Electrochemistry : Molar conductivity

Metallic and Electrolytic conductors

(1) Conductors and Non – conductors : All substances do not conduct electrical current. The substances which allow the passage of electric current are called conductors. The best metal conductors are such as copper, silver, tin, etc. On the other hand, the substances which do not allow the passage of electric current through them are called non-conductors or insulators. Some common examples of insulators are rubber, wood, wax, etc.

(2) Types of conductors : The conductors are broadly classified into two types,

(i) Metallic conductors or electronic conductors

(a) In metallic conductors, flow of electricity takes place without the decomposition of the substances.

(b) Flow of electricity is due to the flow of electrons only i.e., there is no flow of matter.

(c) In addition to metals, graphite and certain minerals also conduct electricity due to presence of free electrons in them, hence they are collectively called as electronic conductors.

(d) Metallic conduction decreases with increase of temperature. This is because kernels start vibrating which produce hinderance in the flow of electrons.

(e) The resistance offered by metals is also due to vibrating kernels.

(f) Metallic conductors obey Ohm’s law.

(ii) Electrolytic conductors or Ionic conductors

(a) In electrolytic conductors flow of electricity takes place by the decomposition of the substance (Electrolyte).

(b) Flow of electricity is due to the movement of ions and hence there is flow of matter.

(c) Solutions of acids, bases and salts are the examples of electrolytic conductors.

(d) The electrolytic conduction will not occur unless the ions of the electrolyte are free to move. Therefore, these substances do not conduct electricity in the solid state but conduct electricity in the molten state or in their aqueous solutions.

(e) The electrical conduction increases with increase of temperature. This is generally due to increase in dissociation or decrease in the interionic attractions.

(f) The resistance shown by an electrolytic solution is due to factors like interionic attractions, viscosity of solvent etc.

(g) Electrolytic conductors also obey Ohm’s law.

(h) All electrolytes do not ionise to the same extent in solution. On this basis, electrolytes are broadly divided into two types: strong electrolytes and weak electrolytes.

Strong electrolytes : The electrolytes which are almost completely dissociated into ions in solution are called strong electrolytes. For example, NaCl, KCl, HCl, NaOH, NH₄NO₃ etc.

Weak electrolytes : The electrolytes which do not ionise completely in solution are called weak electrolytes. For example, CH₃COOH, H₂CO₃, H₃BO₃, HCN, HgCl₂, ZnCl₂, NH₄OH etc. Thus in case of weak electrolytes, an equilibrium is established between the unionised electrolyte and the ions formed in solution. The extent of ionisation of a weak electrolyte is expressed in terms of degree of ionisation or degree of dissociation. It is defined as the fraction of total number of molecules of the electrolyte which ionise in the solution. It is generally denoted by alpha (α) For strong electrolytes, α is almost equal to 1 and for weak electrolytes, it is always less than 1.

The electrical conductivity of the solutions of electrolytes depends upon the following factors,

(a) Interionic attractions : These depend upon the interactions between the ions of the solute molecules, i.e., solute-solute interactions. If the solute-solute interactions are large, the extent of dissociation will be less. These interactions are also responsible for the classification of electrolytes as strong electrolytes and weak electrolytes.

(b) Solvation of ions : These depend upon the interactions between the ions of the solute and the molecules of the solvent and are called solute-solvent interactions. If the solute-solvent interactions are strong, the ions of the solute will be highly solvated and their electrical conductivity will be low.

(c) Viscosity of the solvent: The viscosity of the solvent depends upon the solvent-solvent interactions. Larger the solvent-solvent interactions, larger will be the viscosity of the solvent and lower will be the electrical conductivity of the ions.

Electrolytic conduction.

When a voltage is applied to the electrodes dipped into an electrolytic solution, ions of the electrolyte move and, therefore, electric current flows through the electrolytic solution. The power of the electrolytes to conduct electric current is termed 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 ∞ V

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

or $\[I=\frac{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 Ω The above equation is known as Ohm’s law. Ohm’s law may also be stated as,

“the strength of current flowing through a conductor is directly proportional to the 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 any conductor is directly proportional to the length (l) and inversely proportional to the area of cross-section (a) so that

$\[R\propto \frac{l}{a}\,\,\,\,\text{or}\,\,\,\text{R}=\rho \frac{l}{a}\$

where ρ (rho) is the constant of proportionality and is called specific resistance or resistivity. The resistance depends upon the nature of the material.

Units : The unit of resistance is ohm (Ω) In terms of SI, base unit is equal to (kgm²)/(s³A²).

(3) Resistivity or specific resistance : We know that resistance R is

$\[R=\rho \frac{l}{a}$

Now, if l =1 cm, a = 1 cm² then R = ρ

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 $\[\rho =R.\frac{a}{l}=Ohm\frac{c{{m}^{2}}}{cm}=Ohm.\,\,\,cm$

Its SI units are Ohm metre (Ωm). But quite often Ohm centimetre (Ω cm) is also used.

(4) Conductance : It is a measure of the ease with which current flows through a conductor. It is an additive property. It is expressed as G. It is reciprocal of the resistance, i.e.,

$\[G=\frac{1}{R}\$

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

According to SI system, the units of electrical conductance are Siemens, S (i.e., 1S = 1 Ω⁻¹).

