Arrhenius strong electrolytes
Solutions
The Debye-Hückel limiting law says that
log ± = –|z+z–|A I ,
where A = 0.509 at 25°C and I is the ionic strength, related to charge z and ion molality b by
1
2
I = z j bj .
2
j
Since each solution is 10. g salt per liter of water, the initial concentration of the salt is
b = (10. g/L)/(M g/mol) = (10/M) mol/L = (10/M) mol/kg ,
where M is the molar mass of the salt. Remember that the molality of the ion is twice the
molality of the salt for potassium in potassium sulfate and for chloride in barium chloride. It
turns out that the ionic strength is equal to the molality of the salt for salts consisting only of
singly-charged ions: I = b . For salts with one divalent ion and two monovalent ones, I = 3b .
And for salts with two divalent ions, I = 4b .
Obviously, the more concentrated the salt, the greater the ionic strength and the smaller
±. The concentration of salt is inversely proportional to the molar mass in this series of constant
mass of salt per volume of water; so the greater the molar mass, the smaller the ionic strength and
the greater ± in this series. The more highly charged the ions are, the greater the ionic strength.
In addition to the effect on ionic strength, the greater the charge the greater the magnitude of log
± (i.e., the more negative it is) and the smaller ± itself.
substance
formula

initial
molality
0.171
ionic
strength
0.171
log ±
±
0.82
M
(g/mol)
58.44
sodium
chloride
potassium
sulfate
barium
chloride
cadmium
sulfate
NaCl
-0.211
0.62
K2SO4
0.67
174.27
0.057
0.172
-0.422
0.38
BaCl2
0.77
208.25
0.048
0.144
-0.386
0.41
CdSO4
0.35
208.46
0.048
0.192
-0.892
0.13
The Debye-Hückel limiting law values of ± have trends similar to Arrhenius’s reported 
values, but the quantitative agreement is not very good. (If  is supposed to represent the
deviation from unit activity, then differences between  and  of the same order as differences
between  and 1 can surely not be called quantitative agreement!) Looking at the large body of
data on strong electrolytes in Arrhenius’s paper, one can see the expected trends with molar mass
among salts of the same kinds of ions and the expected stronger trend with charge.