Concise Physical Chemistry

c13 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

214 COULOMETRY AND CONDUCTIVITY

we are using the notation ̃μfor the ionic strength:

μ ̃=^12

∑

i

miZ^2 i

The Debye–Huckel law is applicable only in very dilute solutions; it is a typical ̈

limiting law.

We know how to determine the ionization constantKafor weak acids, say acetic

acid, but we find upon close examination that the results are not quite constant with

different concentrations of HOAc, and we presume that this lack is due to interference

among ions. This nonideality can be expressed in terms of ionic activities:

Ka=

aH+aOAc−

aHOAc

=

γ±mH+γ±mOAc−

γmHOAc

In this model, nonideality is caused by charge interaction but HOAc is uncharged, so

we can consider it an ideal solute and takeγHOAc= 1 .0. The ions, however, are not

ideal. This means thatγ± = 1 .0, so

Ka=

aH+aOAc−

aHOAc

=

γ±mH+γ±mOAc−

γHOAcmHOAc

=γ±^2

m^2 H+

mHOAc

=γ±^2 K

wheremOAc−=mH+because equal numbers of product ions H+and OAc−are

produced in the dissociation reaction

HOAc←→H++OAc−

Taking logarithms of both sides, we obtain

lnKa=2lnγ±+lnK

whereKis a measured (nonideal) value for the acid dissociation constant andKais

the ideal value. Atinfinite dilution,γ±= 1 .0 and lnγ±= 0 .0, so

ln︸︷︷K︸

m→ 0

=lnKa

For a dilute acid in pure water, each ion concentration isαm, whereαis the

degree of dissociation andmis the molar concentration of acid (Section 13.4). The

ionic strength is determined by the concentration of ions in the solution, but this is

by no means the bulk concentration of acid. Many acids—for example, acetic acid

HOAc—ionize to a very limited extent, but even ionization of pure water contributes

to the ionic strength. According to the Debye–Huckel limiting law, we have ̈

lnγ±=− 1. 172

√

μ ̃=− 1. 172

√

αm