Chemical Principles: The Quest for Insight
Chemical Principles: The Quest for Insight
7th Edition
ISBN: 9781464183959
Author: Peter Atkins, Loretta Jones, Leroy Laverman
Publisher: W. H. Freeman
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Chapter 4, Problem 4I.5E
Interpretation Introduction

Interpretation:

The value of ΔS and ΔStotal for the process have to be determined.

Concept Introduction:

The heat capacity is the ratio of the energy supplied in the form of heat to the rise in the temperature of the system.  The mathematical relation for the heat capacity is shown below.

  C=qΔT

The degree of randomness in a system is the predicted according to its respective entropy.  Higher the entropy greater will be the disorder in the system.  The mathematical expression for the calculation of entropy of the system is shown below.

  ΔS=qrevT

Expert Solution & Answer
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Explanation of Solution

The mass of water at 20°C is 50g.  However, the mass of water at 50°C is 65g.  The specific heat capacity of water is 4.184Jg1K1.

The unit conversion of temperature of two different samples of water from °C to K is shown below.

    T1=20+273K=293KT2=50+273K=323K

As per the given data in the question, there is no energy lost to the surroundings.  Therefore, the heat loss by the water at 20°C is equal to the heat gained by the water at 50°C.  The mathematical expression representing this is shown below.

    m1Cs(T1T)=m2Cs(T T2)        (1)

Where,

  • m1 is the mass of first sample.
  • m2 is the mass of second sample.
  • Cs is the specific heat capacity of water.
  • T1 is the initial temperature of first sample.
  • T2 is the initial temperature of second sample.
  • T is the final temperature of the system.

The value of m1 is 50g.

The value of m2 is 65g.

The value of Cs is 4.184Jg1K1.

The value of T1 is 293K.

The value of T2 is 323K.

Substitute the value of m1, mH2O, Cs, T1 and T2 in equation (1).

    (50g)×(4.184Jg1K1)×(293KT)=(65g)×(4.184Jg1K1)×(T323K)(50g)×(293KT)=(65g)×(T323K)14650K50T=65T20995K65T+50T=14650K+20995K

On further calculation the final temperature of the system is calculated as shown below.

    115T=35645KT=35645115K=309.95K

Therefore, the final temperature of the system is 309.95K.

The relation to calculate the change in the entropy of the water at 20°C is shown below.

    ΔS=mCsln(TfTi)        (2)

Where,

  • ΔS is change in entropy.
  • m is the mass of sample.
  • Cs is the specific heat capacity.
  • Ti is the initial temperature of the system.
  • Tf is the final temperature of the system.

The value of m is 50g.

The value of Cs is 4.184Jg1K1.

The value of Ti is 293K.

The value of Tf is 309.95K.

Substitute the value of m, Cs, Ti and Tf in equation (2).

    ΔS=(50g)×(4.184Jg1K1)×ln(309.95K293K)=(209.2JK1)×ln(1.0578)=(209.2JK1)×(0.05619)=+11.75JK1

Therefore, the change in the entropy of the water at 20°C is +11.75JK1.

The relation to calculate the change in the entropy of the water at 50°C is same as equation (2).

The value of m is 65g.

The value of Cs is 4.184Jg1K1.

The value of Ti is 323K.

The value of Tf is 309.95K.

Substitute the value of m, Cs, Ti and Tf in equation (2).

    ΔS=(65g)×(4.184Jg1K1)×ln(309.95K323K)=(271.96JK1)×ln(0.9595)=(271.96JK1)×(0.0413)=11.23JK1

Therefore, the change in the entropy of the water at 50°C is 11.23JK1.

The relation to calculate the total change in the entropy is shown below.

    ΔStotal=ΔS(20°C)+ΔS(50°C)        (3)

Where,

  • ΔStotal is the total change in the entropy.
  • ΔS(20°C) is the change in the entropy at 20°C.
  • ΔS(50°C) is the change in the entropy at 50°C.

The value of ΔS(20°C) is +11.75JK1.

