What is Molar Conductance of a Solution. State its Unit. How is it related to Specific Conductance of a solution?

Answer: Molar conductance (Λₘ) measures the ability of ions in a solution to conduct electricity, calculated for one mole of electrolyte dissolved in a specific volume. Its unit is siemens centimeter squared per mole (S cm² mol⁻¹). Molar conductance is directly related to specific conductance (κ) through the formula: Molar Conductance Formula Λₘ = (κ × 1000) / C, where C is the electrolyte concentration (mol/L). Let’s unpack this concept, its significance in electrochemistry, and how it bridges theory with real-world applications.

Complete Answer:

What is Molar Conductance of a Solution?

Molar conductance quantifies the conductivity of all ions produced by dissolving 1 mole of an electrolyte in a solution. Unlike specific conductance (which depends on the solution’s volume), molar conductance standardizes measurements by accounting for concentration. For instance, a 1M NaCl solution’s molar conductance reflects how efficiently Na⁺ and Cl⁻ ions carry current per mole of NaCl.

Molar vs. Specific Conductance – Key Differences

Specific Conductance (κ): Measures conductivity per unit volume (S cm⁻¹). It’s the inverse of resistivity and depends on ion concentration, temperature, and electrolyte strength.

Molar Conductance (Λₘ): Adjusts specific conductance for concentration, allowing comparison across solutions.

Example: If κ for 0.1M HCl is 0.04 S cm⁻¹, its molar conductance is:

Λₘ = (0.04 × 1000) / 0.1 = 400 S cm² mol⁻¹. 

Why the Unit S cm² mol⁻¹?

The unit combines conductivity (S cm⁻¹) with molarity (mol/L). Multiplying κ (S cm⁻¹) by 1000 cm³/L converts volume to liters, and dividing by concentration (mol/L) gives conductance per mole. This unit ensures consistency in comparing electrolytes.

Relationship Between Molar and Specific Conductance

The formula Λₘ = κ × 1000 / C highlights two critical trends:

1. Dilution Effect: As concentration (C) decreases, molar conductance (Λₘ) increases. Diluted solutions reduce ion crowding, enhancing mobility and conductivity.
2. Strong vs. Weak Electrolytes:
   1. Strong electrolytes (e.g., HCl, NaOH) show high Λₘ even at high concentrations due to complete ionization.
   2. Weak electrolytes (e.g., CH₃COOH) have lower Λₘ at high concentrations but improve with dilution as ionization increases.
3. Industrial Electrolysis: Optimizes electrolyte concentrations in batteries and electroplating.

Factors Affecting Molar Conductance

Temperature: Conductance increases with temperature (ions move faster).

Electrolyte Type: Strong electrolytes (fully dissociated) have higher Λₘ.

Solvent Nature: Polar solvents like water enhance ion mobility.

Fun Fact: Kohlrausch’s Law

German chemist Friedrich Kohlrausch found that Λₘ⁰ (molar conductance at infinite dilution) for an electrolyte equals the sum of the ionic conductances of its ions. For NaCl:Λₘ⁰ = λₙₐ⁺ + λ₅ₕ₋, where λ represents ionic conductance. This law is key to predicting Λₘ⁰ for unknown salts!

Molar conductance bridges the gap between theoretical electrochemistry and practical measurements, offering insights into ion behavior across concentrations. Remember: It’s not just about how many ions are present, but how efficiently they move!