ATKINS' PHYSICAL CHEMISTRY-ACCESS
ATKINS' PHYSICAL CHEMISTRY-ACCESS
11th Edition
ISBN: 9780198834700
Author: ATKINS
Publisher: OXF
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Chapter 2, Problem 2C.8BE
Interpretation Introduction

Interpretation: The value of ΔrH° at 750K has to be calculated for the given reaction.

Concept introduction: Enthalpy is the internal heat content of the system.  Under constant pressure, a system can do expansion work under the effect of energy supplied as heat known as enthalpy change of the system.  Therefore, the measure of amount of heat supplied to the system gives the enthalpy change of the system.

Expert Solution & Answer
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Answer to Problem 2C.8BE

The value of ΔrH° at 750K is 23115.911kJmol1_.

Explanation of Solution

The given reaction is,

  N2(g)+3H2(g)2NH3(g)

The standard enthalpy of the reaction is, ΔrH° is calculated by the expression,

    ΔrHο=mΔHfο(products)nΔHfο(reactants)                                (1)

Where,

  • ΔHfο(products) is the standard enthalpy of formation of products.
  • ΔHfο(reactants) is the standard enthalpy of formation of reactants.
  • m is the stoichiometric coefficient of products.
  • n is the stoichiometric coefficient of reactants.

The temperature dependent heat capacity is given by the expression,

    ΔrCpο=Δa+ΔbT+Δc/T2                                                                             (2)

Where,

  • Δa,Δb,Δc are the temperature dependent variables.
  • T is the temperature.

For the reaction, Δa is calculated by the expression,

    Δa=va(products)va(reactants)                                                      (3)

Where,

  • va(products) is the sum of a of products.
  • va(reactants) is the sum of a of reactants.
  • v is the stoichiometry.

For the reaction, Δb is calculated by the expression,

    Δb=vb(products)vb(reactants)                                                      (4)

Where,

  • vb(products) is the sum of b of products.
  • vb(reactants) is the sum of b of reactants.
  • v is the stoichiometry.

For the reaction, Δc is calculated by the expression,

    Δc=vc(products)vc(reactants)                                                      (5)

Where,

  • vc(products) is the sum of c of products.
  • vc(reactants) is the sum of c of reactants.
  • v is the stoichiometry.

Enthalpy at a temperature T2=750K is calculated by the expression,

    ΔrH°(T2)=ΔrH°(T1)+T1T2ΔrCp°dT=ΔrH°(T1)+T1T2(a+bT+c/T2)dT

    ΔrH°(T2)=ΔrH°(T1)+Δa(T2T1)+12Δb(T22T12)Δc(1T21T1)             (6)

The value of Δa is calculated for the given reaction by equation (3)

    Δa=2×a(NH3,g)[3×a(H2,g)+a(N2,g)]

The value of a for NH3, N2 and H2 is 29.75JK1mol1, 28.58JK1mol1 and 27.28JK1mol1, respectively.  Substitute the values in the above equation to calculate the value of Δa.

    Δa=2×29.75JK1mol1(28.58JK1mol1+3×27.28JK1mol1)=50.92JK1mol1=50.92kJK1mol1

The value of Δb is calculated for the given reaction by equation (4)

    Δb=2×b(NH3,g)[3×b(H2,g)+b(N2,g)]

The value of b for NH3, N2 and H2 is 25.1×103JK2mol1, 3.77×103JK2mol1 and 3.26×103JK2mol1 respectively.  Substitute the values in the above equation to calculate the value of Δb.

  Δb=2×25.1×103JK2mol1(3.77×103JK2mol1+3×3.26×103JK2mol1)=0.03665JK2mol1=0.03665×103kJK2mol1

The value of Δc is calculated for the given reaction by equation (5)

    Δc=2×c(NH3,g)[3×c(H2,g)+c(N2,g)]

The value of c for NH3, N2 and H2 is 1.55×105JKmol1, 0.50×105JKmol1 and 0.50×105JKmol1, respectively.  Substitute the values in the above equation to calculate the value of Δb.

    Δc=2×1.55×105JKmol1(0.50×105JKmol1+3×0.50×105JKmol1)=4.1×105JKmol1=4.1×102kJKmol1

To calculate the value of ΔrH° at 298K, use equation (1).

    ΔrHο=2×ΔHfο(NH3,g)[3×ΔHfο(H2,g)+ΔHfο(N2,g)]

Substitute the values of ΔHfο(NH3,g)=-46.11kJmol-1, ΔHfο(N2,g)=0kJmol1 and ΔHfο(H2,g)=0kJmol1 in the above equation to calculate ΔrH°.

    ΔrHο=2×46.11kJmol1(0+0)kJmol1=92.22kJmol1

To calculate the value of ΔrH° at 750K, use equation (6).

    ΔrH°(750K)=ΔrH°(298K)+Δa(750K298K)+12Δb((750K)2(298K)2)Δc(1750K1298K)=92.22kJmol150.92kJK1mol1(750K298K)+12×(0.03665×103kJK2mol1)((750K)2(298K)2)4.1×102kJKmol1(1750K1298K)=23115.911kJmol1_

Hence, the value of ΔrH° at 750K is 23115.911kJmol1_.