The value of ΔS(50°C) is 11.23JK1.

Substitute the value of ΔS(20°C) and ΔS(50°C) in equation (3).

  ΔStotal=+11.75JK111.23JK1=0.52JK1

Therefore, the total change in the entropy is 0.52JK1.

The mixture of two different samples of water is in the insulated vessel.  The thermally insulated vessel is considered as the isolated system as there is neither exchange of energy nor matter takes place from it.  Therefore, the value of ΔSsurr is zero.

The relation to calculate ΔS is shown below.

    ΔS=ΔStotalΔSsurr        (4)

Where,

  • ΔStotal is the total change in the entropy.
  • ΔS is the change in the entropy of system.
  • ΔSsurr is the change in the entropy of surrounding.

The value of ΔStotal is 0.52JK1.

The value of ΔSsurr is 0.0JK1.

Substitute the value of ΔStotal and ΔSsurr in equation (4).

    ΔS=0.52JK10.0JK1=0.52JK1

Thus, the value of both ΔS and ΔStotal for the process is 0.52JK-1_.

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Chapter 4 Solutions

Chemical Principles: The Quest for Insight

Ch. 4 - Prob. 4A.3ECh. 4 - Prob. 4A.4ECh. 4 - Prob. 4A.5ECh. 4 - Prob. 4A.6ECh. 4 - Prob. 4A.7ECh. 4 - Prob. 4A.8ECh. 4 - Prob. 4A.9ECh. 4 - Prob. 4A.10ECh. 4 - Prob. 4A.11ECh. 4 - Prob. 4A.12ECh. 4 - Prob. 4A.13ECh. 4 - Prob. 4A.14ECh. 4 - Prob. 4B.1ASTCh. 4 - Prob. 4B.1BSTCh. 4 - Prob. 4B.2ASTCh. 4 - Prob. 4B.2BSTCh. 4 - Prob. 4B.3ASTCh. 4 - Prob. 4B.3BSTCh. 4 - Prob. 4B.1ECh. 4 - Prob. 4B.2ECh. 4 - Prob. 4B.3ECh. 4 - Prob. 4B.4ECh. 4 - Prob. 4B.5ECh. 4 - Prob. 4B.6ECh. 4 - Prob. 4B.7ECh. 4 - Prob. 4B.8ECh. 4 - Prob. 4B.9ECh. 4 - Prob. 4B.10ECh. 4 - Prob. 4B.11ECh. 4 - Prob. 4B.12ECh. 4 - Prob. 4B.13ECh. 4 - Prob. 4B.14ECh. 4 - Prob. 4B.15ECh. 4 - Prob. 4B.16ECh. 4 - Prob. 4C.1ASTCh. 4 - Prob. 4C.1BSTCh. 4 - Prob. 4C.2ASTCh. 4 - Prob. 4C.2BSTCh. 4 - Prob. 4C.3ASTCh. 4 - Prob. 4C.3BSTCh. 4 - Prob. 4C.4ASTCh. 4 - Prob. 4C.4BSTCh. 