Electrochemistry - Part 2 | Class 12th

Resistance (R):  
The electrical resistance is the hindrance to the flow of electrons. Its unit is ohm (Ω). The resistance of a conductor is directly proportional to the length of the conductor (Ɩ) and inversely proportional to the area of cross-section (A) of the conductor.          

                    R α Ɩ /A

                                         R = ρ Ɩ /A

where ρ (rho) is a constant called resistivity or specific resistance. Its unit is ohm-metre (Ω m) or ohm-centimetre (Ω cm).

Resistivity: 

It defined as the resistance offered by a conductor having unit 

length and unit area of cross-section.

 Conductance (G): 
It is the inverse of resistance.

        i.e. G = 1/R.

                                        Its unit is ohm^-1 or mho or Siemens (S)

Measurement of the conductivity of ionic solutions:

We know that, conductivity G = ƙ x A/ Ɩ

So conductivity, ƙ = G x Ɩ/A    (ƙ = Kappa) 

The quantity Ɩ/A is called cell constant (G*). It depends on the distance between the electrodes and their area of cross-section. Its unit is m^-1.

i.e. Conductivity = Conductance x Cell Constant

Molar conductivity (λm):

 It is the conductivity of 1 mole of an electrolytic solution kept between two electrodes with unit area of cross section and at a distance of unit length. It is related to conductivity of the solution by the equation,

            λm= ƙ/C   (where C is the concentration of the solution)

            Or,  λm = 1000 ƙ/M (where M is the molarity)

The unit of molar conductivity is Ω^-1 cm² mol^-1 or S cm² mol^-1.

Variation of conductivity and Molar conductivity with concentration:

Both conductivity and molar conductivity change with the concentration of the electrolyte. For both strong and weak electrolytes, conductivity always decreases with dilution. This is because conductivity is the conductance of unit volume of electrolytic solution. As dilution increases, the number of ions per unit volume decreases and hence the conductivity decreases.

For strong electrolytes, as dilution increases, the force of attraction between the ions decreases and hence the ionic mobility increases. So molar conductivity increases. When dilution reaches maximum or concentration approaches zero, the molar conductivity becomes maximum and it is called the limiting molar conductivity (λ⁰m).

            The variation of λm for strong and weak electrolytes is shown in the following                             graphs: 

                 

For strong electrolytes, the value of λ⁰m can be determined by the extrapolation of the graph. But for weak electrolytes, it is not possible since the graph is not a straight line. So their λ⁰m values are calculated by applying Kohlrausch’s law of independent migration of ions.

Kohlrausch’s law:

Molar conductance at infinite dilution of a strong electrolyte is equal to the sum of molar ionic conductance of the cation and anion at infinite dilution.

eg : λ⁰m NaOH = λ⁰m Na+ + λ⁰m OH-

Applications of Kohlrausch’s law:

ü Determination of λ⁰m of weak electrolytes:

By knowing the λ⁰m values of strong electrolytes, we can calculate λ⁰m of weak electrolytes. For e.g. we can determine the λ⁰m of acetic acid (CH₃COOH) by knowing the λ⁰m of CH₃COONa, NaCl and HCl as follows:

λ⁰m (CH₃COONa) = λ⁰CH₃COO^- + λ⁰Na⁺  …………. (1)

λ⁰m (HCl) = λ⁰H+ + λ⁰ Cl- …………….. (2)

λ⁰m (NaCl) = λ⁰Na+ + λ⁰Cl- ………….. (3)

(1) + (2) + (3) gives:

λ⁰m (CH₃COONa) + λ⁰m (HCl) - λ⁰m (NaCl) = λ⁰CH₃COO^- + λ⁰Na⁺ + λ⁰H⁺ + λ⁰Cl^- - λ⁰Na⁺ - λ⁰Cl^-  = λ⁰CH₃COOH

ü Determination of degree of dissociation of weak electrolytes:

By knowing the molar conductivity at a particular concentration (λ^cm) and limiting molar conductivity (λ⁰m), we can calculate the degree of dissociation (α) as,

    

                               

By using α, we can calculate the dissociation constant of acid as:

                   

Related Post:

Electrochemistry - Part 3 
Electrochemistry - Part 2
Electrochemistry - Part 1