Physical Chemistry Third Edition

94 2 Work, Heat, and Energy: The First Law of Thermodynamics

PROBLEMS

Section 2.7: Calculation of Enthalpy Changes of a Class of
Chemical Reactions

2.48 Calculate∆H◦and∆U◦for the reactions at 298.15 K:

a.C 3 H 8 (g)+5O 2 (g)−→3CO 2 (g)+4H 2 O(l)

b.2SO 2 (g)+O 2 (g)−→2SO 3 (g)

c.SO 3 (g) + H 2 O(g)−→H 2 SO 4 (l)

2.49 Calculate∆H◦and∆U◦for the reactions at 298.15 K:

a.4 CuO(s)−→2Cu 2 O(s) + O 2 (g)

b.2 CO(g) + O 2 (g)−→2CO 2 (g)

c.C 2 H 5 OH(l)+3O 2 (g)−→2CO 2 (g)+3H 2 O(l)

2.50 Calculate∆H◦for the reactions of Problem 2.48 at
75 ◦C.

2.51 Calculate∆H◦for the reactions of Problem 2.49 at 75◦C.

2.52a.Find the values of the enthalpy changes of formation of

methane, carbon dioxide, and liquid water at 373.15 K,

using heat capacity values from Table A.8.

b.Using the values from part a, find the standard-state

enthalpy change for the reaction at 373.15 K:

CH 4 (g)+2O 2 (g)−→CO 2 (g)+2H 2 O(l)

c.Find the standard-state enthalpy change of the reaction

of part b, using Eq. (2.7-19). Comment on the

comparison of your answer with that of part b.

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

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

b.Using the value of∆vapHm(H 2 O) and the result of part

a, find∆H◦of this reaction for the case that the water

is vapor.

c.Recalculate this quantity using∆fHm(H 2 O(g)) and

compare with your result of part a. Comment on any

difference.

2.54 The molar enthalpy change of combustion of glycerol at

298.15 K is equal to− 393 .73 kcal mol−^1. Convert this to

kJ mol−^1 and find the value of∆fH◦of glycerol at this

temperature.

2.55 a.The molar enthalpy change of combustion of sucrose,

C 12 H 22 O 11 , at 298.15 K is equal to− 5640 .9kJmol−^1.

Calculate its enthalpy change of formation at 298.15 K.

Calculate∆U◦for the combustion reaction.

b.The molar enthalpy change of combustion of

stearic acid, C 18 H 36 O 2 , at 298.15 K is equal to

–11280.6 kJ mol−^1. Calculate its enthalpy change of

formation at 298.15 K. Compare its enthalpy change of

combustion per gram with that of sucrose.

2.56 Find the value of∆H◦for the combustion of methane

at 125◦C. State any assumptions. Assume that the

heat capacities are constant between 25◦C and

125 ◦C.

2.8 Calculation of Energy Changes of Chemical

Reactions

It would be possible to make tables of energy changes of formation and to calculate

∆Uvalues in the same way as∆Hvalues are calculated from enthalpy changes of

formation. However, adequate accuracy can be achieved without constructing a table

of∆fUvalues. From the definition of the enthalpy we can write an expression for∆U

for a chemical reaction:

∆U∆H−∆(PV) (2.8-1)

Ordinarily∆(PV) is much smaller than∆H, so that a less accurate calculation of

∆(PV) might suffice. For example, if∆His 1000 times larger than∆(PV) and if five

significant digits are desired in∆U, then five significant digits are required in∆Hbut

only two significant digits are needed in∆(PV).