Conductance of Electrolytic Solutions, Specific, Equivalent, and Molar conductivities, Solved Examples

Electrochemistry is a branch of chemistry, and it deals with the study of the production of electricity from the energy released during spontaneous chemical reactions and the use of electrical energy to bring about non-spontaneous (requiring the input of external energy) chemical transformation. Electrochemistry deals with how much chemical energy produced in a redox reaction can be converted into electrical energy. A redox reaction is that in which oxidation and reduction take place simultaneously. The arrangements used to bring about the chemical transformations are called electrochemical cells. The cells are used to convert chemical energy into electrical energy and electrical energy into chemical energy.

Types of Electrochemical Cells

There are two types of electrochemical cells:

• Electrolytic cells: Electrolytic cells are used to convert electrical energy into chemical energy. 
• Galvanic or voltaic cells: Galvanic or voltaic cells are used to convert chemical energy into electrical energy. These galvanic or voltaic cells are also called electrochemical cells. Galvanic cells are further classified into two types they are Chemical cells and Concentration cells. 

Chemical cells

Chemical cells are those in which electrical energy is produced only due to chemical changes occurring within the cell, and no transfer of matter takes place. Example: Batteries. 

Concentration cells

Concentration cells in which electrical energy is produced due to physical changes involving the transfer of matter from one part of the cell to the other. For example – Standard hydrogen electrode

The three main aspects of study in electrochemistry are – Electrolysis or Electrolytic cells, Galvanic or voltaic or Electrochemical cells, and Electrolytic conduction.

Importance of Electrochemistry

Electrochemistry has great importance in everyday life. It has great theoretical and practical importance. There are many examples that indicate the great importance of electrochemistry-

• Many numbers of metals and chemicals are commercially produced by electrochemical methods. Metals like Na, Ca, Mg, etc., and chemicals like NaOH, Chlorine, Fluorine, etc.
• Batteries and cells are used in various gadgets or instruments. Example – torches, calculators, remotes, etc. These are used to convert chemical energy into electrical energy.
• The sensory signals are sent to the brain through the cells, and communication is also possible via these electrochemical processes.
• Electrochemically, reactions carried out are generally energy efficient and less polluting.
• Energy storage, energy conversion, sensing, etc., have a great role in electrochemistry.
• The coating of objects with metals or metal oxides through electrodeposition has a role in electrochemistry.
• Organic electrosynthesis and industrial electrolysis also have a great role in electrochemistry. These processes are feasible because of electrochemistry.

Conductance of Electrolytic Solutions 

Conductors are those substances that allow electricity to pass through them, whereas substances that do not allow electricity to pass through are called insulators. Conductors are divided into two classes,

• Electronic conductors: These are those which conduct electricity without undergoing any decomposition. These are called electronic conductors. The conduction, in this case, is due to the flow of electrons. Example – Metals, Graphite, and certain minerals.
• Electrolytic conductors: These are those which undergo decomposition when current passes through them. These are called Electrolytic conductors. Example: Solution of acids, bases, salts, and salts in water. In this case, the flow of electricity is due to the movements of ions. Hence, electrolytic conductance is also called ionic conductance.

Metallic conductors

Metallic conductors are those in which the flow of electricity is due to the flow of electrons, i.e., there is no flow of matter. In metallic conductors, the flow of electricity takes place without the decomposition of the substances. The conductance depends on the structure and density of metal as well as the number of valance electrons per atom. The electrical conduction decreases with the increase in temperature because Kernels start vibrating, which produces a hindrance in the flow of electrons. The resistance offered by metal is due to vibrating kernels.

Electrolytic Conductor  

In electrolytic conductors, the flow of electricity is due to the movement of ions, and hence there is no flow of matter. The flow of electricity takes place, accompanied by the decomposition of the substance. The electrical conduction increase with the increase in temperature. This is generally due to an increase in dissociation or a decrease in interionic attraction. The resistance shown by electrolytic solution is due to factors like interionic attractions, the viscosity of solvents, etc.

