/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 In each of the following pairs, ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 47

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) or \(\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})\), (b) \(\mathrm{CO}_{2}(g)\) or \(\mathrm{CO}(g)\) ?

Short Answer

Expert verified
In each pair, the compound with a higher molar mass and more complex molecular structure is expected to have the higher standard molar entropy. Thus, for (a) C2H6(g) and for (b) CO2(g) would have higher standard molar entropies in comparison to their respective counterparts.

Step by step solution

01

Comparing C2H2(g) and C2H6(g)

First, let's analyze the two compounds: - C2H2(g): this is an ethylene molecule. It has a molar mass of approximately 26.04 g/mol. - C2H6(g): this is an ethane molecule. It has a molar mass of approximately 30.07 g/mol. Since C2H6(g) has a greater molar mass and more atoms in its structure, we would generally expect it to have a higher standard molar entropy than C2H2(g).
02

Comparing CO2(g) and CO(g)

Next, let's examine the comparison between CO2(g) and CO(g): - CO2(g): this is a carbon dioxide molecule. It has a molar mass of approximately 44.01 g/mol. - CO(g): this is a carbon monoxide molecule. It has a molar mass of approximately 28.01 g/mol. In this case, CO2(g) not only has a greater molar mass, but it also has a more complex linear molecular structure. Thus, it is expected that CO2(g) would have a higher standard molar entropy than CO(g). To summarize our findings: - Between C2H2(g) and C2H6(g), C2H6(g) is expected to have the higher standard molar entropy. - Between CO2(g) and CO(g), CO2(g) is expected to have the higher standard molar entropy.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Molar Mass
Molar mass is crucial in determining the standard molar entropy of substances. It represents the mass of one mole of a compound and is typically expressed in grams per mole (g/mol).

In our analysis, we compare two pairs of compounds based on molar mass. For instance, ethane (\(\mathrm{C}_2\mathrm{H}_6\)) has a higher molar mass (approximately 30.07 g/mol) compared to ethylene (\(\mathrm{C}_2\mathrm{H}_2\)) which is around 26.04 g/mol. This higher molar mass generally indicates a greater number of possible microstates that contribute to higher standard molar entropy.

Similarly, carbon dioxide (\(\mathrm{CO}_2\)) with a molar mass of about 44.01 g/mol surpasses carbon monoxide (\(\mathrm{CO}\)) at 28.01 g/mol. Higher molar mass in these instances tends to correlate with higher standard molar entropy due to increased molecular complexity.
Structure Complexity
The complexity of a molecule's structure significantly influences its standard molar entropy. More complex structures often have more positional and energetic arrangements available.

Take ethane \(\mathrm{C}_2\mathrm{H}_6\) as an example. It is a larger molecule than ethylene \(\mathrm{C}_2\mathrm{H}_2\). This complexity allows ethane to have more vibrational and rotational movements, contributing to a higher standard molar entropy.

In the comparison of carbon dioxide \(\mathrm{CO}_2\) and carbon monoxide \(\mathrm{CO}\), \(\mathrm{CO}_2\) is also more complex. Its linear structure enables additional flexibility in atomic motions, enhancing its ability to occupy a greater number of microstates. Thus, \(\mathrm{CO}_2\) is expected to exhibit higher standard molar entropy.
Comparative Entropy Analysis
When analyzing the standard molar entropy between pairs of molecules, a few key factors must be considered:
  • Molar Mass
  • Structural Complexity
In our examples, for both pairs 鈥� \(\mathrm{C}_2\mathrm{H}_2\) & \(\mathrm{C}_2\mathrm{H}_6\) and \(\mathrm{CO}_2\) & \(\mathrm{CO}\) 鈥� the molecule with the higher molar mass and more complex structure has a greater standard molar entropy.

This is fundamental in thermodynamic studies as it highlights that molecules with greater mass and intricate structures can disperse energy more efficiently.
  • \(\mathrm{C}_2\mathrm{H}_6\) has more complex structure than \(\mathrm{C}_2\mathrm{H}_2\), yielding higher entropy.
  • \(\mathrm{CO}_2\) is more complex than \(\mathrm{CO}\) and thus has a higher entropy.
Understanding these patterns helps in predicting material behavior in chemical processes, ensuring that entropy changes align with theoretical expectations.

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

About \(86 \%\) of the world's electrical energy is produced by using steam turbines, a form of heat engine. In his analysis of an ideal heat engine, Sadi Carnot concluded that the maximum possible efficiency is defined by the total work that could be done by the engine, divided by the quantity of heat available to do the work (for example, from hot steam produced by combustion of a fuel such as coal or methane). This efficiency is given by the ratio \(\left(T_{\text {hyda }}-T_{\text {low }}\right) / T_{\text {high }}\). where \(T_{\text {bigh }}\) is the temperature of the heat going into the engine and \(T_{\text {low }}\) is that of the heat leaving the engine, (a) What is the maximum possible efficiency of a heat engine operating between an input temperature of \(700 \mathrm{~K}\) and an exit temperature of \(288 \mathrm{~K}\) ? (b) Why is it important that electrical power plants be located near bodies of relatively cool water? (c) Under what conditions could a heat engine operate at or near \(100 \%\) efflciency? (d) It is often said that if the energy of combustion of a fuel such as methane were captured in an electrical fuel cell instead of by burning the fuel in a heat engine, a greater fraction of the energy could be put to useful work. Make a qualitative drawing like that in Figure \(5.10\) (p. 175) that illustrates the fact that in principle the fuel cell route will produce more useful work than the heat engine route from combustion of methane.

The reaction $$ \mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons 3 \mathrm{~S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ is the basis of a suggested method for removal of \(\mathrm{SO}_{2}\) from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (a) What is the equilibrium constant for the reaction at \(298 \mathrm{~K}\) ? (b) In principle, is this reaction a feasible method of removing \(\mathrm{SO}_{2}\) ? (c) If \(\mathrm{P}_{\mathrm{so}_{2}}=\mathrm{P}_{\mathrm{A}_{2} \mathrm{~s}}\) and the vapor pressure of water is 25 torr, calculate the equilibrium \(\mathrm{SO}_{2}\) pressure in the system at \(298 \mathrm{~K}\). (d) Would you expect the process to be more or less effective at higher temperatures?

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shewn here for two isomers of pentane, \(\mathrm{C}_{5} \mathrm{H}_{12}\) (a) Do you expect a significant difference in the enthalpy of combustion of the two isomers? Explain. (b) Which isomer do you expect to have the higher standard molar entropy? Explain. [Section 19.4] $$ \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{3} $$ CC(C)(C)C \(n-P e n t a n e\) Neopentane

The following processes were all discussed in Chapter 18 , "Chemistry of the Environment." Estimate whether the entropy of the system increases or decreases during each process: (a) photodissociation of \(\mathrm{O}_{2}(g)\), (b) formation of ozone from oxygen molecules and oxygen atoms, (c) diffusion of CFCs into the stratosphere, (d) desalination of water by reverse osmosis.

(a) Using data in Appendix C, estimate the temperature at which the free- energy change for the transformation from \(I_{2}(s)\) to \(I_{2}(g)\) is zero. What assumptions must you make in arriving at this estimate? (b) Use a reference source, such as Web Elements (www.webelements.com), to find the experimental melting and boiling points of \(I_{2}\) (c) Which of the values in part (b) is closer to the value you obtained in part (a)? Can you explain why this is so?
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemistry Branches

Read Explanation

Making Measurements

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.