4 - Prob. 4C.1ECh. 4 - Prob. 4C.2ECh. 4 - Prob. 4C.3ECh. 4 - Prob. 4C.4ECh. 4 - Prob. 4C.5ECh. 4 - Prob. 4C.6ECh. 4 - Prob. 4C.7ECh. 4 - Prob. 4C.8ECh. 4 - Prob. 4C.9ECh. 4 - Prob. 4C.10ECh. 4 - Prob. 4C.11ECh. 4 - Prob. 4C.12ECh. 4 - Prob. 4C.13ECh. 4 - Prob. 4C.14ECh. 4 - Prob. 4C.15ECh. 4 - Prob. 4C.16ECh. 4 - Prob. 4D.1ASTCh. 4 - Prob. 4D.1BSTCh. 4 - Prob. 4D.2ASTCh. 4 - Prob. 4D.2BSTCh. 4 - Prob. 4D.3ASTCh. 4 - Prob. 4D.3BSTCh. 4 - Prob. 4D.4ASTCh. 4 - Prob. 4D.4BSTCh. 4 - Prob. 4D.5ASTCh. 4 - Prob. 4D.5BSTCh. 4 - Prob. 4D.6ASTCh. 4 - Prob. 4D.6BSTCh. 4 - Prob. 4D.7ASTCh. 4 - Prob. 4D.7BSTCh. 4 - Prob. 4D.1ECh. 4 - Prob. 4D.2ECh. 4 - Prob. 4D.3ECh. 4 - Prob. 4D.4ECh. 4 - Prob. 4D.5ECh. 4 - Prob. 4D.6ECh. 4 - Prob. 4D.7ECh. 4 - Prob. 4D.8ECh. 4 - Prob. 4D.10ECh. 4 - Prob. 4D.11ECh. 4 - Prob. 4D.13ECh. 4 - Prob. 4D.14ECh. 4 - Prob. 4D.15ECh. 4 - Prob. 4D.16ECh. 4 - Prob. 4D.17ECh. 4 - Prob. 4D.18ECh. 4 - Prob. 4D.19ECh. 4 - Prob. 4D.20ECh. 4 - Prob. 4D.21ECh. 4 - Prob. 4D.22ECh. 4 - Prob. 4D.23ECh. 4 - Prob. 4D.24ECh. 4 - Prob. 4D.25ECh. 4 - Prob. 4D.26ECh. 4 - Prob. 4D.29ECh. 4 - Prob. 4D.30ECh. 4 - Prob. 4E.1ASTCh. 4 - Prob. 4E.1BSTCh. 4 - Prob. 4E.2ASTCh. 4 - Prob. 4E.2BSTCh. 4 - Prob. 4E.5ECh. 4 - Prob. 4E.6ECh. 4 - Prob. 4E.7ECh. 4 - Prob. 4E.8ECh. 4 - Prob. 4E.9ECh. 4 - Prob. 4E.10ECh. 4 - Prob. 4F.1ASTCh. 4 - Prob. 4F.1BSTCh. 4 - Prob. 4F.2ASTCh. 4 - Prob. 4F.2BSTCh. 4 - Prob. 4F.3ASTCh. 4 - Prob. 4F.3BSTCh. 4 - Prob. 4F.4ASTCh. 4 - Prob. 4F.4BSTCh. 4 - Prob. 4F.5ASTCh. 4 - Prob. 4F.5BSTCh. 4 - Prob. 4F.6ASTCh. 4 - Prob. 4F.6BSTCh. 4 - Prob. 4F.7ASTCh. 4 - Prob. 4F.7BSTCh. 4 - Prob. 4F.8ASTCh. 4 - Prob. 4F.8BSTCh. 4 - Prob. 4F.9ASTCh. 4 - Prob. 4F.9BSTCh. 4 - Prob. 4F.1ECh. 4 - Prob. 4F.2ECh. 4 - Prob. 4F.3ECh. 4 - Prob. 4F.4ECh. 4 - Prob. 4F.5ECh. 4 - Prob. 4F.6ECh. 4 - Prob. 4F.7ECh. 4 - Prob. 4F.9ECh. 4 - Prob. 4F.10ECh. 4 - Prob. 4F.11ECh. 4 - Prob. 4F.12ECh. 4 - Prob. 4F.13ECh. 4 - Prob. 4F.14ECh. 4 - Prob. 4F.15ECh. 4 - Prob. 4F.16ECh. 4 - Prob. 4F.17ECh. 4 - Prob. 4G.1ASTCh. 4 - Prob. 4G.1BSTCh. 4 - Prob. 4G.2ASTCh. 4 - Prob. 4G.2BSTCh. 