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Chapter 2 Solutions

ATKINS' PHYSICAL CHEMISTRY-ACCESS

Ch. 2 - Prob. 2A.4DQCh. 2 - Prob. 2A.5DQCh. 2 - Prob. 2A.1AECh. 2 - Prob. 2A.1BECh. 2 - Prob. 2A.2AECh. 2 - Prob. 2A.2BECh. 2 - Prob. 2A.3AECh. 2 - Prob. 2A.3BECh. 2 - Prob. 2A.4AECh. 2 - Prob. 2A.4BECh. 2 - Prob. 2A.5AECh. 2 - Prob. 2A.5BECh. 2 - Prob. 2A.6AECh. 2 - Prob. 2A.6BECh. 2 - Prob. 2A.1PCh. 2 - Prob. 2A.2PCh. 2 - Prob. 2A.3PCh. 2 - Prob. 2A.4PCh. 2 - Prob. 2A.5PCh. 2 - Prob. 2A.6PCh. 2 - Prob. 2A.7PCh. 2 - Prob. 2A.8PCh. 2 - Prob. 2A.9PCh. 2 - Prob. 2A.10PCh. 2 - Prob. 2B.1DQCh. 2 - Prob. 2B.2DQCh. 2 - Prob. 2B.1AECh. 2 - Prob. 2B.1BECh. 2 - Prob. 2B.2AECh. 2 - Prob. 2B.2BECh. 2 - Prob. 2B.3AECh. 2 - Prob. 2B.3BECh. 2 - Prob. 2B.4AECh. 2 - Prob. 2B.4BECh. 2 - Prob. 2B.1PCh. 2 - Prob. 2B.2PCh. 2 - Prob. 2B.3PCh. 2 - Prob. 2B.4PCh. 2 - Prob. 2B.5PCh. 2 - Prob. 2C.1DQCh. 2 - Prob. 2C.2DQCh. 2 - Prob. 2C.3DQCh. 2 - Prob. 2C.4DQCh. 2 - Prob. 2C.1AECh. 2 - Prob. 2C.1BECh. 2 - Prob. 2C.2AECh. 2 - Prob. 2C.2BECh. 2 - Prob. 2C.3AECh. 2 - Prob. 2C.3BECh. 2 - Prob. 2C.4AECh. 2 - Prob. 2C.4BECh. 2 - Prob. 2C.5AECh. 2 - Prob. 2C.5BECh. 2 - Prob. 2C.6AECh. 2 - Prob. 2C.6BECh. 2 - Prob. 2C.7AECh. 2 - Prob. 2C.7BECh. 2 - Prob. 2C.8AECh. 2 - Prob. 2C.8BECh. 2 - Prob. 2C.1PCh. 2 - Prob. 2C.2PCh. 2 - Prob. 2C.3PCh. 2 - Prob. 2C.4PCh. 2 - Prob. 2C.5PCh. 2 - Prob. 2C.6PCh. 2 - Prob. 2C.7PCh. 2 - Prob. 2C.8PCh. 2 - Prob. 2C.9PCh. 2 - Prob. 2C.10PCh. 2 - Prob. 2C.11PCh. 2 - Prob. 2D.1DQCh. 2 - Prob. 2D.2DQCh. 2 - Prob. 2D.1AECh. 2 - Prob. 2D.1BECh. 2 - Prob. 2D.2AECh. 2 - Prob. 2D.2BECh. 2 - Prob. 2D.3AECh. 2 - Prob. 2D.3BECh. 2 - Prob. 2D.4AECh. 2 - Prob. 2D.4BECh. 2 - Prob. 2D.5AECh. 2 - Prob. 2D.5BECh. 2 - Prob. 2D.1PCh. 2 - Prob. 2D.2PCh. 2 - Prob. 2D.3PCh. 2 - Prob. 2D.4PCh. 2 - Prob. 2D.5PCh. 2 - Prob. 2D.6PCh. 2 - Prob. 2D.7PCh. 2 - Prob. 2D.8PCh. 2 - Prob. 2D.9PCh. 2 - Prob. 2E.1DQCh. 2 - Prob. 2E.2DQCh. 2 - Prob. 2E.1AECh. 2 - Prob. 2E.1BECh. 2 - Prob. 2E.2AECh. 2 - Prob. 2E.2BECh. 2 - Prob. 2E.3AECh. 2 - Prob. 2E.3BECh. 2 - Prob. 2E.4AECh. 2 - Prob. 2E.4BECh. 2 - Prob. 2E.5AECh. 2 - Prob. 2E.5BECh. 2 - Prob. 2E.1PCh. 2 - Prob. 2E.2PCh. 2 - Prob. 2.1IACh. 2 - Prob. 2.3IACh. 2 - Prob. 2.4IACh. 2 - Prob. 2.5IACh. 2 - Prob. 2.6IACh. 2 - Prob. 2.7IA
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