This question requires matching chemical properties related to conductivity with their correct units. Let's analyze each property and its corresponding unit.

Understanding the Properties and Units

Matching Process

We need to correctly pair the items in List-I (Properties) with the items in List-II (Units). The properties involved are Cell constant, Molar conductance, Specific conductance, and Conductance.

Detailed Explanation

• (A) Cell constant: The cell constant ($K$) is a geometric factor of an electrochemical cell, typically defined as the ratio of the distance between the electrodes ($l$) to the area of the electrodes ($A$). Mathematically, $K = \frac{l}{A}$. In the context of conductivity measurements, where $l$ is in units of length (e.g., cm) and $A$ is in units of area (e.g., $cm^2$), the unit of the cell constant becomes $cm/cm^2 = cm^{-1}$. Thus, (A) matches with (I) $cm^{-1}$.
• (B) Molar conductance ($\Lambda_m$): Molar conductance is defined as the conductance of a solution containing one mole of electrolyte when placed between two electrodes 1 cm apart, such that the volume of the solution has unit cross-section. It is calculated as the ratio of specific conductance ($\kappa$) to the molar concentration ($c$). The formula is $\Lambda_m = \frac{\kappa}{c}$.
  • Unit of $\kappa$ (Specific conductance) is $ohm^{-1} cm^{-1}$.
  • Unit of $c$ (Molar concentration) is $mol \space L^{-1}$ or $mol \space cm^{-3}$.
  Therefore, the unit of molar conductance is $\frac{ohm^{-1} cm^{-1}}{mol \space cm^{-3}} = ohm^{-1} cm^2 mol^{-1}$. Thus, (B) matches with (II) $ohm^{-1} \space cm^2 \space mol^{-1}$.
• (C) Specific conductance ($\kappa$): Specific conductance, also known as conductivity, is the reciprocal of resistivity ($\rho$). Resistivity has units of ohm·cm. Hence, specific conductance has units of $\frac{1}{ohm \cdot cm}$, which is $ohm^{-1} cm^{-1}$. This unit is also often expressed as Siemens per centimeter ($S \space cm^{-1}$). Thus, (C) matches with (III) $ohm^{-1} \space cm^{-1}$.
• (D) Conductance ($G$): Conductance is the reciprocal of electrical resistance ($R$). Resistance is measured in ohms ($\Omega$). Therefore, conductance is measured in reciprocal ohms, denoted as $ohm^{-1}$ or Siemens (S). Thus, (D) matches with (IV) $ohm^{-1}$.

Summary of Matches

Based on the analysis, the correct pairings are:

This corresponds to the first option.