The conductivity of \(0.01 \mathrm{~mol} / \mathrm{dm}^{3}\) aqueous acetic acid at \(300 \mathrm{~K}\) is \(19.5 \times 10^{-5} \mathrm{ohm}^{-1} \mathrm{~cm}^{-1}\) and limiting molar conductivity of acetic acid at the same temperature is \(390 \mathrm{ohm}^{-1} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}\). The degree of dissociation of acetic acid is: (a) \(0.05\) (b) \(0.5 \times 10^{-2}\) (c) \(5 \times 10^{-7}\) (d) \(5 \times 10^{-3}\)

The degree of dissociation, often symbolized as \(\alpha\), is a key concept in understanding how an electrolyte behaves in solution. It tells us the fraction of the total number of solute molecules that separates into ions when dissolved in a solvent.

For weak electrolytes like acetic acid, \(\alpha\) is much less than 1, indicating that only a small fraction of the solute dissociates. To calculate \(\alpha\), you need to know the molar conductivity of the electrolyte at a certain concentration (\(\Lambda_m\)) and the limiting molar conductivity (\(\Lambda_0\)). This ratio \(\alpha = \frac{\Lambda_m}{\Lambda_0}\) gives us the degree of dissociation of the electrolyte in solution. The concept is crucial because it helps us understand the strength of an electrolyte and can be used to deduce various properties of the solution, such as its conductivity and chemical equilibrium.

In our exercise, by following the steps provided, we could determine that the actual degree of dissociation for acetic acid is very small, reflecting its characteristic as a weak acid. Knowing the degree of dissociation helps in fields ranging from analytical chemistry to environmental science, where the behavior of acids and bases in solution is often studied.

Electrolyte conductivity is a measure of how well an electrolyte can conduct electricity in a solution. This conductivity depends on the presence of free ions that are available to move under an electric field. When an ionic substance dissolves in water, it separates into cations and anions, which carry electrical current.

The unit for measuring conductivity is siemens per meter (S/m), but we often encounter units like ohm^(-1) cm^(-1) for aqueous solutions in chemistry. The electrolyte's conductivity is not constant; it varies with concentration, temperature, and the nature of the ions. Typically, strong electrolytes, which fully dissociate into ions, have higher conductivity than weak electrolytes, which dissociate partially.

Understanding electrolyte conductivity is crucial not just in chemistry but also in industries where electrolyte solutions are used, including batteries and wastewater treatment. For example, in the exercise, by knowing the conductivity of acetic acid, we can deduce how it will behave in different chemical processes and what its applications might be.

Limiting molar conductivity, \(\Lambda_0\), represents the molar conductivity of an electrolyte as its concentration approaches zero. At this dilute concentration, the ions are well separated and do not interact with each other, allowing for the inherent conductivity of the ions to be observed.

To find limiting molar conductivity, chemists often conduct a series of measurements at different concentrations and then extrapolate to zero concentration. The value of \(\Lambda_0\) is important for comparing the abilities of different ions to conduct electricity in solution. It is particularly useful for predicting the behavior of weak electrolytes, such as acetic acid in our exercise.

Knowledge of \(\Lambda_0\) allows for accurate calculations of the degree of dissociation and is essential in the analysis of electrolyte solutions in both a theoretical context and practical applications. By comparing \(\Lambda_m\) and \(\Lambda_0\), as with the exercise's step-by-step solution, we can gain insight into the dissociation behavior of acetic acid under the given conditions.