Conductance of electrolytic solutions

Electrolytic Conductance :

Factors Affecting Conductance & Resistance :

1.   Solute – Solute interactions (Inter – Ionic force of attraction) Greater the force of  attraction, greater will be the resistance.

 Force Charge

2.Solute – Solvent Interaction (Hydration/Solvation of Ions) Greater the solvation
Solvation Charge   greater will be resistance Li+ (Hydrated largest)        Cs+ (Hydrated smallest)

 resistance of LiCl > resistance of CsCl

3. Solvent solvent interaction (Viscosity) : greater the viscosity greater will be resistance

4.  Temperature

        T        R

5.  Nature of electrolyte

 Weak electrolyte – high resistance strong electrolyte – Low resistance

Resistance :

R =  (Ohm's law ( )

R =

 – resistivity/specific resistance

     – resistance of unit length wire of unit area of cross section = constant = ( m)

Resistivity of a solution is defined as the resistance of the solution between two electrodes of 1 cm2 area of cross section and 1 cm apart.

          or

Resistance of 1 cm3 of solution will be it's resistivity.

Conductance :

        = S (Siemens)

Conductivity/specific conductance

unit –1 cm–1

= conductivity of 1 cm3 of solution

a  concentration of ions

K =       G =

K  ( no. of ions) no. of charge carries

Since conductivity or resistivity of the solution is dependent on it's concentration, so two more type of conductivities are defined for the solution. 

Molar conductivity/molar conductance ((lm) :

Conductance of a solution containing 1 mole of an electrolyte between 2 electrodes which are 1cm apart.

Let the molarity of the solution 'C'

 C moles of electrolyte are present in 1 Lt. of solution.

so molar conductance = K

Its units are Ohm–1 cm2 mol–1

Equivalent conductance : Conductivity of a solution containing 1 g equivalent of the electrolyte.

leq – equivalent conductivity/conduction.

leq = 

Its units are Ohm–1 cm2 eq–1

Variation of conductivity and molar conductivity with concentration

Conductivity always decreases with the decrease in concentration both for weak and strong electrolytes. 

The number of ions per unit volume that carry the current in a solution decreases on dilution.

Molar conductivity increases with decreases in concentration. This is because the total volume, V of solution containing one mole of electrolyte also increases.

Molar conductivity is the conductance of solution.

When concentration approaches zero, the molar conductivity is known as limiting molar conductivity and is represented by the symbol .

Strong Electrolytes :

For strong electrolytes. increses slowly with dilution and can be represented by the equation


The value of the constant 'A' for a given slovent and temperature depends on the type of electrolyte i.e. the charges on the cations and anion produced on the dissociation of the electrolyte in the solution.

Example : Thus NaCl, CaCl2, MgSO4 are known as 1-1 , 2-1 and 2-2 electrolyte respectively. 

All electrolytes of a particular type have the same value for 'A'.

Weak electrolytes

Weak electrolytes like acetic acid have lower degree of dissociation at higher concentration and hence for such electrolytes, the change in with dilution is due to increases in the number of ions in total volume of solution that contains 1 mol of electrolyte.

At infinite dilution (i.e. concentration c zero) electrolyte dissociates completely (a= 1),but at such low concentration the conductivity of the solution is so low that it connot be measured accurately.

Molar conductivity versus c1/2 for acetic acid  (weak electrolyte) and potassium chloride   

(strong electrolyte in aqueous solutions. 

 

Kohlarausch's Law : 

"At infinite dilution, when dissociation is complete, each ion makes a definite contribution towards equivalent conductance of the electrolyte irrespective of the nature of the ion with which it is associated and the value of equivalent conductance at infinite dilution for any electrolyte is the sum of contribution of its constituent ions."

 

i.e.,  l¥ = l+  + l 

At infinite dilution  or near zero concentration when dissociation is 100%, each ion makes a definite contribution towards molar conductivity of electrolyte irrespective of the nature of the other ion. (because interionic forces of attraction are zero)

 

 V+= no. of cation in one formula unit of electrolyte,  = no. of anions in one formula unit of electrolyte

For NaCl  = 1 v- = 1

For Al2(SO4)3  = 2 v- = 3

Applications of Kohlaraushch's law

Calculate  for any electrolyte from the  of individual ions.

etermine the value of its dissociation constant once we known the  and  at a given concentration c.

 Degree of dissociation : At greater dilution the ionization become 100%, therefore called infinite dilution.

At lower dilution the ionization (dissociation into ions) is less than 100% and equivalent conductance become lower,

 i.e.,   leq < l°eq 

 degree of dissociation

Dissociation constant of weak electrolyte :

KC =   

a = degree of dissociation

C = concentration 

The degree of dissociation then it can be approximated to the ratio of molar conductivity at the concentration c to limiting molar conductivity, , Thus we have :

But we known that for a weak electrolyte like acetic acid.

Solubility(s) and KSP of any sparingly soluble salt.

Sparingly soluble salt = Very small solubility

 Solubility = molarity = 0

so, solution can be considered to be of zero conc or infinite dilution.

Variation of K, lm & leq  of solutions with Dilution

  Kconc. of ions in the solution. In case of both strong and weak electrolytes on dilution the concentration of ions will decrease hence K will decrease.