Contents
Electrochemistry
Molar conductivity
Molar conductivity is defined as the conductance of the solution containing one grammole of the electrolyte such that entire solution is placed between two parallel electrodes one centimetre apart . It is denoted by Λ_{m} . Molar conductivity is related to conductivity (κ) by the relation :
where M is the molarity of the solution.
Units
In S I system the units are S m^{2}mol^{−1}
1 S m^{2} mol^{−1} = 10^{4} S cm^{2} mol^{−1}
1 S cm^{2} mol^{−1} = 10^{−4} S m^{2} mol^{−1}
Variation Of Molar Conductivity
In general the conductance of an electrolytic solution depends up on the following factors:
 Nature of electrolyte.
 Concentration.
 Temperature.
i) Nature of electrolyte
The conductance of the solution depends upon the nature of electrolyte. All electrolytes do not ionise in their aqueous solutions to the same extent. They can be divided into two categories depending upon their extent of ionisation.

Strong electrolytes
An electrolyte which is completely ionised in aqueous solution is called strong electrolyte.
Some examples of strong electrolytes are : mineral acids like HCl, H_{2} SO_{4} etc. bases like NaOH, KOH etc. and salts like KCl, NH_{4} Cl,
CH_{3}COONH_{4} , etc. Such electrolytes have high values of Λ_{m} . 
Weak Electrolytes
An electrolyte which is not completely ionised in aqueous solution is called weak electrolyte . The aqueous solution of weak electrolytes contains ions in equilibrium with undissociated molecules. Some examples of weak electrolytes are CH_{3}COOH, NH_{4}OH etc. Such electrolytes possesses low values of molar conductivities.
ii) Variation of molar conductivity with Concentration
In order to understand this, let us examine the values of Λ_{m} for some electrolytes at different concentrations as given in the following Table.
Molar Conductance Λ_{m} of Electrolytes (S cm^{2}mol^{−1} ) at 298K
Concen( M) 
HCl 
NaOH 
NaCl 
CH_{3} COOH 
NH_{4}OH 
0.1 
391.3 
 
106.7 
5.2 
3 
0.05 
399.1 
 
111.1 
7.4 
11.3 
0.02 
407.2 
 
115.8 
11.6 
34.0 
0.01 
412.0 
238.0 
118.5 
16.2 
46.9 
0.005 
415.8 
240.8 
120.7 
22.8 
 
