Kohlrausch's Law helps to find:

The molar conductivity of a weak electrolyte at infinite dilution.

The correct answer is option 2. The molar conductivity of a weak electrolyte at infinite dilution.

Kohlrausch's Law, formulated by Friedrich Kohlrausch in the late 19th century, describes the behavior of electrolytic conductivity in solutions. It states that the molar conductivity (\(\Lambda_m\)) of an electrolyte at infinite dilution is the sum of the molar conductivities of its constituent ions.

Mathematically, Kohlrausch's Law can be expressed as:

\[\Lambda_m = \lambda_+^0 + \lambda_-^0\]

Where:

\(\Lambda_m\) is the molar conductivity of the electrolyte at infinite dilution.

\(\lambda_+^0\) is the molar conductivity of the cation at infinite dilution.

\(\lambda_-^0\) is the molar conductivity of the anion at infinite dilution.

Application to Weak Electrolytes:

Weak electrolytes only partially dissociate into ions when dissolved in solution, even at relatively high concentrations. This means that their molar conductivity is lower compared to strong electrolytes at the same concentration.

At infinite dilution, however, a weak electrolyte would theoretically dissociate completely, even though practically it's challenging to achieve such dilutions in the laboratory. Kohlrausch's Law helps in predicting the behavior of weak electrolytes at infinite dilution by considering the molar conductivities of their constituent ions.

For example, consider the weak acid acetic acid (\(CH_3COOH\)). In solution, it partially dissociates into acetate ions (\(CH_3COO^-\)) and hydronium ions (\(H_3O^+\)). At high concentrations, the degree of dissociation (\(\alpha\)) is small, and thus the measured molar conductivity is relatively low. However, at infinite dilution, according to Kohlrausch's Law, the molar conductivity of acetic acid would be the sum of the molar conductivities of acetate and hydronium ions at infinite dilution.

Significance:

The prediction of molar conductivity at infinite dilution for weak electrolytes is valuable because it provides insights into their behavior under ideal conditions, which may not be directly measurable experimentally due to practical limitations in achieving such dilutions. This prediction aids in understanding the extent of ionization or dissociation of weak electrolytes in solution, which is crucial for various applications in chemistry, such as in understanding acid-base equilibria, conductivity measurements, and electrolysis processes.

In summary, Kohlrausch's Law provides a theoretical framework for understanding the conductivity of electrolytes, particularly weak electrolytes, at infinite dilution by considering the individual contributions of their constituent ions. It offers valuable insights into the behavior of electrolytes under ideal conditions, aiding in the interpretation of experimental data and enhancing our understanding of solution chemistry.