(5) Conductivity : The inverse of resistivity is called conductivity (or specific conductance). It is represented by the symbol, κ (Greek kappa). The IUPAC has recommended the use of term conductivity over specific conductance. It may be defined as, the conductance of a solution of 1 cm length and having 1 sq. cm as the area of cross-section. In other words, conductivity is the conductance of one centimetre cube of a solution of an electrolyte. Thus, $\[\kappa =\frac{1}{\rho }$

Units : The units of conductivity are $\[\kappa =\frac{1}{Ohm.\,\,cm}=Oh{{m}^{-1}}$ cm^–1 or Ω⁻¹ cm⁻¹

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

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

It is denoted by Λ (lambda). Molar conductance is related to specific conductance (κ) as,

$\[\Lambda =\frac{\kappa }{M}$

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,

$\[\Lambda =\frac{\kappa \times 1000}{M}$

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,

Conductivity (G) = Conductivity = Molar conductivity (Λ)

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

Molar conductivity (Λ) = 100 × Conductivity

In other words, (Λ) = κ × V

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

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

M mole of electrolyte is present in 1000 cm³

1 mole of electrolyte is present in $\[=\frac{1000}{M}c{{m}^{3}}$ of solution

Thus, Λ = κ × Volume in cm³ containing 1 mole of electrolyte.

or $\[\Lambda =\frac{\kappa \times 1000}{M}$

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

$\[\Lambda =\frac{\kappa \times 1000}{M}$

The units of κ are Scm⁻¹ and units of Λ are,

$\[\text{ }\!\!\Lambda\!\!\text{ }=S c{{m}^{-1}}\times \frac{c{{m}^{3}}}{mol}=S\,\,c{{m}^{2}}\,\,\,mo{{l}^{-1}}=S\,\,c{{m}^{2}}\,\,mo{{l}^{-1}}$

According to SI system, molar conductance is expressed as S m² mol⁻¹ if concentration is expressed as mol m⁻³. This is because

$\[mol\,\,\,{{m}^{-3}}=1000\left( \frac{L}{{{m}^{3}}} \right)\,\,\,\,\times \,\,\,\,molarity\left( \frac{mol}{L} \right)$

Now, $\[\Lambda =\frac{\kappa }{M}$ $\[=\frac{\kappa (S{{m}^{-1}})}{(1000\,\,L{{m}^{-3}})\times (Molarity\,\,mol\,\,{{L}^{-1}})}=S\,\,{{m}^{2}}\,\,mo{{l}^{-1}}$

Thus, the units of molar conductivity are S m² mol⁻¹(SI) and S cm² mol⁻¹ Both types of units are used in literature and are related to each other as

1S m² mol⁻¹ = 10⁴ S cm² mol⁻¹

1S cm² mol⁻¹ = 10⁻⁴ S m² mol⁻¹

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

It is expressed as Λ_e and is related to specific conductance as

$\[{{\Lambda }_{e}}=\frac{\kappa \times 1000}{C}=\kappa \times \frac{1000}{M}$ (M is Molarity of the solution)

where C is the concentration in gram equivalent per litre (or Normality). This term has earlier been quite frequently used. Now it is replaced by molar conductance. The units of equivalent conductance are

Ohm⁻¹ cm² (gm equiv)⁻¹

(8) Experimental measurement of conductance

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

We know that unknown resistance can be measured on a Wheatstone bridge. However, for measuring the resistance of an ionic solution, we face following two main difficulties,

(a) Direct current (DC) cannot be passed because it may change the composition of the solution by electrolysis and polarization.

(b) A solution of unknown resistance cannot be connected to the bridge like a metallic wire or other solid conductor.

First difficulty can be solved by passing an alternating current (AC) from ac source of power. The second difficulty can be solved by using a specially designed vessels called conductivity cell.

(ii) Calculation of conductivity : We have seen that conductivity (k) is reciprocal of resistivity (ρ), i.e.,

$\[\kappa =\frac{1}{\rho }$ and $\[\rho =R\frac{a}{l}$ ∴ $\[\kappa =\frac{1}{R}\left( \frac{l}{a} \right)\,\,\,\,\text{or}\,\,\,\kappa =G\left( \frac{l}{a} \right)$

where G is the conductance of the cell, l is the distance of separation of two electrodes having cross section area a cm² The quantity $\[\left( \frac{l}{a} \right)$ 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 calculated as,

κ = G × Cell constant i.e.,

Conductivity = Conductance × Cell constant

(iii) Determination of cell constant : The cell constant is generally not calculated from the values of l and a because these are difficult to measure for a given cell. However, it is usually determined accurately by measuring the conductance of a standard solution whose conductivity is known. For this purpose, a standard solution of KCl is used whose conductivity is known at different concentrations and temperatures. The conductivities of different KCl solutions at 298 K are given in table.

Conductivity and molar conductivity of KCl solutions at 298.15 K

Molarity	Concentration	Conductivity		Molar conductivity
(mol L^–1)	(mol m^–3)	*S cm^–¹*	S m^–1	*S cm² mol^–1*	*S m² mol^–1*
1.000	1000	0.1113	11.13	111.3	111.3×10^–4
0.100	100.0	0.0129	1.29	129.0	129.0×10^–4
0.010	10.00	0.00141	0.141	141.0	141.0×10^–4

Electrochemistry : Molar conductivity

Electrochemistry : Molar conductivity

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