1. Introduction to Conductance
Conductance is a measure of how easily electric current flows through a material or solution. In electrochemistry, conductance is primarily concerned with the movement of ions in electrolyte solutions. When an electrolyte such as sodium chloride, hydrochloric acid, or potassium nitrate dissolves in water, it dissociates into positively charged ions (cations) and negatively charged ions (anions). These ions act as charge carriers and enable the solution to conduct electricity.
Conductance is the reciprocal of resistance and is represented by the symbol G. A solution with high conductance offers less resistance to the flow of electric current, whereas a solution with low conductance offers greater resistance. The SI unit of conductance is the siemens (S).
The study of conductance is important in electrochemistry because it provides valuable information about the concentration, mobility, and behavior of ions in a solution. Conductance measurements are widely used to determine the degree of ionization of electrolytes, monitor chemical reactions, measure water purity, and perform conductometric titrations.
Electricity in ionic solutions is carried by the movement of ions rather than electrons. When an external voltage is applied, positively charged ions move toward the cathode, while negatively charged ions migrate toward the anode. This ionic movement produces an electric current within the solution.
Conductance has numerous practical applications in everyday life. For example, the sulfuric acid solution in automobile batteries conducts electricity efficiently, allowing the battery to function. Salt water has a higher conductance than pure water because it contains dissolved ions. Similarly, drinking water conductivity measurements are used to assess water quality and detect the presence of dissolved minerals and impurities.
2. What is Electrolytic Conduction?
Electrolytic conduction is the process by which electric current passes through an electrolyte solution due to the movement of ions. Electrolytes are substances that dissociate into positively charged ions (cations) and negatively charged ions (anions) when dissolved in water or melted. These ions act as charge carriers and enable the solution to conduct electricity.
Electrolytic conduction differs significantly from metallic conduction. In metals, electric current is carried by the movement of free electrons, and the metal itself does not undergo any chemical change during conduction. In contrast, electrolytic conduction occurs through the movement of ions in a solution or molten electrolyte and is often accompanied by chemical reactions at the electrodes.
When an external electric potential is applied across an electrolyte solution, the ions begin to migrate toward oppositely charged electrodes. Positively charged ions, known as cations, move toward the negatively charged electrode called the cathode. Negatively charged ions, known as anions, move toward the positively charged electrode called the anode.
The simultaneous movement of cations and anions in opposite directions results in the flow of electric current through the solution. Therefore, the conductivity of an electrolyte depends on the number, charge, and mobility of ions present in the solution.
3. Definition of Conductance
Conductance is a measure of the ease with which electric current flows through a conductor or an electrolyte solution. In electrochemistry, conductance indicates how effectively ions present in a solution can carry electric charge. A solution containing a large number of mobile ions exhibits high conductance, whereas a solution with fewer ions exhibits lower conductance.
Conductance is represented by the symbol G and its SI unit is the siemens (S). The concept of conductance is closely related to electrical resistance. While resistance opposes the flow of electric current, conductance measures the ability of a substance to allow current to pass through it.
Mathematically, conductance is defined as the reciprocal of resistance:
G = 1/R
Where:
- G = Conductance of the conductor or electrolyte solution (Siemens, S)
- R = Electrical resistance of the conductor or solution (Ohm, Ω)
Thus, a decrease in resistance results in an increase in conductance, allowing electric current to flow more easily through the medium.
4. Specific Conductance (Conductivity, κ)
Specific conductance, also known as conductivity, is a measure of the ability of an electrolyte solution to conduct electric current. It is represented by the Greek letter κ (kappa). Conductivity depends on the number of ions present in the solution and their ability to move under the influence of an electric field. A solution containing a large concentration of highly mobile ions exhibits greater conductivity than a solution with fewer or less mobile ions.
Specific conductance is defined as the conductance of a solution contained between two electrodes that are 1 unit distance apart and have a cross-sectional area of 1 unit square. The SI unit of conductivity is siemens per meter (S m−1), although S cm−1 is commonly used in laboratory measurements.
