CONDUCTANCE [ ELECTROCHEMISTRY ] CLASS-12

MOLAR- CONDUCTIVITY EQUIVALENT - CONDUCTIVITY

1.ELECTRICAL RESISTANCE(R)

Ohm law states,'If to the ends of a conductor, potential differece V is applied and current I flows through it , then V ∝I ⟹ V = IR. Here, V/I= R, is called resistance.'
S.I. unit of resistance is ohm (Ω).
Current is generally measured in ampere, voltage is measured in volt. If one ampere current flows through a conductor when a voltage of one volt is applied to it, the resistance of the conductor is taken as 1 ohm (1 Ω).
Metallic conductors, solutions of all electrolytes(acids,bases,salts) also obey ohm's law.
A substance which offers greater resistance will allow less electricity to flow through it. This results also follows from ohm's law according to which I ∝ 1/R.

2.ELECTRICAL CONDUCTANCE (G)

The reciprocal of the electrical resistance is called the conductance.
G = 1/R
A solution is electrically characterised by conductance rather than its resistance.
Units of conductance - (i) ohm ^-1 (Ω^-1) (ii) mho (iii) siemens (S)
1S = 1 Ω^-1
If a solution has a resistance of 10 ohm, it is said to have a conductance of 1/10 ohm ^-1 or 1/10 mho or 1/10 siemens.

3.SPECIFIC RESISTANCE ( or RESISTIVITY ), ρ (rho)

Resistance(R) of a conductor is
(i) directly proportional to to its length(l) i.e., R ∝ l
(ii) inversely proportional to its area of cross section (a) i.e., R ∝ 1/a, combining both we get, R ∝ l/a ⟹ R = ρl/a
where ρ is a constant of proportionality, called Specific Resistance or Resistivity.
The value of ρ depends upon the material of the conductor.
If l = 1cm and a = 1cm² then R = ρl/a becomes R = ρ, Hence,
Resistivity is defined as the resistance of a conductor whose length is 1 cm and area of cross section is 1 cm², i.e., it is the resistance of 1 cm³ of the conductor or in terms of S.I. units, it is the resistance of 1 m³ of the conductor.
S.I. unit of resistivity is Ω m

4. SPECIFIC CONDUCTANCE ( or CONDUCTIVITY),κ (kappa)

The reciprocal of resistivity(ρ) is known as specific conductance or simply conductivity(κ).
κ = 1/ρ ........(i)
We know, R = ρ l/a
1/ ρ = (1/R) ×l/a
κ = G × l/a ....... (ii)
In equation (ii), if l = 1cm and a = 1cm² then κ = G . Hence,
The conductance (G) of a solution of 1 cm length and having 1 cm² as the area of cross section, is called the conductivity of the solution.
or,
The conductance of 1 cm³ of the solution of the electrolyte is called its conductivity.
or,
In the term of S.I. base units, the conductance of 1 m³ of the conductor is called its conductivity.
Units of conductivity:-
As κ = 1/ρ , unit of ρ is Ω cm , Ω m (in S.I.). Therefore, unit of κ will be-
ohm^-1cm^-1 [Ω^-1 cm^-1]
or,
siemens cm^-1 [Scm^-1 ]
or,
ohm^-1 m^-1[Ω^-1 m^-1]
or,
siemens m^-1 [Sm^-1 ]
1Scm^-1= 100 Sm^-1
As conductivity expresses the conductance per unit volume, we compare the conductance of different substances in terms of their conductivities.
On the basis of conductivities, different substances have been divided into three categories - conductors, insulators and semiconductors.
Two types of conductivities of solutions are - Equivalent conductivity and Molar conductivity.

5.EQUIVALENT CONDUCTIVITY [Λ_eq,lambda eq.]

Two essential things to compare the conductance of the solutions of different electrolytes :- (i) the volumes of the solutions should be same and (ii) they must contain such definite amounts of the electrolytes which give ions carrying the same total charge.

