Question

The statement of Kohlrausch's law is (a) the equivalent conductance of an electrolyte at infinite dilution is equal to the product of equivalent conductance of the component ions (b) the equivalent conductance of an electrolyte at infinite dilution is equal to the difference of equivalent conductances of the component ions (c) the equivalent conductance of an electrolyte at infinite dilution is equal to the sum of the equivalent conductances of the component ions (d) none of the above

Short answer

(c) the equivalent conductance of an electrolyte at infinite dilution is equal to the sum of the equivalent conductances of the component ions

Step-by-step solution

Understand Kohlrausch's Law

Kohlrausch's Law is a statement about the behavior of electrolytes when they are at a state of infinite dilution. It states that the limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the ions.

Analyze the answer options

Now, analyze each of the answer options in the light of the understanding of Kohlrausch's Law obtained in step 1. The key word to look for in the question is 'sum', as Kohlrausch's Law stipulates the sum of the individual contributions of the ions.

Choose the correct answer

Looking at the options, answer (c) states that the equivalent conductance of an electrolyte at infinite dilution is equal to the sum of the equivalent conductances of the component ions. This matches perfectly with Kohlrausch's Law, hence the correct answer is (c).

Key concepts

Equivalent Conductance

Equivalent conductance is a measure that helps us understand how well an electrolyte can conduct electricity when present in a solution. It is symbolically represented as \( \Lambda \) and defined as the conductance of one equivalent of electrolyte dissolved in a given volume of solution.
This concept is especially significant when studying the behavior of electrolytes because it considers both the type and concentration of ions in the solution.Let's break it down:

• Equivalent conductance changes with dilution. As the solution becomes more dilute, the equivalent conductance usually increases.
• This is because the ions, spread further apart as they become diluted, experience less interference from other ions.
• In highly dilute solutions, ions can move freely, leading to higher conductivity.

In the context of Kohlrausch's Law, focusing on equivalent conductance at infinite dilution allows us to study the intrinsic ability of separated ions to conduct electricity, without any hindrance from their neighbors.

Infinite Dilution

Infinite dilution is a theoretical concept where an electrolyte is dissolved in such a large amount of solvent that further dilution does not lead to any change in properties like conductivity. This idea helps eliminate the effects that ions have on each other, giving pure measures of how individual ions contribute to the solution's properties.
Infinite dilution is crucial because:

• It ensures that ions are independent of one another and not interacting due to proximity.
• The conductance observed here is called limiting molar conductivity, denoted as \( \Lambda^0 \) or \( \lambda^0 \).
• This concept allows us to compare intrinsic conductivities of different ions on a level playing field.

The concept ties back to Kohlrausch's Law, as it facilitates determining the sum of individual ionic conductances, giving us a better understanding of each ion's specific role in conductivity.

Electrolytes

Electrolytes are substances that, when dissolved in a solvent like water, produce a solution that can conduct electricity. This electrical conduction is due to the movement of ions, which are charged particles, within the solution. The study of electrolytes is essential because:

• They play a critical role in chemical reactions and biological processes.
• Electrolytes dissociate into ions in solution, and their ability to conduct electricity relies on the number and mobility of these ions.
• Strong electrolytes fully dissociate into ions, while weak electrolytes only partially dissociate.

Understanding electrolytes and their properties, like equivalent conductance, helps in exploring many practical and theoretical aspects of chemistry, such as solution conductivity, ionic interaction, and the application of laws like Kohlrausch's Law to predict and analyze the behavior of ionic solutions in infinite dilution scenarios.