Elements Of Physical Chemistry
Elements Of Physical Chemistry
7th Edition
ISBN: 9780198796701
Author: ATKINS, P. W. (peter William), De Paula, Julio
Publisher: Oxford University Press
Question
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Chapter 4, Problem 4C.5E

(a)

Interpretation Introduction

Interpretation:

The molar Gibbs energy of mixing when the nitrogen and oxygen are mixed to form air at 298K has to be given.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔG.

Molal Gibbs free energy can be determined using the following formulas as show below,

ΔG=RTlnV1V2Where,ΔG:ChangeinGibbsfreeenergyR:GasconstantT:TemperatureV1:InitialvolumeV2:Finalvolume

The equation for finding ΔGmix is given below:

  ΔGmix=nRTxalnxa+xblnxbn-Numberofmolesxa-molefractionofacomponentxb-molefractionofbcomponentR-UniversalgasconstantT-Temperature

(a)

Expert Solution
Check Mark

Explanation of Solution

Given data:

χN2=0.78χO2=0.22T=298K

The equation for finding ΔGmix is given below:

ΔGmix=RTxalnxa+xblnxb

ΔGmix=RT(xalnxa+xblnxb)=8.314JK-1mol-1×298K(0.78ln0.78+0.22ln0.22)=-1303.2J/mol

(b)

Interpretation Introduction

Interpretation:

The molar entropy of mixing when the nitrogen and oxygen are mixed to form air at 298K has to be given.

Concept introduction:

The equation for finding ΔSmix is given below:

ΔSmix=-nR(xalnxa+xblnxb)n-Numberofmolesxa-molefractionofacomponentxb-molefractionofbcomponentR-Universalgasconstant

(b)

Expert Solution
Check Mark

Explanation of Solution

Given data:

χN2=0.78χO2=0.22T=298K

The equation for finding ΔSmix is given below:

ΔSmix=-R(xalnxa+xblnxb)

ΔSmix=-R(xalnxa+xblnxb)=-8.314JK-1mol-1(0.78ln0.78+0.22ln0.22)=4.373J/K

(c)

Interpretation Introduction

Interpretation:

The mixing is whether spontaneous or not has to be given.

Concept introduction:

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔG.

Molal Gibbs free energy can be determined using the following formulas as show below,

ΔG=RTlnV1V2Where,ΔG:ChangeinGibbsfreeenergyR:GasconstantT:TemperatureV1:InitialvolumeV2:Finalvolume

ΔG=ΔHTΔSwhere,ΔH:EnthalpychangeT:TemperatureΔS:Changeinentropy

For an isomermal reaction enthalpy change is zero, thus this equation can be written as,

ΔG=TΔS=T(CPlnT2T1RlnP2P1)=T(0RlnP2P1)

(c)

Expert Solution
Check Mark

Explanation of Solution

The molar Gibbs energy of mixing when the nitrogen and oxygen are mixed to form air at 298K is calculated to be negative and the molar entropy of mixing when the nitrogen and oxygen are mixed to form air at 298K is calculated to be positive.

ΔGmix=-veΔSmix=+ve

The above conditions satisfies the criteria for spontaneous.

Therefore, the mixing is spontaneous.

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Chapter 4 Solutions

Elements Of Physical Chemistry

Ch. 4 - Prob. 4D.1STCh. 4 - Prob. 4D.2STCh. 4 - Prob. 4D.3STCh. 4 - Prob. 4D.4STCh. 4 - Prob. 4E.1STCh. 4 - Prob. 4E.2STCh. 4 - Prob. 4F.1STCh. 4 - Prob. 4A.1ECh. 4 - Prob. 4A.2ECh. 4 - Prob. 4A.3ECh. 4 - Prob. 4A.4ECh. 4 - Prob. 4A.5ECh. 4 - Prob. 4A.6ECh. 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. 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. 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.9ECh. 4 - Prob. 4D.10ECh. 4 - Prob. 4D.11ECh. 4 - Prob. 4D.12ECh. 4 - Prob. 4D.13ECh. 4 - Prob. 4E.1ECh. 4 - Prob. 4E.2ECh. 4 - Prob. 4E.3ECh. 4 - Prob. 4E.4ECh. 4 - Prob. 4F.1ECh. 4 - Prob. 4F.2ECh. 4 - Prob. 4F.3ECh. 4 - Prob. 4.1DQCh. 4 - Prob. 4.2DQCh. 4 - Prob. 4.3DQCh. 4 - Prob. 4.4DQCh. 4 - Prob. 4.5DQCh. 4 - Prob. 4.6DQCh. 4 - Prob. 4.8DQCh. 4 - Prob. 4.9DQCh. 4 - Prob. 4.10DQCh. 4 - Prob. 4.11DQCh. 4 - Prob. 4.12DQCh. 4 - Prob. 4.13DQCh. 4 - Prob. 4.14DQCh. 4 - Prob. 4.15DQCh. 4 - Prob. 4.1PCh. 4 - Prob. 4.2PCh. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - Prob. 4.8PCh. 4 - Prob. 4.9PCh. 4 - Prob. 4.10PCh. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - Prob. 4.15PCh. 4 - Prob. 4.16PCh. 4 - Prob. 4.17PCh. 4 - Prob. 4.18PCh. 4 - Prob. 4.19PCh. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - Prob. 4.24PCh. 4 - Prob. 4.25PCh. 4 - Prob. 4.26PCh. 4 - Prob. 4.27PCh. 4 - Prob. 4.28PCh. 4 - Prob. 4.29PCh. 4 - Prob. 4.30PCh. 4 - Prob. 4.1PRCh. 4 - Prob. 4.2PRCh. 4 - Prob. 4.3PRCh. 4 - Prob. 4.4PRCh. 4 - Prob. 4.5PRCh. 4 - Prob. 4.6PR
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