Physical Chemistry , 1st ed.

b.Using the enthalpy of formation of Cl^ (aq) from part a, we can apply the

same tactic to the dissolution of sodium chloride:

3.9 kJfH[prods] (^) fH[reacts]
3.9 kJ[fH[Na^ (aq)] ( 167.2)] ( 411.2)
240.1 kJfH[Na^ (aq)]
Entropies and free energies of formation for ions are determined similarly.

8.7 Debye-Hückel Theory of Ionic Solutions

Ionic strength is a useful concept because it allows us to consider some general

expressions that depend only on ionic strength and not on the identities of the

ions themselves. In 1923, Peter Debye and Erich Hückel made some simplify-

ing assumptions about all ionic solutions. They assumed that they would be

dealing with very dilute solutions, and that the solvent was basically a contin-

uous, structureless medium that has some dielectric constant r.Debye and

Hückel also assumed that any deviations in solution properties from ideality

were due to the coulombic interactions (repulsions and attractions) between

the ions.

Applying some of the tools of statistics and the concept of ionic strength,

Debye and Hückel derived a relatively simple relationship between the activity

coefficient and the ionic strength Iof a dilute solution:

ln Az z I1/2 (8.50)

where z and z are the charges on the positive and negative ions, respectively.

Note that the charge on the positive ion is itself positive, and the charge on the

negative ion is itself negative. The constant Ais given by the expression

A(2NAsolv)1/2

4 

e

0

2

rkT



3/2

(8.51)

where:

NAAvog adro’s numb er

solvdensity of solvent (in units of kg/m^3 )

efundamental unit of charge, in C

 0 permittivity of free space

rdielectric constant of solvent

kBoltzmann’s constant

Tabsolute temperature

Equation 8.50 is the central part of what is called the Debye-Hückel theory

of ionic solutions. Since it strictly applies only to very dilute solutions (I0.01

m), this expression is more specifically known as the Debye-Hückel limiting

law.Because Ais always positive, the product of the charges z z is always

negative, so ln is always negative. This implies that is always less than 1,

which in turn implies that the solution is not ideal.

There is one important thing to observe about the Debye-Hückel limiting

law. It depends on the identity of the solvent, since the density and dielectric

constant of the solvent are part of the expression for A. But the limiting law

230 CHAPTER 8 Electrochemistry and Ionic Solutions