Q.Match the terms given in Column I with the items given in Column II.
Column I:

Concept: Molar Conductivity ($\Lambda_m$) — the conducting power of all ions produced from one mole of electrolyte.

Reasoning:

1. $\Lambda_m$ is the conductance of all ions from 1 mole of electrolyte. As dilution increases, more ions are produced per mole, so $\Lambda_m$ increases with dilution → matches (d).

2. $E^\circ_{Cell}$ is the standard cell potential. It does not depend on the amount of substance — it is an intensive property → matches (a). …

Before we match, let’s build a clear mental picture of what each term means and why it behaves the way it does. This isn’t about memorising labels — it’s about understanding the physical meaning behind each property.

The core idea: intensive vs. extensive

An intensive property does not depend on how much of the substance you have. Temperature, density, and concentration are intensive — they stay the same whether you have a drop or a bucket. An extensive property scales with the amount of matter — mass, volume, total energy. If you double the system, an extensive property doubles.

Now apply this lens to electrochemistry.

1. $\Lambda_m$ — Molar conductivity

Molar conductivity is defined as:

where $\kappa$ is the conductivity (how easily ions carry current) and $c$ is the concentration. As you dilute a solution, the number of ions per unit volume drops, so $\kappa$ falls. But $\Lambda_m$ actually increases with dilution because the ions are more free to move — interionic attractions weaken. So $\Lambda_m$ is not a fixed number for a given electrolyte; it changes with concentration. Specifically, it increases with dilution.

So (i) $\Lambda_m$ matches with (d) increases with dilution.

2. $E^\circ_{Cell}$ — Standard cell potential

The standard cell potential is the voltage of an electrochemical cell under standard conditions (1 M concentration, 1 bar pressure, 298 K). It is determined solely by the nature of the electrodes and the redox reaction — not by how much electrolyte you have or how big the cell is. Whether you have a tiny cell or a huge one, $E^\circ_{Cell}$ remains the same. That makes it an intensive property.

So (ii) $E^\circ_{Cell}$ matches with (a) intensive property.

3. $\kappa$ — Conductivity (specific conductance)

Conductivity $\kappa$ is the conductance of a 1 cm cube of solution. It depends on:

• The number of ions per unit volume (concentration)
• The mobility of those ions …

Method: Concept–Property Matching via Definitions

This method works by recalling the exact definition and nature (intensive vs. extensive) of each electrochemical term, then matching it to the correct description.

Step 1: Recall the definition and nature of each term

Step 2: Match each term to Column II

• (i) $\Lambda_m$ → (d) increases with dilution
• (ii) $E^\circ_{Cell}$ → (a) intensive property
• (iii) $\kappa$ → (b) depends on number of ions/volume
• (iv) $\Delta_r G_{Cell}$ → (c) extensive property

Step 3: Final matched pairs

| Column I | Column II |

|----------|-----------| …

Here are the common mistakes students make when matching terms related to Molar Conductivity and Electrochemistry, along with how to avoid each.

Mistake 1: Confusing $\Lambda_m$ (Molar Conductivity) with $\kappa$ (Conductivity)

The Error:

Students often think $\Lambda_m$ is an intensive property or that it depends only on the number of ions per volume. They forget that $\Lambda_m$ is defined as:

where $c$ is concentration. Since $\kappa$ itself depends on ion concentration, $\Lambda_m$ increases with dilution (because interionic attractions decrease, allowing ions to move more freely).

How to Avoid:

• Remember: Conductivity ($\kappa$) is the conductance of a 1 cm cube of solution — it decreases with dilution (fewer ions per volume).
• Molar conductivity ($\Lambda_m$) is conductivity per mole of electrolyte — it increases with dilution.
• Trick: Write the formula $\Lambda_m = \kappa / c$ and think: as $c \to 0$, $\kappa$ drops slowly, but $c$ drops faster, so $\Lambda_m$ rises.

Correct Match:

• (i) $\Lambda_m$ → (d) increases with dilution

Mistake 2: Calling $E^\circ_{Cell}$ an Extensive Property

The Error:

Students see "Cell" and think it depends on size or amount of substance. But standard cell potential is the voltage when all reactants are at 1 M, 1 bar, 298 K — it does not depend on how much solution you have.

How to Avoid:

• Intensive property = does not depend on amount (e.g., temperature, density, voltage).
• Extensive property = depends on amount (e.g., mass, volume, charge).
• $E^\circ_{Cell}$ is like a "driving force per electron" — it's fixed for a given redox pair.

Correct Match:

• (ii) $E^\circ_{Cell}$ → (a) intensive property

Mistake 3: Thinking $\kappa$ (Conductivity) is Intensive

The Error:

Conductivity is often called "specific conductance" — the "specific" part tricks students into thinking it's intensive. But $\kappa$ does depend on the number of ions per unit volume, which changes with concentration.

How to Avoid:

• $\kappa$ is the conductance of a 1 cm × 1 cm × 1 cm cube. If you dilute the solution, fewer ions are in that cube, so $\kappa$ drops.
• Intensive means independent of sample size, but $\kappa$ changes with concentration — so it's not intensive. It is a property that depends on number of ions per volume.

Correct Match:

• (iii) $\kappa$ → (b) depends on number of ions/volume

Mistake 4: Misidentifying $\Delta_r G_{Cell}$ as Intensive

The Error:

Students see "Gibbs energy" and think it's like $E^\circ$ — but $\Delta_r G$ is the total free energy change for the reaction as written. If you double the amount of reactants, $\Delta_r G$ doubles.

How to Avoid: …