/*! 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 23 Diamond and the fullerenes are t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 17: Problem 23

Diamond and the fullerenes are two allotropes of carbon. On the basis of their different structures and properties, predict which has the higher standard molar entropy.

Short Answer

Expert verified
Answer: Fullerene is expected to have a higher standard molar entropy than diamond due to its less ordered and more flexible structure, allowing for more accessible conformations and molecular motions, which contribute to its entropy.

Step by step solution

01

Understand standard molar entropy

Standard molar entropy is a measure of the entropy (disorder or randomness) of one mole of a substance under standard conditions (1 atm pressure and a specified temperature, usually 298K). It is an extensive property, which means it depends on the amount of substance. A higher standard molar entropy implies a higher level of disorder or randomness in the substance.
02

Examine the structures of diamond and fullerenes

Diamond has a highly ordered, crystalline structure where each carbon atom is covalently bonded to four other carbon atoms in a tetrahedral arrangement. This results in a rigid, strong, and stable lattice structure with little disorder. On the other hand, fullerenes are composed of carbon atoms bonded in a combination of pentagonal and hexagonal rings, forming cage-like, closed-shell molecules (e.g., C60). These molecules are relatively less ordered and have weaker forces between adjacent molecules compared to diamond.
03

Consider the contribution of structure, properties, and motion to standard molar entropy

Entropy is a measure of disorder, and it depends on factors such as the structure of a substance, the presence of multiple conformations, vibrational and rotational motions, and translational motion. In general, a more disordered or less rigid structure (e.g., fullerene) will exhibit a higher entropy compared to a more ordered or rigid structure (e.g., diamond).
04

Compare the entropy of diamond and fullerenes

Diamond has a highly ordered, rigid structure, while fullerenes have a less ordered and more flexible structure. Therefore, fullerenes are expected to have a higher standard molar entropy as there is more disorder in their structure, and they possess a greater number of accessible conformations and molecular motions, which contribute to their entropy.
05

Conclusion:

Based on the differences in structures and properties, fullerene is predicted to have a higher standard molar entropy than diamond.

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.

Standard Molar Entropy
Standard molar entropy is a fundamental concept in chemistry that helps us understand the disorder present in a substance. It measures the randomness associated with one mole of a substance at standard conditions, typically 1 atm pressure and 298K temperature.
Under these conditions, the level of disorder or randomness is noted as being the standard molar entropy, which is an extensive property, meaning it scales with the amount of substance.
This value is influenced by several factors, including molecular structure, the presence of multiple molecular conformations, and how molecules vibrate, rotate, or move in space.
In general, substances with more complex structures and more ways to arrange themselves tend to have higher standard molar entropy.
Crystalline Structure
A crystalline structure refers to a systematic, orderly pattern of atoms or molecules. This is in contrast to non-crystalline (amorphous) substances without a defined arrangement.
Diamond serves as an excellent example of a crystalline structure. Each carbon atom in a diamond is covalently bonded to four other carbon atoms in a robust tetrahedral lattice.
This results in a very stable and ordered arrangement, giving diamond its remarkable hardness and rigidity. However, such order means a low level of disorder, leading to a lower standard molar entropy compared to more disordered structures.
On the other hand, structures that are less orderly, like that of fullerenes, have higher standard molar entropy.
Fullerenes
Fullerenes are fascinating molecules and one of novel allotropes of carbon besides diamond and graphite. What makes them unique is their closed-cage structures composed of carbon atoms arranged in pentagonal and hexagonal rings.
These structures resemble a soccer ball shape, like the famous C60, also known as a "buckyball".
Due to these cage-like formations, fullerenes exhibit considerable flexibility and a myriad of possible configurations. This flexibility and the weaker intermolecular forces compared to those in diamonds allow fullerene molecules to be more dynamic.
Hence, fullerenes can move and adjust shapes more freely, contributing to higher standard molar entropy compared to diamonds. Their structural versatility is why they typically have higher entropy, as the diverse molecular motions and accessible conformations increase the disorder.

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

Which of the following reactions has the largest \(K_{\mathrm{p}}\) value at \(25^{\circ} \mathrm{C} ?\) a. \(\mathrm{Cl}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{ClF}(g) \quad \Delta G_{\text {rxn }}^{\circ}=115.4 \mathrm{kJ}\) b. \(\mathrm{Cl}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{ClBr}(g) \quad \Delta G_{\mathrm{mo}}^{*}=-2.0 \mathrm{kJ}\) c. \(\mathrm{Cl}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{ICl}(g) \quad \Delta G_{\mathrm{rm}}^{\circ}=-27.9 \mathrm{kJ}\)

Identify the following systems as isolated or not isolated, identify the processes as spontaneous or nonspontaneous, and explain your choice. a. A photovoltaic cell in a solar panel produces electricity. b. Helium gas escapes from a latex party balloon. c. A sample of pitchblende (uranium ore) emits alpha particles.

Uses of Methane The methane in natural gas is an important starting material, or feedstock, for producing industrial chemicals, including \(\mathrm{H}_{2}\) gas. a. Use the appropriate \(\Delta G_{f}^{\circ}\) value(s) from Appendix 4 to calculate \(\Delta G_{\text {mn }}^{*}\) for the reaction known as steam-metbane reforming: $$\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)$$ b. To drive this nonspontancous reaction, the CO that is produced can be oxidized to \(\mathrm{CO}_{2}\) by using more steam: $$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$$ Use the appropriate \(\Delta G_{f}^{*}\) value(s) from Appendix 4 to calculate \(\Delta G_{\text {rxn }}^{*}\) for this reaction, which is known as the water- gas shift reaction. c. Combine these two reactions and write the chemical equation of the overall reaction in which methane and steam combine to produce hydrogen gas and carbon dioxide. d. Calculate the \(\Delta G_{\text {ren }}^{\circ}\) value of the overall reaction. Is it spontaneous under standard conditions?

Which of the following processes would not result in an entropy increase for the indicated system? a. Melting of an ice cube b. Evaporation of a sample of an alcohol c. Sublimation of a mothball d. Cooling of hot water to room temperature

Super fluids The 1996 Nobel Prize in Physics was awarded to Douglas Osheroff, Robert Richardson, and David Lee for discovering super-fluidity (apparently frictionless flow) in "He. When \(^{3} \mathrm{He}\) is cooled to \(2.7 \mathrm{mK}\), the liquid settles into an ordered super-fluid state. What is the predicted sign of the entropy change for the conversion of liquid ' He into its super-fluid state?
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Ionic and Molecular Compounds

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Analysis

Read Explanation

Physical Chemistry

Read Explanation

Chemical Reactions

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.