Understanding Molar Conductivity and Electrolyte Behavior

This question asks us to match different scenarios involving the molar conductivity ($\lambda_m$) of electrolytes, specifically KCl (a strong electrolyte) and CH₃COOH (acetic acid, a weak electrolyte), with the correct explanations or graphical representations.

Molar conductivity is defined as the conductivity of a solution containing one mole of electrolyte dissolved in a certain volume of solvent, placed between two electrodes 1 cm apart with a large area of cross-section.

Let's analyze each item in List I and find the corresponding match from List II.

Analyzing List I and List II Matches

A. $\lambda_m$ of KCl increases on dilution

KCl is a strong electrolyte. Strong electrolytes are assumed to be completely ionized in solution. When a strong electrolyte solution is diluted, the number of ions per unit volume decreases, but the total number of ions remains constant (as they are already fully dissociated). The increase in molar conductivity upon dilution for strong electrolytes is primarily due to the decrease in interionic attractions between the ions. As the solution becomes more dilute, the ions are farther apart, reducing the electrostatic forces between them. This reduced attraction allows the ions to move more freely towards the electrodes, increasing their mobility and hence the molar conductivity.

Therefore, A matches with IV: Due to weakening of interionic attraction.

B. $\lambda_m$ of CH₃COOH increases on dilution

CH₃COOH is a weak electrolyte. Weak electrolytes do not ionize completely in solution; an equilibrium exists between the undissociated molecule and its ions. When a weak electrolyte solution is diluted, the degree of ionization ($\alpha$) increases. This is explained by Ostwald's Dilution Law. The increased degree of ionization means more ions are formed in the solution. Although the number of ions per unit volume decreases, the total number of ions in the given volume increases significantly compared to a more concentrated solution. This increase in the total number of charge carriers (ions) leads to a substantial increase in molar conductivity.

Therefore, B matches with III: Due to increased degree of ionization.

C. $\lambda_m$ of KCl versus (molarity)$^{1/2}$

For strong electrolytes like KCl, the variation of molar conductivity ($\lambda_m$) with concentration ($c$) is described by the Debye-Hückel-Onsager equation:

\(\lambda_m = \lambda_m^0 - A \sqrt{c}\)

Where $\lambda_m^0$ is the molar conductivity at infinite dilution, $A$ is a constant that depends on the nature of the solvent, temperature, and the type of electrolyte (specifically the charges on the ions), and $\sqrt{c}$ is the square root of molar concentration. This equation shows a linear relationship between $\lambda_m$ and $\sqrt{c}$. Therefore, plotting $\lambda_m$ against (molarity)$^{1/2}$ yields a linear graph for strong electrolytes.

Therefore, C matches with I: is a linear graph.

D. $\lambda_m$ of CH₃COOH versus (molarity)$^{1/2}$

For weak electrolytes like CH₃COOH, the degree of ionization changes significantly with concentration, and the Debye-Hückel-Onsager equation is not directly applicable in its simple form over a wide concentration range. The relationship between $\lambda_m$ and $\sqrt{c}$ for weak electrolytes is non-linear. The graph of $\lambda_m$ versus $\sqrt{c}$ for a weak electrolyte is a curve that is steep at low concentrations and approaches the x-axis slowly at higher concentrations. It does not extrapolate to a definite value of $\lambda_m^0$ at infinite dilution ($\sqrt{c}=0$).

Therefore, D matches with II: is a non-linear graph.

Summary of Matches

Based on the analysis, the matches are:

The correct combination of matches is A-IV, B-III, C-I, D-II.

Revision Table: Electrolyte Conductivity Concepts

Additional Information: Explaining Key Concepts

Electrolytes: Substances that produce ions when dissolved in a solvent, making the solution electrically conductive. They are classified into strong and weak electrolytes.

• Strong Electrolytes: These substances ionize completely in solution. Examples include strong acids (HCl, H₂SO₄), strong bases (NaOH, KOH), and most salts (KCl, NaCl, Na₂SO₄). Their conductivity is high due to the large number of ions present.
• Weak Electrolytes: These substances ionize only partially in solution, establishing an equilibrium between the undissociated molecule and its ions. Examples include weak acids (CH₃COOH, H₂CO₃), weak bases (NH₃), and some salts. Their conductivity is lower compared to strong electrolytes at the same concentration because fewer ions are available to carry charge.

Molar Conductivity ($\lambda_m$): This is a measure of the conducting power of all the ions produced by dissolving one mole of an electrolyte in a given volume of solution. It increases with dilution.

Effect of Dilution:

• For strong electrolytes, dilution increases the distance between ions, reducing interionic attraction and increasing ion mobility. This causes a slight increase in $\lambda_m$.
• For weak electrolytes, dilution increases the degree of ionization, producing more ions. This significant increase in the number of charge carriers causes a large increase in $\lambda_m$.

Debye-Hückel-Onsager Equation: This equation describes the limiting behavior of molar conductivity of strong electrolytes at low concentrations. It quantifies the effect of interionic interactions on ion mobility.

Ostwald's Dilution Law: This law relates the degree of ionization of a weak electrolyte to its dissociation constant and concentration. It explains why the degree of ionization, and hence the molar conductivity, of a weak electrolyte increases significantly upon dilution.