Equivalent Conductivity Formula

Equivalent conductivity is the conductance of a volume of solution containing one equivalent of an electrolyte. It is denoted by the symbol ∧

Consider the volume of a V cm3 solution having one electrolyte equivalent. It has the same conductance as comparable conductance.

Specific conductance is the conductance exhibited by a 1 cm3 solution containing this electrolyte (between two electrodes with a cross-sectional area of 1 cm2 separated by a distance of 1 cm). Here, we will define equivalent conductivity in detail.

Equivalent Conductance Definition in Mathematical Terms 

Equivalent conductance definition and formula in mathematical terms:

the conductance of V cm3 --------- Λ

the conductance of 1 cm3 --------- κ

Therefore:

Λ = κ.V  ---------- equation (3)

We know that the normality (N) of a solution is given by the equation below

N = n/V 1000

Equivalent conductance formula: 

V = 1000/n

For the above electrolytic solution, no. of equivalents, n = 1.

V = K x 1000/n

Hence,

relation between V and N

Equivalent conductance can be written as 

Λ = k x V

Units of Λ: units of equivalent conductance

m2 . ohm-1. equiv-1 = cm2 . mho. equiv-1

or 

m2 . Siemens. Equiv-1

Conductors and Insulators

Materials that allow easy and hindrance-free flow of electrons from one element to another are called conductors. Conductors have electric charges inside them in the form of electrons which makes it easy for the electrons to move freely.

On the other hand, insulators are the type of materials that do not allow for easy flow of the electrons from one element to another by causing hindrance. Any amount of charge that is passed through insulators only remains at the starting point where the materials meet and do not get spread across the material.

Calculation of conductance

We have established that the conductance of a solution is indirectly proportional to the resistance that it poses. Hence, conductance can be determined through finding out the resistivity of the solution being concentrated.

Since, k conductivity is reciprocal of p resistivity we can say that-

k = 1/p and p = R(a/l)

therefore, k = 1/R(l/a) or k = G(l/a)

In the above, G = cell conductance, l = the distance by which two electrodes are separated having acm2 as cross section area, l/a = cell constant which is represented by cm-1.

The conductance can be calculated after knowing the value of cell constant and solution conductance as,

k = G x cell constant

or conductivity = conductance x cell constant.

The electrolytic or ionic conductivity depends on the following factors:

• The properties of the electrolyte which is added in the solution.

• The size of the ions that are produced in the process and their solvation capacity.

• The properties of the solvent and its resistance to change shape or mobility (viscosity).

• The electrolyte’s concentration in the solution

• Temperature at which the solution is being made

Equivalent conductance at infinite dilution

When ionization increases, that is the number of ions in a solution increases, the value of equivalent conductance also increases as the solution dilutes.

For instance, at a constant temperature if we take respective concentrations of two different solutions, the solution with strong electrolyte (a greater number of ions) has a greater conductance than the solution with weak electrolyte (comparatively a smaller number of ions). However, there is an end after which more dilution in either or both of the solutions is not possible, which means it has not even the slightest effect on the concentration of the solution. This whole concept where dilution ends is called the infinite dilution.

Thus, infinite dilution can be defined as the state at which no further concentration can be obtained with any amount of dilution in a solution, as it already contains the maximum quantity of solvent possible. All the ions are completely dissociated at this state of infinite dilution.

Further information on the question of Infinite Dilution can be found here.

Kohlrausch’s Law

The state of infinite dilution can be understood by Kohlrausch’s Law. This law states that the sum of the equivalent conductance of all the anions and the cations that are present in any solution is equal to the equivalent conductance of an electrolyte at the state of infinite dilution of the same solution. Let’s assume, for instance, that salt is being dissolved in water, then the conductivity of the solution can be obtained by finding the sum of the conductance of its cations and anions in the solution.

To know more about the uses or application refer to Kohlrausch’s Law at Vedantu.

Molar Conductivity

Molar conductivity is the conductance of a solution containing one mole of electrolyte or a function of a solution's ionic strength or salt concentration. As a result, it is not a constant.

In other words, molar conductivity is the total conducting power of all the ions generated when a mole of electrolytes is dissolved in a solution. Molar conductivity is a feature of an electrolyte solution that is primarily used to determine an electrolyte's efficiency in conducting electricity in a solution. As a result, it is not a constant.

Molar Conductivity Formula

The expression used to represent molar conductivity mathematically is given below.

μ = K / C 

μ = K / C  = K / C 

K is the specific conductivity, while c is the mole per liter concentration.

The molar conductivity of an electrolytic solution is defined as the conductance of a volume of solution containing a unit mole of electrolyte put between two electrodes of unit area cross-section. The molar conductivity unit is Sm2mol-1.

Relation Between Equivalent Conductance Formula and Molar Conductance

The relation between equivalent conductance and molar conductance can be given by:

 μ = Λ x equivalent factor of an electrolyte

The total charge on either anions or cations present in one formula unit of the electrolyte is usually the equivalent factor. In the case of acids, it can be equal to basicity, while in the case of bases, it can be equal to acidity.

Formula for Equivalent Conductivity and How is it Different from the Molar Conductivity Formula

The conductance of all the ions produced by one gram equivalent of an electrolyte in a given solution is known as equivalent conductance.

k V = equivalent conductance

Where V is the volume in mL that contains 1 g of electrolyte equivalent.

Molar conductance is the total conductance of all the ions produced by ionization of 1 g mole of an electrolyte in V mL of solution.. It is denoted by the symbol l.

Molar conductance = kV

Where V is the volume in mL of the electrolyte having 1 g mole. If c is the solution's concentration.

Formula 

Equivalent conductance= Molar conductance/n

Factors Affecting Equivalent Conductivity

1. Temperature: Because the extent of ionization increases with increasing temperature, the conductance of an electrolyte solution increases.

2. Strong electrolytes undergo complete ionization and so have larger conductivities because they produce a greater number of ions.

3. Weak electrolytes, on the other hand, undergo partial ionization and so have poor conductivities in their solutions.

4. Ionic size and mobility: As the size of an ion increases, its mobility reduces, and its conductivity lowers as well.

5. Ionic mobility is diminished in more viscous solvents due to the nature of the solvent and its viscosity. As a result, the conductivity decreases.

6. As the number of ions per unit volume grows, the specific conductance increases with the increase in solution concentration.

7. However, because the extent of ionization increases with decreasing concentration (i.e. dilution), both the equivalent conductivity and molar conductance increase.

Solved Example: 

Calculation of molar conductivity of KCl solution

Given: 

Molarity (M) = 0.30M

Conductivity at 298 K (k) = 0.023 S cm-

Solution:

Molar conductivity = (1000 × k) /M

= (1000 × 0.023) / 0.30

= 76.66 cm² mol⁻¹

 So molar conductivity of KCl solution is 76.66 cm² mol⁻¹.

Conclusion 

The conductivity of a volume of solution containing one equivalent of an electrolyte is called equivalent conductivity. The conductance property of a solution containing one mole of electrolyte, or a function of a solution's ionic strength or salt concentration, is known as molar conductivity. As a result, it isn't always the same. In other words, when a mole of electrolyte is dissolved in a solution, molar conductivity is the total conducting power of all the ions created.

Equivalent conductance= Molar conductance/n