Answer the question on basis of passage given below:

\(G = \frac{\kappa A}{l} = \kappa \) (both\(A\) and \(l\) are unity in their appropriate units in m or cm)

Molar conductivity of a solution at a given concentration is the conductance of the volume \(V\) of solution containing one mole of electrolyte kept between two electrodes with area of cross section \(A\) and distance of unit length \(l\). Therefore,

\(\Lambda_m = \frac{\kappa A}{l}\)

Since \(l = 1\) and \(A = V\) (volume containing 1 mole of electrolyte) \(\Lambda _m =\kappa V\)

What does \(\kappa \) represent in the paragraph?

Conductivity

The correct answer is option 2. Conductivity.

Let us break down the passage and the concept to explain what \(\kappa\) represents:

Concept of Conductivity and Molar Conductivity

Conductivity (\(\kappa\)): Conductivity, represented by \(\kappa\), is a measure of how well a solution can conduct electricity. It depends on the number of ions present in the solution and their ability to move (mobility). The unit of conductivity is typically Siemens per meter (S/m) or Siemens per centimeter (S/cm).

Molar Conductivity (\(\Lambda_m\)): Molar conductivity is a measure of the conductivity of an electrolyte solution normalized to the concentration of the electrolyte. It is defined as the conductance of a solution containing one mole of electrolyte, with the solution placed between two electrodes of unit distance apart.

Key Equations from the Passage:

The passage provides the equation:

\(G = \frac{\kappa A}{l}\)

Here, \(G\) is the conductance, \(A\) is the area of the electrodes, \(l\) is the distance between the electrodes, and \(\kappa\) is the conductivity.

For molar conductivity, the equation given is:

\(\Lambda_m = \frac{\kappa A}{l}\)

Since the distance \(l\) is taken as 1 unit and the area \(A\) is the volume \(V\) containing 1 mole of electrolyte, this simplifies to:

\(\Lambda_m = \kappa V\)

Here, \(\kappa\) represents the conductivity of the solution, and \(V\) is the volume containing 1 mole of the electrolyte.

Understanding the Role of \(\kappa\):

In the equation \(\Lambda_m = \kappa V\), \(\kappa\) is the intrinsic property of the solution that describes how well it can conduct electricity. Molar conductivity (\(\Lambda_m\)) takes into account both the conductivity (\(\kappa\)) and the volume of the solution containing one mole of the electrolyte.

Why is \(\kappa\) Conductivity?

Conductivity (\(\kappa\)) is the fundamental property that reflects the ability of ions in the solution to carry electrical current. The passage uses \(\kappa\) to describe the conductance of a solution when area \(A\) and distance \(l\) are normalized to specific conditions, leading to the definition of molar conductivity.

Conclusion:

The symbol \(\kappa\) in the passage represents conductivity, which is central to understanding how well the electrolyte solution can conduct electricity under the conditions described.

Thus, the correct answer is: 2. Conductivity