Electrical resistance and conductance 

Resistance (R) is the obstruction to the flow of electric current through the conductor. It is directly proportional to its length and inversely proportional to the area of cross-section (A). And according to ohm’s law, two ends of a conductor are applied with voltage (E), and current (I) flows through it. Then, the resistance of a conductor is:

R = E/I   

Or       

R = ρ l/A 

Resistance (R) is the obstruction to the (R = E/I) flow of electric current through the conductor. Resistance is directly proportional to its length ( l ) and inversely proportional to its area of cross-section (A). The constant of proportionality ρ (rho) is called specific resistance or resistivity. Resistance is measured in ohm, which in terms of SI base units is equal to (kgm²/S³A²). The S.I. unit of resistivity is ohm meter.

Conductance (G) is the inverse of resistance or the reciprocal of resistance is called conductance, and it is denoted by G. The unit of conductance is ohm inverse or reciprocal ohm or siemens or mhos.   

G = 1/R   

Or   

G = A/ρl = κ A/l

The S.I. unit of conductance is siemens, represented by the symbol S, and is equal to ohm^-1.

Specific, Equivalent, and Molar conductivities

Specific Conductivity: It is the conductance (G) of a one-centimeter cubic solution of the electrolyte. It is denoted by (κ), i.e., kappa. It is the conductance of the solution of one-centimeter length (l) and having one square meter area (a) of a cross-section. And specific conductivity is the reciprocal of resistivity is known as conductivity. Its unit is Sm^-1 or ohm^-1cm^-1.

κ = [l × G) / a]

Equivalent Conductivity: Equivalent conductivity of a solution at a dilution (v) is defined as the conductance of all the ions produced from one gram equivalent of electrolyte dissolved in v centimeter cubic of the solution when the distance between the electrodes is one centimeter, and the area of electrodes is so large that whole of the solution is contained between them. It is represented by lambda of equivalent conductivity. Unit of equivalent conductivity is siemens meter square per equivalent.  And  Equivalent conductivity = Specific Conductivity × V; V is the volume of solution containing one gram equivalent of the electrolyte is V centimeter cubic. If the solution has a concentration of c gram equivalent per liter, then the volume of the solution containing one gram equivalent will be 1000/c i.e., V = 1000/c

Λ_eq   = [κ × (1000/c_eq )] = [κ × (1000/Normality)]

Its unit is Sm²eq^-1 or Scm²eq^-1

Molar Conductivity: Molar Conductivity of a solution at a dilution (v) is defined as the conductance of all ions produced from one mole of the electrolyte dissolved in the v centimeter cubic of the solution when the electrodes are one centimeter, and the area of the electrode is so large that whole solution is contained between them. It is also represented by lambda of molar conductivity. Its unit is siemens meter square per mole.                                        

Molar conductivity = Specific Conductivity × V

Conductivity Cell (G*) is used to measure the resistance of an ionic solution. It consists of two platinum electrodes coated with platinum black. These have an area of cross-section equal to A and are separated by distance (l).  

Cell constant (G*) = l / A ; 

Conductivity (K) = Conductance (G)  × Cell constant ( G*)

Its unit is Sm²mol^-1. 

Strong Electrolyte: Those electrolytes which dissociate almost completely in the aqueous solution or in a molten state are called strong electrolytes. Example – HCl, Sulfuric acid, nitric acid, etc.

Weak Electrolyte: Those electrolytes which have a low degree of dissociation and hence conduct electricity to a small extent are called weak Electrolytes. Example – Ammonium hydroxide, Calcium hydroxide, etc. 

Kohlrausch Law of Independent migration of ions: Limiting molar conductivity of an electrolyte is the sum of the individual contribution of the anion and cation of the electrolyte. The limiting molar conductivity of an electrolyte is the sum of limiting ion conductivities of the cation and the anion, each multiplied by a number of ions present in the one formulae unit of electrolyte.