What thing do we need to provide same total charge in solutions of different electrolytes ? :- gram equivalent weights.
What is gram equivalent weight ? :- If equivalent weight is expressed in gram , then it is termed as gram equivalent weight.
What is equivalent weight ? :-
(i) Eq. wt. of an element = Atomic mass / valency
(ii) Eq. wt. of an acid = Molar mass of the acid / Basicity of the acid
Basicity is the number of displaceable H⁺ ions from one molecule of the acid.
(iii) Eq. wt. of a base = Molar mass of the base / acidity of the base
Acidity is the number of displaceable OH^- ions from one molecule of the base.
(iv) Equivalent wt. of a salt = Molar mass of the salt / Total +ve valency of the metal atoms
(v) Equivalent wt. of an ion = Formula mass of the ion/ charge of the ion
DEFINITION :-EQUIVALENT CONDUCTIVITY :
If 1 gram equivalent of an electrolyte is dissolved in a solution then the total conductance of all ions generated is called equivalent conductivity.
Relation between equivalent conductivity and specific conductivity :-
If the volume of the solution containing one gram equivalent of the electrolyte is V cm³ then,
Equivalent conductivity = specific conductivity × V
Λ_eq = κ_v × V .....(i)
In terms of concentration :-
If the solution has the concentration of c gram equivalent per litre ( i.e. c gram equivalents are present in 1000 cm³ of the solution) then volume,V = 1000/c then eq (i) becomes ,
Λ_eq = κ_c × 1000/c = κ_c × 1000/Normality..........(ii)
Units of Λ_eq:-
As, Λ_eq = κ_v × V
therefore, unit of Λ_eq = unit of κ × unit of V = Ω^-1 cm^-1 × cm³/gram eq.
= Ω^-1cm²eq^-1 = S cm²eq^-1
In S.I., S m²eq^-1
[ In expression (ii), Λ_eq is in S cm²eq^-1, κ is in Scm^-1, 1000 is in cm³L^-1 and Normality is in g eq L^-1]
In the term of S.I., expression (ii) becomes as :-
Λ_eq = κ /Normality
Here, Λ_eq is in S m²eq^-1, κ is in Sm^-1, and Normality is in g eq m^-3
However, if normality is expressed in g eq L^-1, then expression (ii) becomes

6. MOLAR CONDUCTIVITY [Λ_m]

If 1 mole of an electrolyte is dissolved in a solution then the total conductance of all ions generated is called molar conductivity.
Relation between molar conductivity and specific conductivity :
Λ_m = κ_v × V or Λ_m = κ_c × 1000/c = κ_c × 1000/molarity
Where
κ = conductivity
V = Volume of the solution containing 1 mole of the electrolyte
c = molar concentration i.e., mol L^-1 ( or mol dm^-3)
Units of Λ_m:-
Ω^-1cm²mol^-1 = S cm²mol^-1
In S.I., S m²mol^-1

1 S m²mol^-1 = 10⁴ S cm²mol^-1
1 S cm²mol^-1 = 10^-4 S m²mol^-1
In terms of S.I. units the formula becomes,

However, if molarity is expressed in mol L^-1, then

7. Variation of G,κ,Λ_eq and Λ_m with dilution

In general, for weak as well as strong electrolytes,

Electrolytic conductance G increases with dilution because ions increase .
Specific conductance or conductivity κ decreases with dilution because number of ions per cm³ decrease.
Equivalent conductivity Λ_eq and molar conductivity Λ_m increase with dilution because Λ = κ × V and though κ decreases but V increases much more .

