# Which substance has the higher entropy? (a) dry ice (solid CO 2 ) at −78 °C or CO 2 (g) at 0 °C (b) liquid water at 25 °C or liquid water at 50 °C (c) pure alumina, Al 2 O 3 (s), or ruby (ruby is Al 2 O 3 in which some Al 3+ ions in the crystalline lattice are replaced with Cr 3+ ions) (d) one mole of N 2 (g) at 1 bar pressure or one mole of N 2 (g) at 10 bar pressure (both at 298 K)

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

Chapter
Section

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 18, Problem 1PS
Textbook Problem
800 views

## Which substance has the higher entropy? (a) dry ice (solid CO2) at −78 °C or CO2(g) at 0 °C (b) liquid water at 25 °C or liquid water at 50 °C (c) pure alumina, Al2O3(s), or ruby (ruby is Al2O3 in which some Al3+ ions in the crystalline lattice are replaced with Cr3+ ions) (d) one mole of N2(g) at 1 bar pressure or one mole of N2(g) at 10 bar pressure (both at 298 K)

(a)

Interpretation Introduction

Interpretation: From the given substances that is dry ice at -78oC or CO2 at 0oC the substance with higher entropy should be identified.

Concept introduction: Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more value of entropy.

The substance which has the highest entropy is CO2(g) at °C.

### Explanation of Solution

Entropy increases in the order solid < liquid < gas.  In the gaseous state, the particles are more random. In solids, the particles have fixed positions and entropy is less. In liquids, there are constraints due to forces between the particles.

Hence, entropy is more for CO2(g) at °C than for solid CO2 at -78 °C since CO2(g) is in gaseous state.

(b)

Interpretation Introduction

Interpretation: From the given substances that is liquid water at 25oC or liquid water at 50oC the substance with higher entropy should be identified.

Concept introduction: Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more value of entropy.

The substance which has the highest entropy is liquid water at 50 °C.

### Explanation of Solution

The entropy of a substance increase when the temperature is increased. At higher temperature, the substance is more disordered and thus the entropy is high. Also, when the temperature raised the additional energy added in the form of heat.

Therefore, liquid water has higher entropy at 50 °C than at 25 °C.

(c)

Interpretation Introduction

Interpretation: From the given substances that is pure alumina and ruby the substance with higher entropy should be identified.

Concept introduction: Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more value of entropy.

The substance which has the highest entropy is Ruby.

### Explanation of Solution

Al2O3 is pure alumina. The entropy of a pure crystal is zero. Ruby is Al2O3 doped with chromium ions. Some of the Al3+ ions are replaced by Cr3+ due to which the disorderness of the crystal increases and the entropy increases.

Thus, entropy is more for ruby than for pure Al2O3.

(d)

Interpretation Introduction

Interpretation: From the given substances that is 1molofN2(g)at1bar or 1molofN2(g)at10bar the substance with higher entropy should be identified.

Concept introduction: Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more value of entropy.

The substance which has the highest entropy is N2(g) at 1 bar pressure.

### Explanation of Solution

The entropy of the system increase when the pressure is decreased. At high pressure, the substance is more ordered and the randomness is less. Thus, the entropy is less.

Thus, N2(g) at 1 bar pressure has more entropy than N2(g) at 10 bar pressure.

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
Trabecular bone readily gives up its minerals whenever blood calcium needs replenishing. T F

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

What are the moral implications of using ergogenic aids?

Understanding Nutrition (MindTap Course List)

What is the definition of science?

An Introduction to Physical Science

2.53 What is meant by the phrase organic chemistry?

Chemistry for Engineering Students

What are sister chromatids?

Human Heredity: Principles and Issues (MindTap Course List)

You stand in a flat meadow and observe two cows (Fig. P1.73). Cow A is due north of you and 15.0 m from your po...

Physics for Scientists and Engineers, Technology Update (No access codes included)

Convert 741 torr to bar and inches of mercury.

Introductory Chemistry: An Active Learning Approach