Degree of dissociation of weak electrolyte: It is represented by alpha. It is defined as the Molar conductivity of a solution at any concentration (c) divided by limiting molar conductivity.

Dissociation Constant of a Weak electrolyte: The dissociation constant of a weak electrolyte is directly proportional to the concentration of the solution and the square of the degree of dissociation of the weak electrolyte.

Solved Examples on Conductance of Electrolytic Solutions

Example 1: The resistance of a conductivity cell containing 0.001M KCl solution at 298K is 1500 ohm in a conductivity cell. If the cell constant of the cell is 0.367 per cm, calculate the molar conductivity of the solution.

Solution:

Cell constant = Conductivity/Conductance = Conductivity × Resistance

= (0.146 × 10^-3) Scm^-1 × 1500 ohm 

= 0.219cm^-1

Example 2: The Conductivity of 0.20 m solutions of KCl at 298K is 0.0248 Scm^-1. Calculate its molar conductivity.

Solution: 

Molar conductivity = (κ × 1000)/Molarity = [(0.0248Scm^-1 × 1000cm³ L^-1)/ 0.20 molL^-1]

= 124 Scm² mol^-1

Example 3: The electrical resistance of a column of 0.05mol/L NaOH solution of diameter 1 cm and length 50 cm is 5.55 × 10³ ohm. Calculate resistivity, conductivity, molar conductivity.

Solution:

Area = πr² = 3.14 × 0.5² cm = 0.785 cm² = 0.785 ×10^-4 m², ρ = 5.55 × 10³ ohm 

R = ρ l/A = [(5.55× 103 ohm × 0.785cm2)/50 cm] 

= 87.135 ohm cm

Conductivity = κ = 1/ρ = (1/87.135)Scm^-1  = 0.01148 Scm^-1 

Molar Conductivity = [(κ × 1000)/c] cm³L^-1 = (0.01148 Scm^-1 × 1000 cm³L^-1)/0.05molL^-1

= 229.6 Scm² mol^-1

FAQs on Conductance of Electrolytic Solutions

Question 1: How does the conductivity of the solution vary with concentration?

Answer: 

Conductivity is conductance between two opposite faces of the one-centimeter cube. On dilution, the number of ions per centimeter cubic decreases; therefore, conductivity decrease on dilution. 

Question 2: How does the Molar Conductivity of Strong and Weak electrolytes vary with concentration?

Answer:

In the case of Strong Electrolytes, the molar conductivity increases slightly with dilution as the mobility of ions increases. In case of weal electrolytes the degree of ionization increases with dilution. Therefore, there is a large increase in molar conductivity with dilution.

Question 3: What is the application of Kohlrausch law?

Answer: 

Application of Kohlrausch law is,

• Calculation of molar conductivity at infinite dilution for weak electrolytes: The molar conductivity of a weak electrolyte at infinite dilution cannot be determined experimentally. Firstly, because the conductance of such solution is low, and secondly, because the dissociation of such electrolyte is not complete even at very high dilution. 
•  Calculation of Degree of Dissociation 
• Calculation of Dissociation constant of a weak electrolyte 
• Calculation of solubility of a sparingly soluble salt – Salts such as AgCl, Barium sulfate, Lead sulfate, etc., which dissolved to a very small extent in water called sparingly  soluble salt.
• Calculation of ionic product of water

Question 4: Explain Metallic Conductor.

Answer:

In a metallic conductor, the flow of electricity takes place without the decomposition of the substance. Here, the flow of electricity is due to the flow of electrons only. The electrical conduction decrease with increase of temperature. This is because Kernels start vibrating, which produces a hindrance in the flow of electrons.

Question 5: Explain Electrolytic Conductor.

Answer:

In an Electrolytic Conductor, the flow of electricity takes place accompanied by the decomposition of the substance. Here, flow of electricity is due to the movement of ions. The electrical conduction increase with increase of temperature. This is generally due to an increase in dissociation or decrease in dissociation or a decrease in the interionic attraction.