Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.4 ENTHALPIES OFSOLUTION ANDDILUTION 331

0 0.5 1.0 1.5 2.0

q

mB=mol kg^1

(a)

H

.m

sol

/=

kJ mol

^1

2 :0

2 :5

3:0

3:5

4 :0

4 :5

5:0

L

=kJ mol

^1

1:5

1:0

0:5

0

0:5

1:0

3:0

 2 :5

 2 :0

1:5

1:0

0:5

0

0:5

0 1:0 2 :0 3:0 4 :0

mB=mol kg^1

(b)

L

=B

kJ mol

^1

Figure 11.10 Thermal properties of aqueous NaCl at25:00C.

(a) Left axis: molar integral enthalpy of solution to produce solution of molalitymB.a

The dashed line has a slope equal to the theoretical limiting value of the slope of the

curve. Right axis: relative apparent molar enthalpy of the solute.

(b) Relative partial molar enthalpy of the solute as a function of molality.b

aCalculated from molar enthalpy of formation values in Ref. [ 165 ], p. 2-301.

bBased on data in Ref. [ 126 ], Table X.

In order to be able to use Eq.11.4.23, we need to relate the derivative dL=dmBto the
slope of the curve ofLversus
p
mB. We write

d

p

mBD

1

2 pmB

dmB dmBD 2

p

mB d

p

mB (11.4.26)

Substituting this expression for dmBinto Eq.11.4.23, we obtain the following operational
equation for evaluatingLBfrom the plot ofLversus
p
mB:

LBDLC

p

mB

2

dL

d

p

mB

(11.4.27)

(constantTandp)

The value ofLgoes to zero at infinite dilution. When the solute is an electrolyte, the
dependence ofLonmBin solutions dilute enough for the Debye–Huckel limiting law to ̈
apply is given by

LDCL

p

mB (11.4.28)

(very dilute solution)

For aqueous solutions of a 1:1 electrolyte at 25 C, the coefficientCLhas the value^10

CLD1:988 103 J kg1=2mol3=2 (11.4.29)

(^10) The fact thatC
Lis positive means, according to Eq.11.4.25, that dilution of a very dilute electrolyte solution
is an exothermic process.