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Chapter 11

Electrochemistry

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Molar conductivity

Molar conductivity is defined as the conductance of the solution containing one gram-mole of the electrolyte such that entire solution is placed between two parallel electrodes one centimetre apart . It is denoted by Λm . 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 m2mol−1
1 S m2 mol−1 = 104 S cm2 mol−1
1 S cm2 mol−1 = 10−4 S m2 mol−1

Variation Of Molar Conductivity

In general the conductance of an electrolytic solution depends up on the following factors:

  1. Nature of electrolyte.
  2. Concentration.
  3. 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, H2 SO4 etc. bases like NaOH, KOH etc. and salts like KCl, NH4 Cl,
    CH3COONH4 , etc. Such electrolytes have high values of Λm .
  • 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 CH3COOH, NH4OH 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 Λm for some electrolytes at different concentrations as given in the following Table.

                                                                      Molar Conductance Λm of Electrolytes (S cm2mol−1 ) at 298K

Concen( M)

HCl

NaOH

NaCl

CH3 COOH

NH4OH

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 Λm versus √C for KCl , a strong electrolyte and CH3COOH , 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 Λmo 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 Λm . 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        inter-ionic interactions. Such inter-ionic attractions effectively reduce the speed of the ions and are responsible for the lower value of Λm. On        increasing dilution the ions move apart and inter-ionic attractions are decreased. As a result the value of Λm increases. In general, Λm and
      Λmo for strong electrolytes are related as :
                                          
      where Λm is molar conductivity and Λmo 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 Λm is molar conductivity and Λmo 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 :
                                          Λm = Λmo

KOHLRAUSCH'S LAW

The molar conductivity, Λm of electrolytes increases with increase in dilution till a limiting value Λmo 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
λo+ and λorepresent the molar conductivities of cation and anion respectively at infinite dilution, then the molar conductivity of electrolyte at infinite dilution Λom is given by :
                                         Λmo = n+ λo+ + n λo
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 BaCl2 furnishes one Ba2+ and two Cl ions. Therefore,
                                       
iii) One formula unit of Na2SO4 furnishes two Na+ ions and one SO42− 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 ,
                                          Λoeq= λoc + λoa
where λoc and λoa 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

λo (S cm2mol−1 )

Anion

λo (S cm2 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

NH4+

53.0

NO3

71.40

Cu2+

108.0

CH3COO

40.90

Mg2+

106.0

SO42−

160.0

Applications of Kohlrausch's law

Some of the important applications of Kohlrausch's law are :

  1. Calculation of Molar conductivities of weak electrolytes at infinite dilution
    Λmo for weak electrolytes cannot be obtained directly by the extrapolation of plot of Λm versus √C .The limiting molar conductivities of weak electrolytes,Λmo can be easily calculated with the help of Kohlrausch's law.
    For example, the value of Λmo for acetic acid can be calculated from the knowledge of molar conductivities at infinite dilution of strong electrolytes like
    CH3COONa, HCl and NaCl as follows :
                                             
    Now add and substract λo(Na+) and λo(Cl) to the expression on right hand side snd rearrange :
                                           
    In the same way :
                                          
  2. 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 :

                                        Λmc = molar conductivity of the solution at any concentration,
                                        Λmo
    = molar conductivity at infinite dilution.
                                                                             

 

 

 

 

 

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