Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.4 ENTHALPIES OFSOLUTION ANDDILUTION 326

bc

a

c b

0 5 10 15 20

 120

 100

 80

 60

 40

 20

0

sol=mol

H

.sol

/=

kJ

Figure 11.9 Enthalpy change for the dissolution of NaCH 3 CO 2 (s) in one kilogram

of water in a closed system at298:15K and 1 bar, as a function of the amountsolof

dissolved solute.a The open circle atsolD 15 mol indicates the approximate satura-

tion limit; data to the right of this point come from supersaturated solutions. At the

compositionmBD 15 mol kg^1 , the value ofÅHm(sol,mB) is the slope of line a and

the value ofÅsolHis the slope of line b. The value ofÅsolH^1 is the slope of line c.

aData from Ref. [ 165 ], page 2-315.

The slope of the curve atsolD 0 isÅsolH^1 , the molar enthalpy of solution at infinite
dilution. If the measurements are made at the standard pressure,ÅsolH^1 is the same as
the standard molar enthalpy of solution,ÅsolH, because the standard molar enthalpy of a
solute is the molar enthalpy atpDpand infinite dilution.

11.4.2 Enthalpy of dilution

Next let us consider a dilution process in which solvent is transferred from a pure solvent
phase to a solution phase. Themolar differential enthalpy of dilutionis the rate of change
ofHwith the advancementdilat constantTandpof the dilution process, wheredilis the
amount of solvent transferred:

ÅdilHD



@H

@dil



T;p;nB

(11.4.6)

For the dilution reaction A!A(sln), the general relationÅrXD

P

iiXibecomes

ÅdilHDHAHA (11.4.7)

whereHAis the partial molar enthalpy of the solvent in the solution. In the limit of infinite
dilution,HAmust approach the molar enthalpy of pure solvent,HA; then Eq.11.4.7shows
thatÅdilHapproaches zero in this limit.
Anintegral enthalpy of dilution,ÅH(dil), refers to the enthalpy change for transfer
of a finite amount of solvent from a pure solvent phase to a solution,T andpbeing the