Match List I with List II:

Choose the correct answer from the  options given below:

A-IV, B-III, C-I, D-II

The correct answer is option 4. A-IV, B-III, C-I, D-II.

Let us go through each item in detail to understand why option 4 is the correct answer:

A. \(\Lambda_m\) of \(KCl\) increases on dilution: IV. due to weakening of interionic attraction

Potassium chloride (KCl) is a strong electrolyte, which means it dissociates completely into ions in solution. As the concentration of KCl decreases (i.e., as the solution is diluted), the interionic attractions between the potassium ions (\(K^+\)) and chloride ions (\(Cl^-\)) weaken. This weakening of interionic attractions allows the ions to move more freely, increasing the molar conductivity (\(\Lambda_m\)) of the solution. Thus, \(\Lambda_m\) of \(KCl\) increases on dilution due to weakening of interionic attraction.

B. \(\Lambda_m\) of \(CH_3COOH\) increases on dilution:III. due to increased degree of ionzation

Acetic acid (CH\(_3\)COOH) is a weak electrolyte, meaning it does not dissociate completely in solution. Instead, it partially ionizes, and the degree of ionization increases as the solution is diluted. With increasing dilution, more acetic acid molecules dissociate into ions (CH\(_3\)COO\(^-\) and H\(^+\)), which increases the molar conductivity (\(\Lambda_m\)) of the solution. Thus, \(\Lambda_m\) of \(CH_3COOH\) increases on dilution due to increased degree of ionization.

C. \(\Lambda_m\) of \(KCl\) versus \((molarity)^{1/2}\):I. is a linear graph

For strong electrolytes like KCl, the molar conductivity (\(\Lambda_m\)) increases linearly with the square root of the molarity (\(m^{1/2}\)). This is because the increase in \(\Lambda_m\) is directly proportional to the decrease in concentration, which follows a linear relationship with \((molarity)^{1/2}\). Thus, the graph of \(\Lambda_m\) of \(KCl\) versus \((molarity)^{1/2}\) is a linear graph.

D. \(\Lambda_m\) of \(CH_3COOH\) versus \((molarity)^{1/2}\)

For weak electrolytes like acetic acid, the relationship between molar conductivity (\(\Lambda_m\)) and \((molarity)^{1/2}\) is non-linear. This is because the degree of ionization of weak electrolytes does not follow a simple linear relationship with \((molarity)^{1/2}\) and is more complex due to equilibrium effects. Thus, the graph of \(\Lambda_m\) of \(CH_3COOH\) versus \((molarity)^{1/2}\) is a non-linear graph.

Therefore, the correct answer is Option 4: A-IV, B-III, C-I, D-II.