The conductance of an ion depends on its size in an aqueous medium or in the solvent. Bigger is the ionic size lesser is its conductance

Example: The order of size of hydrated ionic radii of alkali metal cations is as Li⁺_(aq) < Na⁺_(aq) < K⁺_(aq)< Rb⁺_(aq)< Cs⁺_(aq). Hence the ease of ionic conductance is Li⁺_(aq) > Na⁺_(aq) > K⁺_(aq) > Rb⁺_(aq) > Cs⁺_(aq)

Concept of Molar Conductivity of an Electrolyte (Λ):

The different solutions may have different concentrations and hence contain a different number of ions. Hence electrolytic conductivity is not a suitable quantity to compare conductance of different solutions. In 1880 the German physicist George Kohlrausch introduced the concept of molar conductivity which is used to compare conductance of different solutions.

The molar conductivity of an electrolyte is defined as the electrolytic conductivity divided by the molar concentration C of the dissolved electrolyte.

Λ = κ / C    or   Λ  = κV

S.I. unit of electrolytic conductivity is siemens per metre (Sm^-1) or S cm^-1. S.I. unit of molar conductivity is siemens square metre per mole (S m² mol^-1). or S cm² mol^-1

If concentration C is measured in M i.e. mol L^-1 or mol dm^-3, then the relationship can be written as

If normality of solution is given then the conductivity is called equivalent conductivity and the relation can be written as

The relation between molar conductivity and equivalent conductivity is

Λ _M =   n Λ_E

Where n is total positive or negative valencies.

Variation of Electrolytic Conductivity with Concentration:

The electrolytic conductivity depends on the number of ions present in a unit volume of a solution. on dilution the degree of dissociation increases. Thus the number of current-carrying ions in the solution increases. But actually, the number of current-carrying ions per unit volume decreases. Hence the activity of the number of ions decreases and hence the electrolytic conductivity also decreases.

For the strong electrolyte, the electrolytic conductivity increases sharply with increasing concentration. For the weak electrolyte, the electrolytic conductivity is very low in dilute solutions and increases much more gradually with increase in the concentration. and this increase is due to an increase in active ions in the solution.

Variation of Molar Conductivity with Concentration:

The molar conductivity of both strong and weak electrolytes increases with dilution i.e. decrease in the concentration.

The molar conductivity is the conductance of all the ions produced by one mole of the electrolyte. Due to an increase in dilution degree of dissociation increases and which results in an increase in the molar conductivity.

For the strong electrolyte, the molar conductivity increases sharply with increasing concentration. Similarly weak electrolyte the molar conductivity increases gradually with an increase in the concentration.

Friedrich Kohlrausch Relation:

Friedrich Kohlrausch performed repeated experiments and plotted a graph of molar conductivity versus the square root of the concentration of a solution.

They showed that the molar conductivity of strong electrolytes varies linearly with the square root of concentration and established the following relation

Where Λ = Molar conductivity at given concentration
Λ_o = Molar conductivity at zero concentration or infinite dilution
C = Concentration of solution
α = constant.

The graph of molar conductivity versus the square root of the concentration of a solution is linear for a strong electrolyte. But such a graph for weak electrolytes is not a straight line.

Kohlrausch Law:

The law states that at infinite dilution, each ion migrates independently of its co-ion and makes its own contribution to the total molar-conductivity of an electrolyte. irrespective of the nature of the other ion with which it is associated.

Thus according to the law at infinite dilution, the total molar conductivity is the algebraic sum of molar conductivities of cation and anion.

Where, Λ = Molar conductivity of a solution
λ ₊^o = Molar conductivity of a cation
λ _–^o = Molar conductivity of an anion

For electrolyte A_mB_n, the molar conductivity at infinite dilution is

Illustration:

In both the cases the difference in of K and Na salt is the difference between Λ_o values of K and Na ions, and it is constant. This illustrates the law.

Applications of Kohlrausch Law:

• The law can be used to calculate the molar-conductivity of any electrolyte at zero concentration.
• The law is particularly useful in the calculation of Λ_o of weak electrolyte for which extrapolation method is not useful.
• Using the extrapolation method value of Λo for strong electrolytes is found and using that value of Λ_o weak electrolyte can be calculated.

