Conductivity and electrolytic cells (specific, molar and equivalent conductivity)

Electrochemistry is a branch of chemistry that deals with the relationship between electrical energy and chemical changes. It has various applications in batteries, fuel cells, and electrolysis. One of the essential concepts in electrochemistry is the concept of conductivity, especially in electrolytic cells. In this article, we will deeply understand conductivity and various parameters associated with it, such as specific conductivity, molar conductivity, and equivalent conductivity.

Basic concepts of conductivity

Conductivity describes how well a substance allows the flow of electrical current. In an electrolytic cell, where the medium is a liquid solution, conductivity is determined by the ions present in the solution. The ability of these ions to carry an electrical charge contributes to the conductivity of the solution.

Electrical conductivity (G) is the inverse of electrical resistance (R) and is given by the formula:

g = 1/r

Where:

• G is the conductivity, measured in siemens (S).
• R is the resistance, measured in ohms (Ω).

For a given electrolytic solution, the resistance depends on the nature of the electrolyte, its concentration, and the temperature of the solution.

Specific conductivity (κ)

Specific conductivity, also known as conductivity, is a measure of how well a solution can conduct electricity. It is defined as the conductivity of a solution per unit length and unit cross-sectional area. The SI unit of specific conductivity is siemens per meter (S/m).

The formula for specific conductivity is:

κ = G * (L / A)

Where:

• κ (kappa) is the specific conductivity.
• G is the conductivity.
• L is the length of the conductor (in meters).
• A is the cross-sectional area of the conductor (in square metres).

The specific conductivity of an electrolytic solution depends on the concentration and nature of the electrolyte. Generally, as the concentration of ions in the solution increases, the specific conductivity also increases.

Molar conductivity ( _Λm )

Molar conductivity is a measure of the driving force of all the ions produced by dissolving one mole of an electrolyte in a solution. It is usually expressed in units of siemens meters squared per mole (S m²/mol).

The formula for molar conductivity is:

Λm = κ/c

Where:

• _{Λ m} is the molar conductivity.
• κ is the specific conductivity.
• C is the molar concentration of the solution (in moles per liter).

Molar conductivity increases with dilution due to the increase in ionic mobility. At infinite dilution, the ions are very far from each other, and their interaction becomes negligible. This is called the limiting molar conductivity.

Understanding limiting molar conductivity

The concept of limiting molar conductivity is important. It represents the molar conductivity when the electrolytic solution is so dilute that any further dilution does not change the conductivity. It is expressed as:

Λ m ∞ = Λ m when C → 0

This helps to understand the intrinsic conductivity of the electrolyte and is useful in comparing different electrolytes.

Equivalent conductivity (Λ _eq )

Equivalent conductivity is similar to molar conductivity, but it is based on equivalent concentration rather than molar concentration. It is defined as the conductivity of a solution containing one gram equivalent of the electrolyte. It is expressed in siemens meter square per equivalent (S m²/eq).

The formula for equivalent conductivity is:

Λ eq = κ / N

Where:

• Λ eq is the equivalent conductivity.
• κ is the specific conductivity.
• N is the normality of the solution (gram equivalents per liter).

Relation between molar and equivalent conductivity

There is a direct relationship between molar conductivity and equivalent conductivity. For a given electrolyte with valency z, the relation is given by:

Λ eq = Λ m / z

This equation shows that the equivalent conductivity can be obtained from the molar conductivity by considering the equivalence factor of the electrolyte, which depends on the number of ions it produces.

Applying concepts with examples

Let's take the example of a sodium chloride (NaCl) solution:

1. Calculate the specific conductivity with known resistance:

• If the resistance of NaCl solution is 5 Ω, the specific conductivity (κ) can be calculated as:

g = 1 / r = 1 / 5 = 0.2 s
κ = g * (l/a) = 0.2 * (1/1) = 0.2 s/m
    

2. Find the molar conductivity with concentration:

• Assuming a molar concentration of 0.1 mol/L for NaCl solution, the molar conductivity is:

Λ m = κ / C = 0.2 / 0.1 = 2 S m²/mol

3. Equivalent conductivity:

• Using the same solution, equivalent conductivity (z = 1 for NaCl), you find:

Λ eq = Λ m / z = 2 / 1 = 2 S m²/eq

Conclusion

Understanding conductivity and its parameterization in terms of specific, molar, and equivalent conductivity is fundamental in predicting and measuring the ability of a solution to conduct electricity. These parameters are important for industrial applications, academic research, and educational purposes.

Understanding how conductivity behaves under different conditions helps in better design of electrochemical devices and processes, leading to increased efficiency and productivity.

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