Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.4 ENTHALPIES OFSOLUTION ANDDILUTION 330

ÅH(sol)DsolÅHm(sol,mB) and take the derivative of the expression with respect tosol:

ÅsolHD

dåsolÅHm(sol,mB)ç

dsol

DÅHm(sol,mB)Csol

dÅHm(sol,mB)

dsol

(11.4.20)

At constantnA,mBis proportional tosol, so that dsol=solcan be replaced by dmB=mB.
When we combine the resulting expression forÅsolHwith Eq.11.4.19, we get the follow-
ing expression for the relative partial molar enthalpy of the solute:

LBDÅHm(sol,mB)CmB

dÅHm(sol,mB)

dmB

ÅsolH^1 (11.4.21)

It is convenient to define the quantity

L defD ÅHm(sol,mB)ÅsolH^1 (11.4.22)

known as therelative apparent molar enthalpy of the solute. BecauseÅsolH^1 is indepen-
dent ofmB, the derivative dL=dmBis equal to dÅHm(sol,mB)=dmB. We can therefore
write Eq.11.4.21in the compact form

LBDLCmB

dL

dmB

(11.4.23)

(constantTandp)

Equation11.4.23allows us to evaluateLBat any molality from the dependence ofLon
mB, withLobtained from experimental molar integral enthalpies of solution according to
Eq.11.4.22.
OnceL andLBhave been evaluated for a given molality, it is a simple matter to
calculateLAat that molality. By combining Eqs.11.4.16and11.4.22, we obtain the relation

LADMAmB.LLB/ (11.4.24)

For an electrolyte solute, a plot ofÅHm(sol,mB) versusmBhas a limiting slope ofC1
atmBD 0 , whereas the limiting slope ofÅHm(sol,mB) versus
p
mBis finite and can be
predicted from the Debye–H ̈uckel limiting law. Accordingly, a satisfactory procedure is to
plotÅHm(sol,mB) versus
p
mB, perform a linear extrapolation of the experimental points
to
p
mBD 0 , and then shift the origin to the extrapolated intercept. The result is a plot ofL
versus
p
mB. An example for aqueous NaCl solutions is shown in Fig.11.10(a) on the next
page.
We can also evaluateLfrom experimental enthalpies of dilution. From Eqs.11.4.10
and11.4.22, we obtain the relation

L.m^00 B/L.m^0 B/DÅHm.dil,m^0 B!m^00 B/ (11.4.25)

We can measure the enthalpy changes for diluting a solution of initial molalitym^0 Bto various
molalitiesm^00 B, plot the values ofÅHm.dil,m^0 B!m^00 B/versus
p
p mB, extrapolate the curve to
mBD 0 , and shift the origin to the extrapolated intercept, resulting in a plot ofLversus
p
mB.