Specific and Molar Conductivity Variation

At a given concentration, the specific conductivity, also known as conductivity seen in an electrolytic and ionic solution, is the conductance of a volume of solution balanced in the middle of two different electrodes made up of platinum, having a specific area of the sample over an area and located at the distance of a unit length between them. Diluting the solution reduces the amount of ions over a given volume that will carry a strong current, lowering the conductivity.

Conductivity is a physical property of the electrolytes in terms of the ability to conduct electricity. It is usually denoted by the symbol σ. The molar conductivity and conductivity of robust electrolytes decreases due to the decrease in concentration as the ions’ number per unit volume, which carries the current in the solution, goes down on dilution.

Molar conductivity formula

One unit of electrolyte per mole of the solution is maintained in the middle of two electrodes with a cross-sectional area A and a distance of one unit length. This is known as a solution’s molar conductivity when held at a specific concentration.

Ʌm = К/c

As given, 

c = concentration that can be expressed in moles over a volume

К = specific or constant conductivity

Ʌm = molar conductivity

Since we know that the solution only has one mole of electrolyte present, the above-listed equation could be modified and re-written as:

Ʌm =К.V

As the given overall volume V in the solution, which has a single mole of electrolyte, increases, molar conductivity increases with decreasing concentration. The concentration drops as a result of dilution. The molar conductivity with the given solution is also called limiting molar conductivity, Ʌ°m , as the concentration approaches zero. Strong and comparatively weak electrolytes have different variations of molar conductivity with concentration.

The concentration of the electrolyte affects conductivity. Dilution reduces the amount of ions per unit volume carrying the current; hence, conductivity constantly drops as concentration lowers.

Dilution, on the other hand, improves molar conductivity. Due to the fact that the conductivity of a given solution is the conductance of one unit volume of the solution, and molar conductivity is the conductance of that volume solution containing one mole of electrolyte, the two terms are used interchangeably.

Variation of molar conductivity with concentration

The molar conductivity of a specific solution containing a single mole of electrolyte rises with increasing total volume, V, whereas decreasing concentration increases with increasing total volume, V. As a result of dilution, the concentration decreases. When the concentration of a given solution hits zero, its molar conductivity is known as limiting molar conductivity. The molar conductance of solid and weak electrolytes varies with a concentration in distinct ways.

Strong Electrolytes

The molar conductivity of electrolytes having a strong concentration diminishes with dilution. The following equation may be used to illustrate this decrease: 

Ʌm = Ʌ°m – A.C1/2. 

If you draw the graph between Ʌm and C1/2, you’ll get a graph denoting a straight bar with an intercept equal to that same limiting molar conductivity Ʌ°m and a slope equal to (-A). The charges on both the cation and anion acquired during the dissociation of an electrolyte in a solution determine the value of A. As a result, either a graph or the Kohlrausch law may be used to determine the value of the limiting molar conductivity. Kohlrausch’s law of independent ion migration states that an electrolyte limiting molar conductivity equals the sum of the electrolyte’s cation and anion. 

Ʌ°m = Ʌ°cation + Ʌ°anion.

Weak Electrolyte

Weak electrolytes’ molar conductivity, on the other hand, increases with concentration. Such electrolytes exhibit lower molar conductivity at greater concentrations due to a reduced dissociation. When it comes to basic conductivity, it’s obvious that as the electrolyte concentration rises, so does the conductivity. The specific conductivity of a given solution is determined by the number of ions in a unit volume of the solution. With dilution, the dissociation rises, enabling the amount of current-carrying ions in the solution to grow. Dilution, on the other hand, lowers the number of ions in a given volume of solution. As a result, the conductivity is reduced.

The ability of a solution with electrolytes to carry an electric current is characterised as the conductivity of the electrolyte. It shows how quickly a particular quantity of electrical charge travels through a solution. Molar conductivity is another term for conductivity. This number, like thermal and specific heat capacity, may be thought of as both a physical and an intensive feature of matter. One thing to keep in mind is that the electrical current and the concentration are both measured in moles.

Limiting molar conductivity

Limiting molar conductivity is the molar conductivity of a particular solution when the dilution is taken to infinity. Or, to put it another way, when the electrolyte concentration is next to negligible, molar conductivity is referred to as the “limiting molar conductivity.”

Conductivity drops as the number of ions per unit volume that retain the current in a solution reduces with dilution, but molar conductivity increases as the concentration of a given solution lowers. The increase in the total volume containing one mole of the electrolyte causes the rise in molar conductivity.

Explain the relation between molar conductivity and concentration

For powerful electrolytes, Λ increases slowly with dilution and can be depicted by the equation: Ʌm =Ʌ°m – AC ½

If we plot a figure, we can see this. When we plot m versus C1/2, we get a straight line with an intercept of m° and a slope of ‘–A.’ The value of the constant ‘A’ varies on the kind of electrolyte for a specific solvent and temperature.

Em’s variant in relation to C1/2

The charges on the cation and anion formed when the electrolyte in the solution dissociates. As a result, the electrolytes NaCl, CaCl2, and MgSO4 are referred to as 1-1, 2-1, and 2- 2 electrolytes, respectively. The value of ‘A’ is the same for all electrolytes of a certain type.

Conclusion 

It is the conductance of volume V in the middle of two electrodes with a cross-sectional area A and a distance equal to one unit length that determines a solution’s molar conductivity at a particular concentration. With a reduction in concentration, molar conductivity rises. This is due to the fact that when a solution containing a single mole of electrolyte is diluted, the total volume of the solution rises.