Page 226 - Modern physical chemistry

9.7 Determining Solubilities and Degrees of Ionization 219

9.7 Determining Solubilities and Degrees of Ionization

Solving equation (9.40) for the equivalent concentration of an ion in an electrolytic
solution yields
1000IC
Ci:::--' [9.47]
Ai
So if one knew the equivalent conductance of the ions together, 1\, one could obtain the
equivalent concentration of the cation and the anion making up the solution from a mea-
sured specific conductance /c. But since Ai varies only slightly with ci> an approximate
value for c i serves in determining it.
For a slightly soluble, or a weak, electrolyte, one may determine Ai from the conduc-
tances of related strong electrolytes. Suppose the electrolyte to be studied is AD. Also
suppose that electrolytes AB, CD, and CB exist which are completely ionized and soluble
enough so that equivalent conductances can be measured at the necessary concentra-
tions. We then have

Ai::: AA + + Au- ::: (AA + + As- )+ (AC+ + Au- )-(AC+ + As-)::: AAB + ACD - ACE [9.48]

In determining the solubility of a strong electrolyte AD, a person prepares a saturated
solution in sufficiently pure water and measures its specific conductance /c. The equiva-
lent conductance Ai is found using formula (9.48). Then the concentration C ::: ci is cal-
culated with equation (9.47).
In determining the ionization of a weak electrolyte AD, a person prepares a solution
of AD of known concentration c total in sufficiently pure water. The specific conductance
/C is then measured and substituted into equation (9.40). The conventional equivalent con-
ductance A is calculated. This may be placed in the form
lOOOlC
ctotal :::--. [9.49]
A
Then the equivalent conductance at the estimated ionic concentration is found employ-
ing formula (9.48). This is used in formula (9.47) in the form
10OO/C
c A + :::c - :::--. [9.50]
D
Ai
For the reaction
AD ( ) A + +D-, [9.51 ]

we now have
C A + 1000lC / Ai A
a:::--::: :::-. [9.52]
Ctotal 1000lC / A Ai
As a first approximation to Ai one may employ Ao, the equivalent conductance at infi-
nite dilution, as Arrhenius did in his seminal work.

Example 9.5

If a solution of BaS0 4 contains 1.00 mg t\ what is its specific conductance at 25° C?