Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.3 MOLARREACTIONENTHALPY 322

notinclude the formation of the solvent H 2 O from H 2 and O 2. Instead, the solute once
formed combines with the amount of pure liquid water needed to form the solution. If the
aqueous solute is formed in its standard state, the amount of water needed is very large so
as to have the solute exhibit infinite-dilution behavior.
There is no ordinary reaction that would produce an individualion in solutionfrom its
element or elements without producing other species as well. We can, however, prepare
a consistent set of standard molar enthalpies of formation of ions by assigning a value to
a single reference ion.^7 We can use these values for ions in Eq.11.3.3just like values of
ÅfHfor substances and nonionic solutes. Aqueous hydrogen ion is the usual reference
ion, to which is assigned the arbitrary value

ÅfH(HC, aq)D 0 (at all temperatures) (11.3.4)
To see how we can use this reference value, consider the reaction for the formation of
aqueous HCl (hydrochloric acid):
1
2 H^2 .g/C

1

2 Cl^2 .g/!H

C.aq/CCl.aq/

The standard molar reaction enthalpy at298:15K for this reaction is known, from reaction
calorimetry, to have the valueÅrH D 167:08kJ mol^1. The standard states of the
gaseous H 2 and Cl 2 are, of course, the pure gases acting ideally at pressurep, and the
standard state of each of the aqueous ions is the ion at the standard molality and standard
pressure, acting as if its activity coefficient on a molality basis were 1. From Eq.11.3.3, we
equate the value ofÅrHto the sum

^12 ÅfH(H 2 , g)^12 ÅfH(Cl 2 , g)CÅfH(HC, aq)CÅfH(Cl, aq)

But the first three terms of this sum are zero. Therefore, the value ofÅfH(Cl, aq) is
167:08kJ mol^1.
Next we can combine this value ofÅfH(Cl, aq) with the measured standard molar
enthalpy of formation of aqueous sodium chloride

Na.s/C^12 Cl 2 .g/!NaC.aq/CCl.aq/

to evaluate the standard molar enthalpy of formation of aqueous sodium ion. By continuing
this procedure with other reactions, we can build up a consistent set ofÅfHvalues of
various ions in aqueous solution.

11.3.3 Molar reaction heat capacity

The molar reaction enthalpyÅrHis in general a function ofT,p, and. Using the relations
ÅrHD

P

iiHi(from Eq.11.2.15) andCp;iD.@Hi=@T /p;(Eq.9.2.52), we can write



@ÅrH

@T



p;

D



@

P

iiHi

@T



p;

D

X

i

iCp;iDÅrCp (11.3.5)

whereÅrCpis the molar reaction heat capacity at constant pressure, equal to the rate at
which the heat capacityCpchanges withat constantTandp.
Under standard state conditions, Eq.11.3.5becomes
dÅrH=dT DÅrCp (11.3.6)

(^7) This procedure is similar to that described on page 234 for partial molar volumes of ions.