Calculation of the Molar Conductivity of any Electrolyte at Zero Concentration:

Let us calculate Λ_o for weak electrolyte acetic acid (CH₃COOH|) using Λ_o values of strong electrolytes sodium acetate (CH₃COONa|) and sodium chloride (NaCl).

The values of  Λ_o for strong electrolytes can be found by extrapolation method and using them for weak electrolyte Λ_o  can be calculated.

Relation Between Molar Conductivity and Dissociation Constant (Theory of Weak Electrolyte) :

Where α = degree of dissociation
Λ = Molar conductivity at concentration C

Λ_o  = Molar conductivity at zero concentration

Now, the dissociation constant k for weak electrolyte is given by

This is the relation between dissociation constant and molar conductivity of the weak electrolyte. This relation is called Ostwald’s equation.

Measurement of Conductivity:

The determination of conductivity and molar conductivity of a solution consists of a measurement of the resistance of the solution using Wheatstone’s metre bridge.

The cell used for measurement consists of a glass tube with two platinum plates coated with a thin layer of finely divided platinum called platinum black. The cell is to be dipped in a solution whose resistance is to be measured as shown in fig.

Now conductivity of a cell is given by

The quantity l/a  is constant and called cell constant and is defined as the ratio of the distance between the electrodes and the area of cross-section of the electrode. It is denoted by ‘b’

The resistance of the solution is found using Wheatstone’s metre bridge. Using the above relation the conductivity of the solution is calculated. The molar conductivity is obtained by using the formula and value of cell constant b can be obtained using the formula b = kR

The circuit arrangement is as shown below.

Types of Conduction:

Metallic Conduction:

The charge transfer through electronic conductors is called metallic conduction

Characteristics of metallic conduction:

• In this conduction, charge transfer occurs through metal.
• It involves the flow of electrons.
• There is no movement of metal atoms.
• There is no chemical change of metal.

Ionic or Electrolytic Conduction:

The charge transfer through electrolytic conductors is called electrolytic conduction

Characteristics of metallic conduction:

• In this conduction, charge transfer occurs through molten electrolyte or its aqueous solution
• It involves the motion of ions in the solution.
• There is a movement of ions.
• There is a chemical change in an electrolyte.

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In this article, we shall study the concept of electrochemistry, its cause, and its terminology.

Electrochemistry is a branch of chemistry which deals with the interrelationship between chemical energy and electrical energy. The study of electrochemistry is broadly divided into two branches. a) Conversion of chemical energy into electrical energy and b) Conversion of electrical energy into chemical energy. Electrochemistry has wide applications in engineering and science. Michael Faraday is called the father of electrochemistry.

Basic Terminology of Electrochemistry:

Oxidation Reaction:

The loss of an electron or electrons by a species is called oxidation.  Example

Na    →    Na⁺ +    e^–

In oxidation, the oxidation number of elements increases as a result of the loss of electrons. In the above example, the oxidation number of sodium increases from 0 to +1. Thus the oxidation can also be defined as the process in which the oxidation number of an element increase.

Reduction Reaction:

The gain of an electron by a species is called reduction.  Example.

Cl    +     e^–   →     Cl^–

In reduction, the oxidation number of an element decreases as a result of the gain of electrons. In the above example the oxidation number of chlorine decreases from 0 to -1. Thus the reduction can also be defined as the process in which the oxidation number of an element decreases.

Oxidizing Agent (Oxidant):

The substance which accepts electrons and makes the other substance to lose electrons is called oxidizing agent or oxidant. Consider reaction

2Mg     +   O₂    →   2MgO

In this reaction oxygen is making magnesium to lose electrons and hence in this reaction oxygen is the oxidizing agent.

Reducing Agent (Reductant):

The substance which loses electrons and makes the other substance to accept electrons is called a reducing agent or reductant. Consider reaction

2Mg     +   O₂    →   2MgO

In this reaction, magnesium is making oxygen to accept electrons and hence in this reaction magnesium is reducing agent.

