/*! 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 22 Suppose we vaporize a mole of li... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 22

Suppose we vaporize a mole of liquid water at \(25^{\circ} \mathrm{C}\) and another mole of water at \(100{ }^{\circ} \mathrm{C}\). (a) Assuming that the enthalpy of vaporization of water does not change much between \(25^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C}\), which process involves the larger change in entropy? (b) Does the entropy change in either process depend on whether we carry out the process reversibly or not? Explain.

Short Answer

Expert verified
The larger entropy change occurs when vaporizing water at \(25^{\circ} \mathrm{C}\) compared to \(100{ }^{\circ} \mathrm{C}\) since the ratio of the entropy changes is greater than 1. The entropy change in either process does not depend on whether the process is carried out reversibly or not, as it is determined by enthalpy change and temperature during the process.

Step by step solution

01

Calculate the entropy change

In both cases, the process can be considered as isothermal since the temperature remains constant throughout the process (either at \(25^{\circ} \mathrm{C}\) or at \(100{ }^{\circ} \mathrm{C}\)). For an isothermal process, we can calculate the entropy change using the relation: \[ \Delta S = \frac{\Delta H}{T} \] Where \(\Delta S\) is the entropy change, \(\Delta H\) is the enthalpy change, and \(T\) is the temperature.
02

Calculate the entropy change at 25掳C and 100掳C

For process (a) at \(25^{\circ} \mathrm{C}\) (\(298 K\)), and process (b) at \(100{ }^{\circ} \mathrm{C}\)(\(373 K\)), we can calculate the entropy change using the given relation: \[ \Delta S_{25} = \frac{\Delta H}{298 K} \] \[ \Delta S_{100} = \frac{\Delta H}{373 K} \] Since the enthalpy of vaporization is assumed to be constant, we can compare the ratios of the entropy changes directly.
03

Compare the entropy changes

From the equations in step 2, we can observe that \[\frac{\Delta S_{25}}{\Delta S_{100}} = \frac{373}{298}\] Since the ratio is greater than 1, the entropy change \(\Delta S_{25}\) at \(25^{\circ} \mathrm{C}\) is larger than the entropy change \(\Delta S_{100}\) at \(100{ }^{\circ} \mathrm{C}\).
04

Effects of a reversible or irreversible process

Since the entropy change is given by the ratio of the enthalpy change to the temperature, this relationship holds in both reversible and irreversible processes, as long as the temperature and enthalpy are constant during the process. Therefore, the entropy change in either process does not depend on whether the process is carried out reversibly or not. In summary: (a) The entropy change is larger when vaporizing water at \(25^{\circ} \mathrm{C}\) compared to vaporizing water at \(100{ }^{\circ} \mathrm{C}\). (b) The entropy change in either process does not depend on whether the process is carried out reversibly or not.

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!

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

Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly? (b) If the ice cube melts reversibly, is \(\Delta E\) zero for the process? Explain.

How does the entropy of the system change when (a) the temperature of the system increases, (b) the volume of a gas increases, (c) equal volumes of ethanol and water are mixed to form a solution.

(a) What is meant by calling a process irreversible? (b) After an irreversible process the system is restored to its original state. What can be said about the condition of the surroundings after the system is restored to its original state? (c) Under what conditions will the condensation of a liquid be an irreversible process?

Consider what happens when a sample of the explosive TNT (Section 8.8: "Chemistry Put to Work: Explosives and Alfred Nobel") is detonated. (a) Is the detonation a spontaneous process? (b) What is the sign of \(q\) for this process? (c) Can you determine whether \(w\) is positive, negative, or zero for the process? Explain. (d) Can you determine the sign of \(\Delta E\) for the process? Explain.

Consider the reaction \(2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) .\) (a) Using data from Appendix \(C\), calculate \(\Delta G^{\circ}\) at \(298 \mathrm{~K}\). (b) Calculate \(\Delta G\) at \(298 \mathrm{~K}\) if the partial pressures of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) are \(0.40 \mathrm{~atm}\) and \(1.60 \mathrm{~atm}\), respectively.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Kinetics

Read Explanation

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Organic Chemistry

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.