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 5, Problem 5G.22E

(a)

Interpretation Introduction

Interpretation:

The equilibrium constant at 25oC has to be determined for the given reaction.

  CH4(g)+Cl2(g)CH3Cl(g)+HCl(g)

Concept Introduction:

The equilibrium constant of a reaction can be calculated using the given expression,

  lnK=-ΔGroRTwhere,R=Gas constant (8.314JK-1mol-1)ΔG°r=StandardGibb'sfreeenergyT=TemperatureK= Equilibrium constant

(a)

Expert Solution
Check Mark

Answer to Problem 5G.22E

The equilibrium constant of the given reaction is 2.0×101.

Explanation of Solution

Given reaction is

The synthesis of trichloromethane (chloroform) from natural gas (methane):

  CH4(g)+Cl2(g)CH3Cl(g)+HCl(g)

Temperature of the reaction is 298K,

The ΔG°f value of CH3Cl is 48.5kJmol-1

The ΔG°f value of HCl is 95.30kJmol-1

The ΔG°f value of Cl2 is 0

The ΔG°f value of CH4 is 50.72kJmol-1

R=8.3145 JK-1mol-1

T=298K

Here, ΔG°r is calculated using given formula,

  ΔG°r=[ΔG°fCH3Cl(g)+ΔG°fHCl(g)]-[ΔG°fCH4(g)+ΔG°fCl2(g)]=(48.5×10395.30×103)(50.72×1030)=4.0×103

Now, the equilibrium constant of the reaction is calculated as

  lnK=-ΔGroRT=-4.0×103Jmol-1(8.3145JK-1mol-1)×(298K)=1.61

To calculate K value, inverse logarithm is taken for the above reaction.

  K=e1.61=2.0×101

Therefore, the K value of given reaction is 2.0×101.

(b)

Interpretation Introduction

Interpretation:

The equilibrium constant at 25oC has to be determined for the given reaction.

  C2H2(g)+2H2(g)C2H6(g)

Concept introduction:

Refer to part (a).

(b)

Expert Solution
Check Mark

Answer to Problem 5G.22E

The equilibrium constant of the given reaction is.

Explanation of Solution

Given reaction is

The hydrogenation of acetylene to ethane:

  C2H2(g)+2H2(g)C2H6(g)

Temperature of the reaction is 298K,

The ΔG°f value of C2H6 is 32.82kJmol-1

The ΔG°f value of C2H2 is +209.20kJmol-1

The ΔG°f value of H2 is 0

R=8.3145 JK-1mol-1

T=298K

Here, ΔG°r is calculated using given formula,

  ΔG°r=ΔG°f(C2H6(g))-[ΔG°f(C2H2(g))+2ΔG°f(H2(g))]=(-32.82×103)[209.20×1030]=2.42×105

Now, the equilibrium constant of the reaction is calculated as

  lnK=-ΔGroRT=2.42×105Jmol-1(8.3145JK-1mol-1)×(298K)=97.7

To calculate K value, inverse logarithm is taken for the above reaction.

  K=e97.7=2.7×1042

Therefore, the K value of given reaction is 1×1090.

(c)

Interpretation Introduction

Interpretation:

The equilibrium constant at 25oC has to be determined for the given reaction.

  3NO2(g)+H2O(l)2HNO3(aq)+NO(g)

Concept introduction:

Refer to part (a).

(c)

Expert Solution
Check Mark

Answer to Problem 5G.22E

The equilibrium constant of the given reaction is 1.8×109.

Explanation of Solution

Given reaction is

The final step in the industrial production of nitric acid:

  3NO2(g)+H2O(l)2HNO3(aq)+NO(g)

Temperature of the reaction is 298K,

The ΔG°f value of HNO3 is 111.25kJmol-1

The ΔG°f value of NO is +86.55kJmol-1

The ΔG°f value of NO2 is +51.31

The ΔG°f value of H2O is 237.13kJmol-1

R=8.3145 JK-1mol-1

T=298K

Here, ΔG°r is calculated using given formula,

  ΔG°r=[ΔG°f2HNO3(aq)+ΔG°fNO(g)]-[3ΔG°fNO2(g)+ΔG°fH2O(aq)]=[2×(-111.25×103)+86.55×103][3×(51.31×103)237.13×103]=5.28×104

Now, the equilibrium constant of the reaction is calculated as

  lnK=-ΔGroRT=5.28×104Jmol-1(8.3145JK-1mol-1)×(298K)=21.31

To calculate K value, inverse logarithm is taken for the above reaction.

  K=e21.31=1.8×109

Therefore, the K value of given reaction is 1.8×109.

(d)

Interpretation Introduction

Interpretation:

The equilibrium constant at 25oC has to be determined for the given reaction.

  N2H4(l)+O2(g)N2(g)+2H2O(l)

Concept introduction:

Refer to part (a).

(d)

Expert Solution
Check Mark

Answer to Problem 5G.22E

The equilibrium constant of the given reaction is 2.4×10109.

Explanation of Solution

Given reaction is

The reaction of hydrazine and oxygen in a rocket:

  N2H4(l)+O2(g)N2(g)+2H2O(l)

The ΔG°f value of N2 is 0

The ΔG°f value of H2O is 237.13kJmol-1

The ΔG°f value of N2H4 is +149.34kJmol-1

The ΔG°f value of O2 is 0

Temperature of the reaction is 298K

R=8.3145 JK-1mol-1

T=298K

Here, ΔG°r is calculated using given formula,

  ΔG°r=[ΔG°fN2(g)+2ΔG°fH2O(l)]-[ΔG°fN2H4(l)+ΔG°fO2(g)]=[0+2×(237.13×103)][149.34×103)0]=6.24×105

Now, the equilibrium constant of the reaction is calculated as

  lnK=-ΔGroRT=6.24×105Jmol-1(8.3145JK-1mol-1)×(298K)=251.84

To calculate K value, inverse logarithm is taken for the above reaction.

  K=e251.84=2.4×10109

Therefore, the K value of given reaction is 2.4×10109.

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Chapter 5 Solutions

Chemical Principles: The Quest for Insight

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