish between enthalpies of reaction, formation, and combustion. b. On what basis are enthalpies of formation and combustion defined?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

Nuclear Chemistry

Read Explanation

Making Measurements

Read Explanation

Physical Chemistry

Read Explanation

Chemistry Branches

Read Explanation

The Earths Atmosphere

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free