Match List - I with List - II:
List - I (Parameter)                                         List - II (Unit)
(a) Cell constant                                            (i) S cm$$^2$$ mol$$^{-1}$$
(b) Molar conductivity                                   (ii) Dimensionless
(c) Conductivity                                            (iii) m$$^{-1}$$
(d) Degree of dissociation of electrolyte     (iv) $$\Omega^{-1}$$ m$$^{-1}$$
Choose the most appropriate answer:

We begin with the quantity called the cell constant. By definition, the cell constant is the ratio of the distance between the electrodes to the cross-sectional area of the electrodes:

$$\text{Cell constant}= \dfrac{\ell}{A}$$

Here $$\ell$$ is measured in metres (m) and $$A$$ in square metres (m$$^2$$). Hence

$$\text{Unit of cell constant}= \dfrac{\text{m}}{\text{m}^2}= \text{m}^{-1}$$

In List - II this corresponds to item (iii) $$\text{m}^{-1}$$. So we have the pair $$\text{(a)} \rightarrow \text{(iii)}$$.

Next we consider molar conductivity (also called molar conductance). The formula used is

$$\Lambda_m = \kappa \dfrac{1000}{C}$$

where $$\kappa$$ is the conductivity in $$\text{S m}^{-1}$$ or $$\text{S cm}^{-1}$$, and $$C$$ is concentration in $$\text{mol dm}^{-3}$$ (or $$\text{mol L}^{-1}$$). Working in centimetre units, the factor $$1000$$ converts dm$$^3$$ to cm$$^3$$, giving

$$\text{Unit of } \Lambda_m = \text{S cm}^{-1}\times \text{cm}^3\text{ mol}^{-1}= \text{S cm}^2\text{ mol}^{-1}$$

This is item (i) in List - II, so we have $$\text{(b)} \rightarrow \text{(i)}$$.

Now we take up conductivity (specific conductance) $$\kappa$$. From Ohm’s law for a cell of length $$\ell$$ and area $$A$$ we write

$$\kappa = \dfrac{1}{R}\dfrac{\ell}{A}$$

Resistance $$R$$ has unit $$\Omega$$, therefore $$1/R$$ has unit $$\Omega^{-1}$$ (siemens, S). Multiplying by $$\ell/A$$ introduces an additional $$\text{m}^{-1}$$, giving

$$\text{Unit of conductivity}= \Omega^{-1}\text{ m}^{-1} = \text{S m}^{-1}$$

This matches item (iv) in List - II. Hence $$\text{(c)} \rightarrow \text{(iv)}$$.

Lastly, the degree of dissociation $$\alpha$$ is defined as

$$\alpha = \dfrac{\text{number of moles dissociated}}{\text{total number of moles initially present}}$$

It is a pure ratio of two identical quantities, so it carries no physical unit; it is dimensionless. List - II item (ii) is “dimensionless,” giving $$\text{(d)} \rightarrow \text{(ii)}$$.

Collecting all the matches, we have

$$(a)-(iii),\; (b)-(i),\; (c)-(iv),\; (d)-(ii)$$

Comparing with the options, this set appears in Option A.

Hence, the correct answer is Option A.