Electrolytic conduction

When a voltage is applied to the electrodes dipped into an electrolytic solution, ions of electrolyte move and, thus, electric current flows throughout the electrolytic solution. The power of electrolytes to conduct electric current is termed as conductance or conductivity.

(1) Ohm's law : This law states that the current flowing through a conductor is directly proportional to the potential difference across it, i.e., I is directly proportional to V   

where I is the current strength (In Amperes) and V is the potential difference applied across the conductor (In Volts)

or  I=V/R or V=IR 

where R  is the constant of proportionality and is known as resistance of the conductor. It is expressed in Ohm's and is represented as the above equation is known as Ohm's law. Ohm's law can also be stated as,

The strength of the current flowing through the conductor is directly proportional to potential difference applied across the conductor and inversely proportional to the resistance of the conductor.

(2) Resistance: It measures the obstruction to the flow of current. The resistance of the specific conductor is directly proportional to the length (l) and inversely proportional to the area of cross-section (a) so that

Here  ( rho ) is the constant of proportionality and is called specific resistance or resistivity. The resistance depends on nature of the material.

Units : The unit of resistance is ohm In terms of the SI unit, base unit is equal to (Kgm²)/(s³A²)

(3) Resistivity or specific resistance : We know that resistance R is ; Now, if l = 1 cm, a = 1 cm² then 

Thus, resistivity is defined as the resistance of a conductor of 1 cm length and having area of cross-section equal to 1 cm²

Units : The units of resistivity are     

Its SI units are Ohm metre   But quite often Ohm centimetre   is also used.

(4) Conductance : It is a measure of the ease with which current flows throughout the conductor.  This is an additive property. It can be expressed as G. It is reciprocal of the resistance,

G=1/R

Units : The units of conductance are reciprocal Ohm (ohm^-1) or mho. Ohm is also abbreviated as   so that Ohm^-1 may be written as 

According to SI system, the units of electrical conductance is Siemens, S (i.e.,

(5) Conductivity : The inverse of resistivity is called conductivity (or specific conductance). It is represented by the symbol, k (Greek kappa). The IUPAC has recommended the use of term conductivity over specific conductance. It can be defined as, conductance of a solution of 1 cm length and having 1 suare cm as area of the cross-section. Or we can say that conductivity is the conductance of one centimetre cube of a solution of an electrolyte.

Thus,                                             

Units : The units of conductivity are  

In SI units, l is expressed in m area of cross-section in m² so that the units of conductivity are S m^-1

      (6) The Molar conductivity or the molar conductance : Molar conductivity can be defined as the conducting power of all the ions produced by dissolving one mole of an electrolyte in solution.

It is denoted by (λ). Molar conductance is related to specific conductance () as,

where, M  is the molar concentration.

 If M is in the units of molarity i.e., moles per litre (mol L^-1) the λ may be expressed as,

For the solution containing 1 gm mole of electrolyte placed between two parallel electrodes of 1 sq. cm area of cross-section and one cm apart,

But if solution contains 1 gm mole of the electrolyte therefore, the measured conductance will be molar conductivity.

where V is the volume of solution in cm³ containing one gram mole of the electrolyte.

If M is the concentration of solution in the mole per litre,

M mole of electrolyte is present in the 1000cm³

1 mole of electrolyte is present in 1000/Mcm³ of solution

Thus,  containing 1 mole of electrolyte.

or             

Units of Molar Conductance : The units of molar conductance can be derived from the formula ,

The units of Κ are S cm^-1 and units λ of are,

According to SI system, molar conductance is expressed as S m² mol^-1, if concentration is expressed as mol m^-3. 

       (7) Equivalent conductivity : This can be defined as the conducting power of all the ions produced by dissolving one gram equivalent of an electrolyte in solution.

It is expressed as  and is related to specific conductance as

  (M is Molarity of the solution)

where C is the concentration in gram equivalent per litre (or Normality). This term has previously been quite frequently used. Now it is replaced by the molar conductance. The units of the equivalent conductance are ohm^-1 cm² (gm equiv)^-1

       (8) The Experimental measurement of conductance

(i) The conductance of the solution is reciprocal of its resistance, therefore, the experimental determination of the conductance of a solution involves the measurement of its resistance.

(ii) Calculation of conductivity :  We have seen that conductivity (k) is reciprocal of resistivity (Ρ)    ,

where G  is the conductance of cell, l is the distance of the separation of two electrodes having cross section area a cm²

 The quantity (1/a) is called cell constant and is expressed in cm^-1 Knowing the value of cell constant and conductance of the solution, the specific conductance can be  obtained as follows,

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