Physical Chemistry
Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 3, Problem 3.24E

SO 2 in a piston chamber kept in a constant-temperature bath at 25.0 ° C expands from 25.0 mL to 75.0 mL very, very slowly. Assume SO 2 behaves as a van der Waals gas, and its van der Waals parameters are a = 6.714 atm L 2 / mol 2 and b = 0.05636 L / mol . If there is 0.00100 mole of ideal gas in the chamber, calculate Δ S sys , Δ S surr , and Δ S univ for the process.

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation:

The values of ΔSsys,ΔSsurr, and ΔSuniv for the process of expansion of SO2 gas are to be calculated.

Concept introduction:

The change in entropy of the system is given by the equation shown below.

ΔSsys=qrevT

This equation is in the terms of heat for the reversible processes. The change in entropy of the system is given by the equation as shown below.

ΔSsurr=qsurrT

The change in entropy of the universe is the sum of the change in entropy of system and surrounding.

Answer to Problem 3.24E

The values of ΔSsys,ΔSsurr, and ΔSuniv for the process of expansion of SO2 gas are 9.12×103JK1, 0.0164JK1 and 0.0255JK1 respectively.

Explanation of Solution

The given process occurs at constant temperature, therefore ΔU=0 for the process. Thus, the q=w.

The work done is calculated using the formula given below.

w=pexΔV…(1)

Where,

pex is the external pressure.

ΔV is the change in volume.

w is the work done.

The pressure of SO2 gas can be calculated using the van der Waals gas equation as shown below.

p=nRTVnba(nV)2

Where,

p is the pressure.

V is the volume.

R is the gas constant.

T is the temperature.

a,b are the van der Waals coefficients.

n is the number of moles.

The number of moles, volume and temperature given for SO2 gas are 0.00100mol, 25.0mL and 25.0°C respectively. The values of a and b for SO2 gas are given as 6.714atmL2/mol2 and 0.05636L/mol respectively.

Substitute the values of number of moles, volume and temperature in the above equation as shown below.

p=nRTVnba(nV)2=((0.00100mol)(0.0821Latmmol1K1)(25+273.15K)(25.0mL×1L1000mL)(0.00100mol×0.05636L/mol)(6.714atmL2/mol2)(0.00100mol25.0mL×1L1000mL)2)=(0.02440.0255.636×105)0.01074=0.9676atm

The initial and final volume given is 25.00mL and 75.00mL respectively. Substitute the values in the equation (1) as shown below.

w=pexΔV=0.9676atm×(75.00mL25.00mL)×1L1000mL×101.32JLatm=0.9676atm×(50.0mL)×1L1000mL×101.32JLatm=4.90J

Thus, q=4.90J. Since this heat is given to the surrounding, therefore the ΔSsurr is calculated as shown below.

ΔSsurr=qsurrT

Substitute the values in above equation as shown below.

ΔSsurr=qsurrT=4.90J298.15K=0.0164JK1

The work done for the reversible process is calculated using the formula given below.

w=nRTlnVfVi

Where,

n is the number of moles.

R is the gas constant.

T is the temperature.

Vf is the final volume.

Vi is the initial volume.

Substitute the values of R, T, Vf and Vi in the above equation as shown below.

w=nRTlnVfVi=0.00100mol×8.314Jmol1K1×298.15K×ln75.00mL25.00mL=2.4788×(1.0986)=2.72J

Thus, qrev=2.72J. The ΔSsys is calculated using the equation given below as shown below.

ΔSsys=qrevT

Substitute the values in above equation as shown below.

ΔSsys=qrevT=2.72J298.15K=9.12×103JK1

The value of ΔSuniv is calculated using the equation given below as shown below.

ΔSuniv=ΔSsys+ΔSsurr

Substitute the values in above equation as shown below.

ΔSuniv=ΔSsys+ΔSsurr=9.12×103JK1+0.0164JK1=0.0255JK1

Conclusion

The values of ΔSsys,ΔSsurr, and ΔSuniv for the process of expansion of SO2 gas are 9.12×103JK1, 0.0164JK1 and 0.0255JK1 respectively.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 3 Solutions