4 - Prob. 4G.1ECh. 4 - Prob. 4G.2ECh. 4 - Prob. 4G.3ECh. 4 - Prob. 4G.5ECh. 4 - Prob. 4G.7ECh. 4 - Prob. 4G.8ECh. 4 - Prob. 4G.9ECh. 4 - Prob. 4G.10ECh. 4 - Prob. 4H.1ASTCh. 4 - Prob. 4H.1BSTCh. 4 - Prob. 4H.2ASTCh. 4 - Prob. 4H.2BSTCh. 4 - Prob. 4H.1ECh. 4 - Prob. 4H.2ECh. 4 - Prob. 4H.3ECh. 4 - Prob. 4H.4ECh. 4 - Prob. 4H.5ECh. 4 - Prob. 4H.6ECh. 4 - Prob. 4H.7ECh. 4 - Prob. 4H.8ECh. 4 - Prob. 4H.9ECh. 4 - Prob. 4H.10ECh. 4 - Prob. 4H.11ECh. 4 - Prob. 4I.1ASTCh. 4 - Prob. 4I.1BSTCh. 4 - Prob. 4I.2ASTCh. 4 - Prob. 4I.2BSTCh. 4 - Prob. 4I.3ASTCh. 4 - Prob. 4I.3BSTCh. 4 - Prob. 4I.4ASTCh. 4 - Prob. 4I.4BSTCh. 4 - Prob. 4I.1ECh. 4 - Prob. 4I.2ECh. 4 - Prob. 4I.3ECh. 4 - Prob. 4I.4ECh. 4 - Prob. 4I.5ECh. 4 - Prob. 4I.6ECh. 4 - Prob. 4I.7ECh. 4 - Prob. 4I.8ECh. 4 - Prob. 4I.9ECh. 4 - Prob. 4I.10ECh. 4 - Prob. 4I.11ECh. 4 - Prob. 4I.12ECh. 4 - Prob. 4J.1ASTCh. 4 - Prob. 4J.1BSTCh. 4 - Prob. 4J.2ASTCh. 4 - Prob. 4J.2BSTCh. 4 - Prob. 4J.3ASTCh. 4 - Prob. 4J.3BSTCh. 4 - Prob. 4J.4ASTCh. 4 - Prob. 4J.4BSTCh. 4 - Prob. 4J.5ASTCh. 4 - Prob. 4J.5BSTCh. 4 - Prob. 4J.6ASTCh. 4 - Prob. 4J.6BSTCh. 4 - Prob. 4J.1ECh. 4 - Prob. 4J.2ECh. 4 - Prob. 4J.3ECh. 4 - Prob. 4J.4ECh. 4 - Prob. 4J.5ECh. 4 - Prob. 4J.6ECh. 4 - Prob. 4J.7ECh. 4 - Prob. 4J.8ECh. 4 - Prob. 4J.9ECh. 4 - Prob. 4J.11ECh. 4 - Prob. 4J.12ECh. 4 - Prob. 4J.13ECh. 4 - Prob. 4J.14ECh. 4 - Prob. 4J.15ECh. 4 - Prob. 4J.16ECh. 4 - Prob. 4.8ECh. 4 - Prob. 4.14ECh. 4 - Prob. 4.16ECh. 4 - Prob. 4.19ECh. 4 - Prob. 4.20ECh. 4 - Prob. 4.21ECh. 4 - Prob. 4.23ECh. 4 - Prob. 4.25ECh. 4 - Prob. 4.27ECh. 4 - Prob. 4.28ECh. 4 - Prob. 4.29ECh. 4 - Prob. 4.30ECh. 4 - Prob. 4.31ECh. 4 - Prob. 4.32ECh. 4 - Prob. 4.33ECh. 4 - Prob. 4.34ECh. 4 - Prob. 4.35ECh. 4 - Prob. 4.36ECh. 4 - Prob. 4.37ECh. 4 - Prob. 4.39ECh. 4 - Prob. 4.40ECh. 4 - Prob. 4.41ECh. 4 - Prob. 4.45ECh. 4 - Prob. 4.46ECh. 4 - Prob. 4.48ECh. 4 - Prob. 4.49ECh. 4 - Prob. 4.53ECh. 4 - Prob. 4.57ECh. 4 - Prob. 4.59E
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