0.001 
421.4 
244.7 
123.7 
48.6 
 
0.0005 
422.7 
245.6 
124.5 
 
 
From the above table, it is clear that the molar conductivity of electrolytes generally increases with increase with dilution. The relative increase in the molar conductivity in case of strong electrolytes is not so large as that in the case of weak electrolytes. The variation of Λ_{m} versus √C for KCl , a strong electrolyte and CH_{3}COOH , a weak electrolyte has been shown in Fig .
From the figure , it is evident that in the case of strong electrolytes there is a tendency for molar conductivity to approach a certain limiting value when concentration approaches zero, i.e., when dilution is infinite. The value of molar conductivity when the concentration approaches zero is known as molar conductivity at zero concentration or at infinite dilution . It is denoted by Λ_{m}^{o} and is determined by extrapolating the graph to zero concentration (Fig ).
In the case of weak electrolytes such as acetic acid, there is no indication that the limiting value can be attained when the concentration approaches zero. Thus, for weak electrolytes the value of molar conductivity at infinite dilution cannot be obtained by extrapolating the graph. It may , however, be obtained indirectly by Kohlrausch's law.
Explanation for the variation of Molar conductivity
a) For weak electrolytes , the variation in the value of L m with dilution can be explained on the basis of number of ions furnished by it in the solution. The number of ions furnished by the electrolytes in solution depends upon the degree of ionisation of the electrolyte. On dilution, the degree of ionisation of the weak electrolyte increases, thereby increasing the value of Λ_{m} . Therefore , it is evident that when the limiting value of molar conductivity is reached, the degree of dissociation of the electrolytes approaches unity i.e., whole of solute dissociates into ions. Therefore, at any other concentrations, the degree of dissociation, a is given by the expression :
b) For strong electrolytes , the number of ions in the solution do not increase because, these are almost completely ionised in solution at all concentrations. However, in concentrated solutions of strong electrolytes the density of the ions is relatively high which results in the significant interionic interactions. Such interionic attractions effectively reduce the speed of the ions and are responsible for the lower value of Λ_{m}. On increasing dilution the ions move apart and interionic attractions are decreased. As a result the value of Λ_{m} increases. In general, Λ_{m} and
Λ_{m}^{o} for strong electrolytes are related as :
where Λ_{m}^{ }is molar conductivity and Λ_{m}^{o} is molar conductivity at infinite dilution. b is a constant which depends upon the viscosity and dielectric constant of the solvent, C is the concentration of solution.
where Λ_{m}^{ }is molar conductivity and Λ_{m}^{o} is molar conductivity at infinite dilution. b is a constant which depends upon the viscosity and dielectric It is quite evident that as C approaches zero :
Λ_{m}^{ } = Λ_{m}^{o}
KOHLRAUSCH'S LAW
The molar conductivity, Λ_{m} of electrolytes increases with increase in dilution till a limiting value Λ_{m}^{o} is obtained at infinite dilution. In this limit, the positive and negative ions may be thought of as behaving essentially independent of each other. Based up on his exhaustive experimental studies, Kohlrausch gave a generalisation, which is known as Kohlrausch law. It states that at infinite dilution, when the dissociation of the electrolyte is complete, each ion makes a definite contribution towards the molar conductivity of electrolyte, irrespective of the nature of the other ion with which it is associated.
This implies that the molar conductivity of an electrolyte at infinite dilution can be expressed as the sum of the contributions from its individual ions. If
λ^{o}_{+} and λ^{o}_{− }represent the molar conductivities of cation and anion respectively at infinite dilution, then the molar conductivity of electrolyte at infinite dilution Λ_{om }is given by :
Λ_{m}^{o }= n_{+} λ^{o}_{+} + n_{−} λ^{o}_{−
}where n_{+} and n_{−} represent the number of positive and negative ions furnished by each formula unit of the electrolyte.
For example :
i) One formula unit NaCl furnishes one Na^{+}and one Cl^{−} ion, therefore,
_{}ii) One formula unit of BaCl_{2} furnishes one Ba^{2+} and two Cl^{−} ions. Therefore,
_{}iii) One formula unit of Na_{2}SO_{4 }furnishes two Na^{+} ions and one SO_{4}^{2−} ions, therefore ,
_{}In terms of equivalent conductance , Kohlrausch's Law is stated as :
The equivalent conductance of an electrolyte at infinite dilution is the sum of two values  one depending on the cation and other depending on anion.
Mathematically ,
Λ^{o}_{eq}= λ^{o}_{c} + λ^{o}_{a}where λ^{o}_{c} and λ^{o}_{a } are called the ionic conductances at infinite dilution for cation and anion respectively.
The ionic conductivities at infinite dilution for some ions at 298 K are given in the following Table.
Ionic conductivities at Infinite dilution at 298 K
Cation 
λ^{o} (S cm^{2}mol^{−1} ) 
Anion 
λ^{o }(S cm^{2} mol^{−1} ) 
H^{+} 
349.6 
OH^{−} 
199.1 
K^{+} 
73.5 
Cl^{−} 
76.3 
Na^{+} 
50.1 
Br^{−} 
78.1 
Ag^{+} 
61.9 
I^{−} 
76.80 
NH_{4}^{+} 
53.0 
NO_{3}^{−} 
71.40 
Cu^{2+} 
108.0 
CH_{3}COO^{−} 
40.90 
Mg^{2+} 
106.0 
SO_{4}^{2−} 
160.0 
Applications of Kohlrausch's law
Some of the important applications of Kohlrausch's law are :

Calculation of Molar conductivities of weak electrolytes at infinite dilution
Λ_{m}^{o} for weak electrolytes cannot be obtained directly by the extrapolation of plot of Λ_{m} versus √C .The limiting molar conductivities of weak electrolytes,Λ_{m}^{o} can be easily calculated with the help of Kohlrausch's law.
For example, the value of Λ_{m}^{o} for acetic acid can be calculated from the knowledge of molar conductivities at infinite dilution of strong electrolytes like
CH_{3}COONa, HCl and NaCl as follows :
Now add and substract λ^{o}(Na^{+}) and λ^{o}(Cl^{−}) to the expression on right hand side snd rearrange :
_{ }
In the same way :
_{ } 
Calculation of degree of dissociation of weak electrolytes
Molar conductivity of an electrolyte depends upon its degree of dissociation. Higher the degree of dissociation, higher is the molar conductivity. As dilution increases, the degree of dissociation of weak electrolyte also increases and consequently, molar conductivity of electrolyte increases. At infinite dilution molar conductivity becomes maximum because degree of dissociation approaches unity.
Thus, if :
_{ }Λ_{m}^{c} = molar conductivity of the solution at any concentration,
_{ }Λ_{m}^{o} = molar conductivity at infinite dilution.
_{ }

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