Physical Chemistry

Ch. 3 - The Carnot cycle is defined as having a certain...Ch. 3 - In thermodynamics, the pathway in a...Ch. 3 - A refrigerator is the reverse of an engine: Work...Ch. 3 - Efficiency is given by equations 3.5, 3.6, and...Ch. 3 - What is the entropy change for an ideal Carnot...Ch. 3 - What is the entropy change for the melting of...Ch. 3 - What is the entropy change for the solidification...Ch. 3 - Explain why the statement No process is 100...Ch. 3 - What is the change in entropy of 1.00mole of water...Ch. 3 - Prob. 3.20ECh. 3 - One mole of He warms up irreversibly at constant...Ch. 3 - Consider a monatomic ideal gas in a piston...Ch. 3 - A 0.500-mol sample of an ideal gas has an initial...Ch. 3 - SO2 in a piston chamber kept in a...Ch. 3 - A normal breath has a volume of about 1L. The...Ch. 3 - An automobile tire contains 15.6L of air at...Ch. 3 - An automobile tire contains 15.6L of air at...Ch. 3 - A sample of ideal gas from a compressed gas...Ch. 3 - Prob. 3.29ECh. 3 - In Example 3.5, a heat capacity of 20.78J/molK was...Ch. 3 - Prob. 3.31ECh. 3 - 4.00L of Ar and 2.50L of He, each at 298K and...Ch. 3 - Dentists might use a mixture of 40N2O and 60O2 as...Ch. 3 - A 5.33-g piece of Cu metal is heated to 99.7C in...Ch. 3 - A sample of 1.00mol of silver at 150C is placed in...Ch. 3 - Prob. 3.36ECh. 3 - What is the change in entropy when 2.22mol of...Ch. 3 - Estimate the entropy change of an 800-lb engine...Ch. 3 - Calculate the molar entropy change of the gas that...Ch. 3 - A normal breath is about 1L in volume. Assume you...Ch. 3 - The first law of thermodynamics is sometimes...Ch. 3 - Troutons rule states that the entropy of boiling...Ch. 3 - Prob. 3.43ECh. 3 - Argue from Boltzmanns definition for entropy that...Ch. 3 - Prob. 3.45ECh. 3 - Which system has the higher entropy? a A clean...Ch. 3 - Which system has the higher entropy? a 1g of solid...Ch. 3 - The absolute entropy of He at 298.15K is...Ch. 3 - The absolute entropy of Kr at 298.15K is...Ch. 3 - The element helium is thought to remain a liquid...Ch. 3 - Order the following substances in order of...Ch. 3 - The molar entropy change for a process is...Ch. 3 - What is the entropy change of a process if ...Ch. 3 - One mole of ideal gas expands isothermally and...Ch. 3 - Why isnt the entropy of elements in their standard...Ch. 3 - Determine the entropy of formation, fS, of the...Ch. 3 - The thermite reaction has solid aluminum powder...Ch. 3 - Prob. 3.58ECh. 3 - Determine the differences in the rxnS under...Ch. 3 - Calcium carbonate has two crystalline forms,...Ch. 3 - The chemical formula for gasoline can be...Ch. 3 - Prob. 3.62ECh. 3 - Prob. 3.63ECh. 3 - Plants take in CO2(g) and H2O(l) and make glucose,...Ch. 3 - Prob. 3.65ECh. 3 - Prob. 3.66ECh. 3 - Plots of Cp/T versus T are used to determine the...
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
  • Text book image
    Chemistry: Principles and Reactions
    Chemistry
    ISBN:9781305079373
    Author:William L. Masterton, Cecile N. Hurley
    Publisher:Cengage Learning
    Text book image
    Principles of Modern Chemistry
    Chemistry
    ISBN:9781305079113
    Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
    Publisher:Cengage Learning
    Text book image
    General Chemistry - Standalone book (MindTap Cour...
    Chemistry
    ISBN:9781305580343
    Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
    Publisher:Cengage Learning
  • Text book image
    Chemistry
    Chemistry
    ISBN:9781305957404
    Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
    Publisher:Cengage Learning
    Text book image
    Chemistry: An Atoms First Approach
    Chemistry
    ISBN:9781305079243
    Author:Steven S. Zumdahl, Susan A. Zumdahl
    Publisher:Cengage Learning
    Text book image
    Chemistry
    Chemistry
    ISBN:9781133611097
    Author:Steven S. Zumdahl
    Publisher:Cengage Learning
Text book image
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Text book image
Principles of Modern Chemistry
Chemistry
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:Cengage Learning
Text book image
General Chemistry - Standalone book (MindTap Cour...
Chemistry
ISBN:9781305580343
Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry: An Atoms First Approach
Chemistry
ISBN:9781305079243
Author:Steven S. Zumdahl, Susan A. Zumdahl
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781133611097
Author:Steven S. Zumdahl
Publisher:Cengage Learning
Step by Step Stoichiometry Practice Problems | How to Pass ChemistryMole Conversions Made Easy: How to Convert Between Grams and Moles; Author: Ketzbook;https://www.youtube.com/watch?v=b2raanVWU6c;License: Standard YouTube License, CC-BY