Physical Chemistry Third Edition

100 2 Work, Heat, and Energy: The First Law of Thermodynamics

From enthalpy changes of formation at 298.15 K,

∆H∆fH◦(C 2 H 6 )−∆fH◦(C 2 H 4 )−∆fH◦(H 2 )

− 84 .68 kJ mol−^1 −(52.26 kJ mol−^1 )− 0 − 136 .94 kJ mol−^1

∆U− 136 .94 kJ mol−^1 −(− 1 )

(

8 .3145 J K−^1 mol−^1

)

(298.15 K)

− 136 .94 kJ mol−^1 + 2 .48 kJ mol−^1 − 134 .46 kJ mol−^1

The error of 9 kJ mol−^1 in the previous example is typical. It is larger than the

difference between∆Hand∆U, so that the value of∆Uobtained from average

bond energy values is ordinarily used for∆Hwithout correction for the value of

∆(PV). Average bond energies are used only if accurate enthalpy changes of for-

mation are not available, since the results are only approximately correct. Average

bond energies cannot be used for reactions involving solids or liquids, where inter-

molecular forces make important contributions. Various schemes have been devised

to improve on the simple scheme that we have presented and have produced better

results.^7

Exercise 2.32

Using average bond energy values, estimate∆Hfor the reaction:

C 2 H 2 (g)+H 2 (g)−→C 2 H 6 (g)

Compare your value with the value of∆Hobtained from enthalpy changes of formation.

PROBLEMS

Section 2.8: Calculation of Energy Changes of Chemical
Reactions

2.57 a.Calculate∆H◦for the reaction at 298.15 K:

CH 4 (g)+O 2 (g)−→CO 2 (g)+H 2 O(l)

(Balance the reaction first.)

b.Calculate∆U◦, neglecting the volume of the liquid

water.

c.Calculate∆U◦without neglecting the volume of the

liquid water, takingVm 18 .0cm^3 mol−^1 for liquid

water.

2.58 a.Calculate the value of∆fU◦for carbon dioxide and for

carbon monoxide at 298.15 K.

b. Calculate∆U◦for the following reaction at 298.15 K,

using the results of part a:

2CO(g)+O 2 (g)−→2CO 2 (g)

c.Calculate∆H◦using Eq. (2.8-4) and compare with

your result from part a.

2.59 a.Estimate the enthalpy change of the following reaction,

using average bond energies:

2C 2 H 6 (g)+7O 2 (g)−→4CO 2 (g)+6H 2 O(g)

(^7) See for example D. W. Smith,J. Chem. Soc., Faraday Trans., 94 , 3087 (1998).