Q.Match the items of Column I and Column II.
Column I:

Concept: Molar Conductivity — the quantities in Column I are fundamental electrochemical terms; Column II gives their defining expressions.

Step 1 — $\kappa$ (conductivity) is measured as $G^*/R$, where $G^*$ is the cell constant and $R$ the resistance. So (i) matches (d).

Step 2 — $\Lambda_m$ (molar conductivity) is $\kappa$ divided by concentration $c$: $\Lambda_m = \frac{\kappa}{c}$. So (ii) matches (c). …

Before we jump into matching, let’s build the intuition. Electrochemistry is full of quantities that look similar but measure very different things. Conductivity ($\kappa$) tells you how well a solution conducts electricity — it’s a property of the solution itself, independent of how much you have. Molar conductivity ($\Lambda_m$) normalises that by concentration, so you can compare different electrolytes fairly. The degree of dissociation ($\alpha$) tells you what fraction of the electrolyte has actually split into ions — it’s a ratio of actual conductivity to the theoretical maximum. And charge ($Q$) is simply how much electricity has flowed, which is current times time.

The trap here is mixing up $\kappa$ and $\Lambda_m$ — they are related but not the same. Let’s work through each match carefully.

1. $\kappa$ (conductivity)

   Conductivity is the reciprocal of resistivity. In a conductivity cell, you measure resistance $R$ of the solution. The cell constant $G^*$ (which depends on electrode area and separation) relates them: $\kappa = \frac{G^*}{R}$. So $\kappa$ matches with (d) $\frac{G^*}{R}$.

2. $\Lambda_m$ (molar conductivity)

   Molar conductivity is defined as the conductivity of the solution divided by the molar concentration: $\Lambda_m = \frac{\kappa}{c}$. This lets you compare how well one mole of electrolyte conducts. So $\Lambda_m$ matches with (c) $\frac{\kappa}{c}$.

3. $\alpha$ (degree of dissociation) …

Concept: Conductivity, Molar Conductivity, Degree of Dissociation, and Charge in Electrochemistry

Method: Direct Definition Matching

This method uses the exact definitions of each symbol from Column I and matches them with the correct formula/expression in Column II.

Steps:

Step 1: Recall the definition of each symbol in Column I

Step 2: Recall the formula for each

• Conductivity $\kappa$ is related to cell constant $G^*$ and resistance $R$:

  $\kappa = \frac{G^*}{R}$

  → matches with (d)

• Molar conductivity $\Lambda_m$ is defined as:

  $\Lambda_m = \frac{\kappa}{c}$

  → matches with (c)

• Degree of dissociation $\alpha$ is the ratio:

  $\alpha = \frac{\Lambda_m}{\Lambda_m^0}$ …

Common Mistakes in Matching Electrochemistry Quantities

This question tests your understanding of conductivity ($\kappa$), molar conductivity ($\Lambda_m$), degree of dissociation ($\alpha$), and quantity of electricity ($Q$) — and their interrelationships.

Here are the most frequent errors students make, with how to avoid each:

1. Confusing $\kappa$ (conductivity) with $\Lambda_m$ (molar conductivity)

Mistake: Matching $\kappa$ with $\frac{\kappa}{c}$ or $\frac{G^*}{R}$.

Why it happens: Both involve $\kappa$, so students rush to match without checking the formula.

How to avoid:

• Remember: $\kappa$ is conductivity — it depends on the cell constant $G^*$ and resistance $R$:

So $\kappa$ matches with (d) $\frac{G^*}{R}$.

• $\Lambda_m$ is molar conductivity — it is conductivity per unit concentration:

So $\Lambda_m$ matches with (c) $\frac{\kappa}{c}$.

Key trick: Think of $\Lambda_m$ as "conductivity divided by concentration" — the $c$ in denominator is the clue.

2. Mixing up $\alpha$ (degree of dissociation) with $\Lambda_m$

Mistake: Matching $\alpha$ with $\frac{\kappa}{c}$ or $\frac{G^*}{R}$.

Why it happens: Students forget the definition of $\alpha$ in terms of molar conductivities.

How to avoid:

• $\alpha$ is defined as:

where $\Lambda_m^0$ is limiting molar conductivity.

• So $\alpha$ matches with (b) $\Lambda_m / \Lambda_m^0$.

Key trick: $\alpha$ is a ratio of two molar conductivities — look for the fraction with $\Lambda_m$ in numerator and $\Lambda_m^0$ in denominator.

3. Forgetting the formula for quantity of electricity ($Q$)

Mistake: Matching $Q$ with $\frac{G^*}{R}$ or $\frac{\kappa}{c}$.

Why it happens: Students confuse $Q$ (charge) with conductivity-related terms.

How to avoid:

• $Q$ is charge passed through a circuit:

where $I$ is current and $t$ is time.

• So $Q$ matches with (a) $I \times t$.

Key trick: $Q$ is the only quantity here that involves time — look for $t$ in the column.

4. Rushing without checking units/dimensions

Mistake: Matching based on superficial similarity (e.g., both have $\kappa$ in them). …