The conductivity of an electrolyte solution can be calculated using the following relationship:
κ = G(l/A)
Where:
- κ = Specific conductance or conductivity
- G = Conductance of the solution
- l = Distance between the electrodes
- A = Area of the electrode surface
Several factors affect conductivity, including the concentration of the electrolyte, temperature, nature of the ions, degree of ionization, and viscosity of the solvent. Generally, conductivity increases with an increase in ion concentration and temperature.
Conductivity measurements are important in electrochemistry because they help determine the strength of electrolytes, monitor chemical reactions, assess water quality, and study ionic behavior in solutions. Therefore, conductivity serves as a valuable tool in both scientific research and industrial applications.
5. Cell Constant
The cell constant is a characteristic property of a conductivity cell that depends on the geometry of the electrodes used in conductivity measurements. It accounts for the distance between the electrodes and their effective surface area. Since conductivity measurements are influenced by the dimensions of the conductivity cell, the cell constant is used to obtain accurate conductivity values.
The cell constant is represented by the ratio of the distance between the electrodes (l) to the electrode area (A). It is usually expressed in units of cm−1 or m−1.
Cell Constant = l/A
Where:
- l = Distance between the electrodes
- A = Effective area of the electrodes
The cell constant is required because the exact dimensions of practical conductivity cells may vary slightly. To determine its value accurately, the conductivity cell is calibrated using a standard solution of known conductivity, most commonly a potassium chloride (KCl) solution. By measuring the conductance of the standard KCl solution and comparing it with its known conductivity, the cell constant can be calculated.
Once determined, the cell constant is used to calculate the conductivity of unknown electrolyte solutions with high accuracy.
6. Molar Conductance
Molar conductance is the conductance of the volume of solution that contains one mole of an electrolyte when placed between two electrodes that are sufficiently far apart. It provides information about the conducting ability of all the ions produced by one mole of an electrolyte in solution. Molar conductance is represented by the symbol Λm.
The SI unit of molar conductance is S m2 mol−1. However, in electrochemistry, it is commonly expressed as S cm2 mol−1. Unlike specific conductance, molar conductance depends not only on the conductivity of the solution but also on the concentration of the electrolyte.
Molar conductance is particularly useful for comparing the conducting abilities of different electrolytes because it relates conductivity to the amount of electrolyte present. As the concentration decreases, the ions experience less interionic attraction and can move more freely, causing molar conductance to increase.
Molar conductance is calculated using the following equation:
Λm = (κ × 1000) / C
Where:
- Λm = Molar conductance (S cm2 mol−1)
- κ = Specific conductance or conductivity (S cm−1)
- C = Concentration of the electrolyte (mol L−1)
The study of molar conductance helps chemists understand ion mobility, electrolyte dissociation, and the behavior of strong and weak electrolytes in solution. It also plays an important role in determining limiting molar conductance and analyzing ionic equilibria.
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 [Λeq,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
Λeq = κv × 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 ,
Λeq = κc × 1000/c = κc × 1000/Normality..........(ii) - Units of Λeq:-
As, Λeq = κv × V
therefore, unit of Λeq = 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), Λeq 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 :-
Λeq = κ /Normality
Here, Λeq 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 [Λm]
- 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 :
Λm = κv × V or Λm = κc × 1000/c = κc × 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 Λm:-
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,Λeq and Λm 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 Λeq and molar conductivity Λm increase with dilution because Λ = κ × V and though κ decreases but V increases much more .
8. Variation of Λm 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
Λmc = Λm0 - 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.
Λm0 is the molar conductivity at infinite dilution, called limiting molar conductivity.
'C' is the concentration of the solution.
Λmc is the molar conductivity at concentration 'C'.
⟹ This equation is found to hold good at low concentration .
⟹ If Λm 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 Λm0 or Λm∞ . - For weak electrolytes:-
Λmc increases as c decreases but doesnot reach a constant value even at infinite dilution . Hence, their Λm0 cannot be found experimentally.
⟹ For strong electrolytes, Λmc increases with dilution because inter- ionic attractions decrease but for weak electrolytes, Λmc increases with dilution because dissociation increases.
⟹ For weak electrolytes , Λm0 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:- Λm= 241.67 S cm2mol-1, Λeq= 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,Λm=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:- Λeq= 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