Concise Physical Chemistry

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

206 COULOMETRY AND CONDUCTIVITY

When a voltageVis applied to aconductance cellwith parallel plates of areaA

separated by a distanceland containing an electrolyte solution, the current is

I=JA=

κA

l

V

whereJis theflux d Q/dtof chargeQpassing through unit cross-sectional areaA.

When we combine these two equations, the current becomesI=JA=LV, which

is another way of writing Ohm’s lawV=IR.

With these equations, it is possible to determine the conductivity of any solution

from the resistance and a knowledge ofl/A. It is not easy to measurel/Ato the high

level of accuracy required for good work in this field, but the task has already been

done for solutions of KCl at several concentrations and temperatures. The results

of these measurements are available (CRC Handbook of Chemistry and Physics

2008–2009, 89th ed). A selected value isκKCl= 0 .1408 ohm−^1 m−^1 for 1. 00 × 10 −^2

molal KCl at 298 K.

Suppose we construct a cell looking something like the one in Fig. 13.1, fill it with

1. 00 × 10 −^2 molal KCl, and measure the resistanceR=650 ohms. We have

κKCl= 0. 1408 =L

(

l

A

)

=

1

650

(

l

A

)

l

A

=650(0.1408)= 91 .52 m−^1

We now know the geometric ratiol/Awithout having to make precise measurements

of eitherlorA.

13.3 MOLAR CONDUCTIVITY

For chemical applications to solutions of varying concentrationsc, an additional

definition is necessary. Themolar conductivityof an electrolyte solution is

≡

κ

c

wherecis the concentration of the solution in mol L−^1 or mol dm−^3.

We shall be concerned largely withaqueous solutions. More than 100 years ago,

F. Kohlrausch published a series of research results on conductivity of electrolytes in

aqueous solutions. The conclusions he drew included what is now called Kohlrausch’s

law. The law is a linear connection between the molar conductivity and the square

root of the electrolyte concentration:

=◦−K ̃

√

c

whereK ̃ is an empirical constant. Kohlrausch’s law leads to a graphical way of

determining the parameter◦, a characteristic of the electrolyte alone, without