Limiting Molar Conductance

Limiting Molar Conductance

From Kohrausch’s equation (eqn. 9) and Onsager’s equation (eqn. 10) when C=0, m =_m .. Thus extrapolation to zero concentration (infinite dilution) gives_m .. the limiting molar conductance at infinite dilution. As figure 2. shows, this is practicable with strong electrolytes. In the case of weak electrolytes, there is strong dependence of _m on concentration at low concentrations and hence extrapolations do not give correct _m, values. For weak electrolytes an indirect method is used to obtain _m values.

Table Molar Conductances for various Electrolytes at Infinite Dilution at 25⁰C

Electrolyte Pairs	m/-1cm2mol-1	Difference/-1cm2mol-1
KCI NaCl KNO3 NaNO3 KCI KNO3 BaCl2 Ba(NO3)2	149.46 126.45 144.96 121.55 149.86 144.96 139.94 135.04	23.41 23.41 4.90 4.90

For pairs of salts that either have a common anion or a common cation (Table 3) the difference between the _m values are constant. For those that have a common anion, the differences in _m values can be attributed to cations and similarly for those with a common cation, the difference in _m values is due to the anions.

These observations led Kohlrausch to postulate Kohlrausch’s law of independent migration of ions. “Each ion is assumed to make its own contribution to the molar conductance irrespective of the nature of the other ion with which it is associated”. Thus in general;

_m =v⁺₊  + v^-_-                                                                                          (11)

where ₊    and _-    are the ionic conductances of the cation and anion, respectively at infinite dilution and v⁺ and v^- are the numbers of moles of cations and anions needed to form one mole of the salt (e.g. v⁺ = v^- =1 for NaCI, but v⁺ 1, v^- = 2 for MgCl₂).

Table  Limiting Molar Conductances of Ions at 25°C

Cation	+/-1cm2mol-1	Anion	-/-1cm2mol-1
H+ Na+ K+ Ag+ Mg2+	349.8 50.11 73.52 61.92 53.06	OH- Cl- NO3- SO42- CH3COO-	197.6 76.34 71.44 80.0 40.9

Using the values in table 4, the limiting molar conductances of various electrolytes may be determined, e.g.

_m .(KCI)=_k+_Cl = 73.52 + 76.34

                        =149.86^-1cm²mol^-1

and

_m (KCI)-_m (NaCl) = _K⁺ + _Cl^- - _Na⁺ - _Cl^-

= _K⁺  - _Na⁺

= 73.52 – 50.00

=23.42 ^-1cm²mol^-1

This difference, 23.42 ^-1cm²mol^-1 will be the same whatever the nature of the anion. .