Physical Chemistry Third Edition

10.5 Electrical Conduction in Electrolyte Solutions 481

EXAMPLE10.21

Following are data on the molar conductivity of NaOH as a function of concentration at 25◦C:

concentration/mol L−^1 Λ/ohm−^1 cm^2 mol−^1

0.0010 244.5

0.0100 238.0

0.0500 227.6

0.1000 221.2

0.2000 213.0

0.5000 197.6

1.0000 178.8

Find the value ofΛ 0 for NaOH. Compare the value obtained with the value from Table A.20.

Solution

As indicated in Eq. (10.6.19), a plot ofΛversus c^1 /^2 for a strong electrolyte should be nearly

linear at small concentrations. Such a plot is shown in Figure 10.10.

The extrapolation to zero concentration was accomplished by fitting the data to a poly-

nomial of degree 5, since the plot is not linear over the range of concentrations given. The

formula for the polynomial is shown in the figure, and the intercept was found to be

Λ 0  247 .7 ohm−^1 cm^2 mol−^1

From Table A.20,

Λ 0 λ(Na+)+λ(OH−)

 19. 8 × 10 −^3 ohm−^1 m^2 mol−^1 + 5. 011 × 10 −^3 ohm−^1 m^2 mol−^1

 24. 8 × 10 −^3 ohm−^1 m^2 mol−^1 248 ohm−^1 cm^2 mol−^1

in good agreement with the value from the extrapolation.

260

240

220

200

180

160

0.0 0.2 0.4

Square root of

concentration /(mol L–^1 )1/2

Molar conductivity / ohm

-^1

cm

2 mol

-^1

0.6 0.8 1.0

Figure 10.10 The Molar Conductivity
of Sodium Hydroxide as a Function
of the Square Root of the Concentra-
tion in mol L−^1.

An extrapolation such as that in Example 10.21 is difficult for weak electrolytes,

since the percent ionization and the ion mobilities are both changing with concentration.

However, one can easily determine the limiting molar conductivity of a weak electrolyte

such as acetic acid from the values for the ions.

Exercise 10.22

a.Find the value of the limiting molar conductivity for acetic acid from the values in

Table A.20.

b.Following are data on the molar conductivity of acetic acid as a function of concentration

at 25◦C:

concentration/mol L−^1 Λ/ohm−^1 cm^2 mol−^1

0.0001 134.6

0.0010 49.2

0.0100 16.18

0.0500 7.36

0.1000 5.20

0.2000 3.65

Can you carry out an extrapolation as in Example 10.21 to determine the limiting molar

conductivity?