Q.Molar conductivity of ionic solution depends on ___________. (Two or more than two options may be correct.)

The key idea is Molar Conductivity ($\Lambda_m$), defined as the conductivity of a solution divided by its molar concentration. It measures how well a given mole of electrolyte conducts electricity.

Reasoning:

1. Temperature (i): Increasing temperature increases ionic mobility (lower viscosity, higher kinetic energy), so $\Lambda_m$ increases. This is a direct dependence.
2. Concentration (iii): $\Lambda_m$ varies strongly with concentration — for strong electrolytes it decreases slightly as concentration rises (due to ion-ion interactions), while for weak electrolytes it increases sharply on dilution (due to increased dissociation). …

Molar conductivity ($\Lambda_m$) is a property of the solution itself, not of the measuring apparatus. It is defined as the conductivity of a solution containing one mole of electrolyte, placed between two electrodes 1 cm apart. The formula is:

where $\kappa$ is the specific conductivity (conductance of a 1 cm × 1 cm column) and $c$ is the molar concentration. This definition already removes the geometry of the cell — so any factor that changes $\kappa$ or $c$ will affect $\Lambda_m$, but the physical setup of the electrodes will not.

Let’s examine each option carefully.

1. Temperature (i) — This is a clear yes. Conductivity of an electrolyte solution increases with temperature because ions move faster (higher kinetic energy, lower viscosity of the solvent). Since $\kappa$ rises, $\Lambda_m$ rises too. For aqueous solutions, a typical rule: a 1 °C rise increases conductivity by about 2%. So temperature is a direct factor.

2. Distance between electrodes (ii) — This is a trap. Conductance ($G$) depends on electrode distance: $G = \kappa \cdot \frac{A}{l}$. But molar conductivity is defined per mole and normalised to unit length and area. The $\kappa$ in $\Lambda_m = \kappa / c$ is the specific conductivity — a material property independent of how far apart the electrodes are. Changing the distance changes the measured conductance, but not $\kappa$ or $\Lambda_m$. So this option is incorrect.

3. Concentration of electrolytes (iii) — Yes, and this is the most important dependence. For strong electrolytes, $\Lambda_m$ decreases slowly with increasing concentration (due to ion-ion interactions). For weak electrolytes, $\Lambda_m$ drops sharply as concentration rises (due to decreased dissociation). Kohlrausch’s law describes this: $\Lambda_m = \Lambda_m^\circ - A\sqrt{c}$ for strong electrolytes. So concentration is a key factor. …

Method: Conceptual Analysis of Molar Conductivity Dependence

Step 1 — Recall the definition of molar conductivity

Molar conductivity ($\Lambda_m$) is the conductivity of all ions produced by one mole of electrolyte in a given volume of solution. It is given by:

where $\kappa$ is the specific conductivity and $c$ is the concentration.

Step 2 — Identify factors that affect $\kappa$ and $c$

• Temperature — affects ion mobility and viscosity of the solution. As temperature increases, $\kappa$ increases, so $\Lambda_m$ increases.
• Concentration — directly appears in the formula. $\Lambda_m$ changes with concentration (e.g., increases on dilution for weak electrolytes, decreases for strong electrolytes at high concentration).

Step 3 — Eliminate geometry-dependent factors …

Here are the common mistakes students make on this question, along with how to avoid each.

Mistake 1: Confusing Molar Conductivity with Conductance

The most frequent error is treating molar conductivity ($\Lambda_m$) as if it were simply the conductance ($G$) of the solution.

• The Trap: Students see that conductance depends on the geometry of the cell (distance between electrodes and area of electrodes). They then assume molar conductivity also depends on these factors.
• The Correct Understanding: Molar conductivity is conductance per unit concentration, normalized for the cell geometry. It is defined as:

where $\kappa$ is the conductivity (which already accounts for cell geometry via the cell constant $G^* = \frac{l}{A}$). Since $\kappa$ is multiplied by the cell constant to remove geometry, $\Lambda_m$ becomes independent of the physical dimensions of the electrodes.

• How to Avoid: Always remember the formula. If a factor cancels out in the definition, it cannot be a variable that $\Lambda_m$ depends on.

Mistake 2: Forgetting the "Per Mole" Normalization

Students often think that because adding more electrolyte increases conductance, it must also increase molar conductivity.

• The Trap: Selecting surface area of electrodes or distance between electrodes because they affect the raw conductance reading.
• The Correct Understanding: Molar conductivity is the conducting power of all the ions produced by one mole of electrolyte. As you dilute a solution (decrease concentration), the ions move more freely (less interionic attraction), so $\Lambda_m$ increases. It is not a fixed property of the electrolyte alone; it varies with concentration.
• How to Avoid: Visualize the experiment. If you increase the distance between electrodes, the conductance drops, but the molar conductivity of the solution itself remains unchanged. The property is intrinsic to the solution's composition and temperature, not the apparatus.

Mistake 3: Ignoring Temperature Dependence

Some students treat molar conductivity as a constant for a given electrolyte.

• The Trap: Selecting only concentration-related options and missing temperature.
• The Correct Understanding: Temperature directly affects ion mobility. As temperature increases:
  • Viscosity of the solvent decreases.
  • Ions move faster.
  • Molar conductivity increases (typically by 2–3% per degree Celsius). …