8. Variation of Λ_m with concentration

For strong electrolyte :-
The molar conductivity of strong electrolytes is found to vary with concentration according to Debye Huckel - Onsagar equation , which is given as
Λ_m^c = Λ_m⁰ - A √c
Where ,
A is a constant depending upon the temperature, nature of the solvent and type of the electrolytes. NaCl , BaCl₂ , MgSO₄ are called 1-1, 2-1 and 2-2 electrolytes respectively depending upon the charges on cation and anion. For a given solvent and temperature , all electrolytes of a particular type have the same value for the constant A.
Λ_m⁰ is the molar conductivity at infinite dilution, called limiting molar conductivity.
'C' is the concentration of the solution.
Λ_m^c is the molar conductivity at concentration 'C'.
⟹ This equation is found to hold good at low concentration .
⟹ If Λ_m is plotted against √c , a linear graph is obtained for low concentrations (with slope = -A ) but it is not linear for higher concentrations as shown in the figure given below in which KCl has been taken as an example of strong electrolyte.

The curve obtained for a strong electrolyte shows that there is only a small increase in conductance with dilution. This is because a strong electrolyte is completely dissociated in solution and so the number of ions remains constant. At higher concentrations, the greater inter - ionic attractions retard the motion of ions and, therefore, the conductance fals with increasing concentrations. With decrease in concentration, i.e., with dilution, the ions are far apart and , therefore , the interionic attractions decrease due to which the conductance increases with dilution and approaches a maximum limiting value at infinite dilution, designated as Λ_m⁰ or Λ_m^∞ .
For weak electrolytes:-
Λ_m^c increases as c decreases but doesnot reach a constant value even at infinite dilution . Hence, their Λ_m⁰ cannot be found experimentally.
⟹ For strong electrolytes, Λ_m^c increases with dilution because inter- ionic attractions decrease but for weak electrolytes, Λ_m^c increases with dilution because dissociation increases.
⟹ For weak electrolytes , Λ_m⁰ can be determined by using KOHLRAUSCH'S LAW.

9. NUMERICALS

Specific conductivity of a 0.12 normal solution of an electrolyte is 0.024 Ω^-1 cm^-1. Determine its equivalent conductivity.
Ans:- 200 Scm²eq^-1
The conductivity of a solution containing 1 gram of anhydrous BaCl₂ in 200 cm₃ of water has been found to be 0.0058 S cm^-1. What are the molar conductivity and equivalent conductivity of the solution ? ( Atomic weight of Ba = 137 and Cl = 35.5 ).
Ans:- Λ_m= 241.67 S cm²mol^-1, Λ_eq= 120.83 S cm²eq^-1
The electrical resistance of a column of 0.05 M NaOH solution of diameter 1 cm and length 50 cm is 5.55 × 10³ . Calculate its resistivity , conductivity and molar conductivity.
Ans:- ρ = 87.135 Ω cm ,κ = 0.01148Scm^-1,Λ_m=229.6Scm²mol^-1
0.5 normal solution of a salt placed between two platinum electrodes 2.0 cm apart and of area of cross section 4.0 sq. cm has a resistance of 25 ohms. Calculate the equivalent conductivity of solution.
Ans:- Λ_eq= 40 Scm²eq^-1
If specific conductivity of N/50 KCl solution at 298 K is 0.002765 Ω^-1 cm^-1 and resistance of a cell containing this solution is 100 ohms. Calculate the cell constant.
Ans:- 0.2765 cm^-1
The resistance of a decinormal solution of an electrolyte in a conductivity cell was found to be 245 ohms. Calculate the equivalent conductivity of the solution if the electrodes in the cell were 2 cm apart and each has an area of 3.5 sq. cm .
Ans:-23.32 Scm²eq^-1
Calculate the equivalent conductivity of 1 M H₂SO₄ solution, if its conductivity is 26 × 10^-2 Ω^-1 cm^-1. ( Atomic weight of sulphur = 32).
Ans:- 130 Scm²eq^-1
Molar conductivity of a 1.5M solution of an electrolyte is found to be 138.9 Scm². What would be the specific conductance of this solution ?
Ans:-0.208 Scm^-1
The conductivity of 0.2M solution of KCl at 298 K is 0.0248 Scm^-1. Calculate its molar conductivity.
Ans:-124 S cm²mol^-1