Redox Reactions:

In any of a chemical reaction, if one of the reactants is oxidized, the other is surely reduced. Consider reaction

2Mg     +   O₂    →   2MgO

In this reaction, Mg is oxidized to MgO (loss of electrons by Mg), whereas oxygen is reduced to MgO (gain of electrons by oxygen). Hence oxidation and reduction take place simultaneously.  Therefore, all such reactions are called as reduction-oxidation reactions or redox reactions. In all such reactions, one of the reactants loses the electrons (oxidized) while other gains those electrons (reduced). Such a reaction may be expressed as the sum of two half-reactions. One reaction involving loss of electrons by a species and another involving gain of electrons by a species. This is the basis of all electrochemical processes.

Conductance:

The substances that allow the flow of electricity through them are called conductors.  The flow of electricity through a conductor involves the transfer of electrons from one point to the other. Depending on the mechanism of the transfer of electrons, the conductors are classified into two types.  a)  Electronic conductors b) Electrolytic conductors

Electronic Conductors:

The conductors through which the conduction of electricity occurs by direct flow of electrons under the influence of applied potential are known as electronic conductors. e.g. copper, aluminium, silver, mercury etc.

Characteristics of Electronic Conductors:

• In electronic conductors, the flow of electricity occurs by the migration of electrons through the conductor.
• In electronic conductors, the conduction does not involve the transfer of matter.
• In electronic conductors, the conduction process does not involve chemical change.
• The resistance of electronic conductors increases and their conductivity decreases with the increase in temperature.
• Ohm’s law is followed but Faraday’s laws are not followed.

Electrolytic Conductors:

The conductors through which the conduction of electricity occurs by the migration of positive and negative ions under the influence of applied potential are known as electrolytic conductors. e.g. electrolysis of fused NaCl.

Characteristics of Electrolytic Conductors:

• In electronic conductors, the flow of electricity occurs by the migration of positive and negative ions through the conductor.
• In electrolytic conductors, the conduction involves the transfer of matter.
• In electrolytic conductors, the conduction process always involves chemical change.
• The resistance of electronic conductors decreases and their conductivity increases with the increase in temperature.
• Both Ohm’s law and Faraday’s laws are followed.

Resistance and Conductance:

By ohm’s law, V = IR

Where R = Resistance of a conductor V = Potential difference across the conductor I = current through the conductor. S. I. unit of resistance is ohm (Ω), that of potential difference is volt (V) and that of current is ampere (A)

Resistance of an Electronic Conducting Wire:

Experimentally it is found that the value of resistance (R) depends on the length (L) of a conductor, the area of cross-section (A) of conductor and nature of a conductor as follows:-

The resistance is directly proportional to the length of a conductor.

R α  L   ………………. (1)

The resistance is inversely proportional to the area of a cross-section.

R α  1/A   ………………. (2)

The resistance depends on the nature of the conductor.

From equation (1) & (2)

R = ρl / A

This is an expression for the specific resistance or the resistivity of a material of a conductor.

Resistivity or Specific Resistance:

We have, ρ = RA / l

Let A = 1 unit  and L = 1 unit, then ρ = R

Thus specific resistance or resistivity of a material of a conductor is defined as that resistance of a conductor whose area of cross-section and its length is unity.

Unit of Resistivity or Specific Resistance:

We have, ρ = RA / l

Hence unit of ρ  = Unit of R x Unit of Area / Unit of Length = ohm x metre² / metre   = ohm metre

Therefore, S.I. unit of resistivity or specific resistance is ohm metre (Ωm)

Conductance:

Reciprocal of resistance is called conductance (K). Its S.I. unit is mho or siemens.

Conductivity:

Reciprocal of resistivity is called as conductivity (κ)

Conductance of an Electronic Conducting Wire:

Experimentally it is found that 1. The conductance (G) is directly proportional to the area of cross-section (A) of a conductor

G α  A   ………………. (1)

The conductance (G) is inversely proportional to the length (L) of the conductor  

G α  1/L     ………..  (2)

It also depends on the material of the conductor.

From equation (1) & (2)

G α  A / L

G =  κA / L

k is constant called specific conductance or conductivity.

This is an expression for the resistance of a conducting wire.

Now,         Let A = 1 unit  and L = 1 unit , then G = κ

Thus specific conductance or conductivity of a material of a conductor is defined as that conductance of a conductor whose area of cross-section and its length is unity. S.I. unit of conductivity is siemens per metre (S m-1). Other units used are S cm-1, W-1m-1, and W^-1cm^-1.

Next Topic: Ionic Conduction

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