Question

The limiting equivalent conductivity of \(\mathrm{NaCl}, \mathrm{KCl}\) and \(\mathrm{KBr}\) are \(126.5,150.0\) and \(151.5 \mathrm{~S} \mathrm{~cm}^{2}\) \(\mathrm{eq}^{-1}\), respectively. The limiting equivalent ionic conductance for \(\mathrm{Br}^{-}\) is \(78 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{eq}^{-1}\). The limiting equivalent ionic conductance for \(\mathrm{Na}^{+}\) ions would be : (a) 128 (b) 125 (c) 49 (d) 50

Short answer

The limiting equivalent ionic conductance for Na+ ions would be 53 S cm^2 eq^-1, which is not listed among the options provided.

Step-by-step solution

Understand the concept of limiting equivalent conductance

The limiting equivalent conductance is the conductance of ions in a solution at infinite dilution, where the ions are far apart and do not interact. The values given for NaCl, KCl, and KBr are the total limiting equivalent conductances of the respective salts, which are the sum of the conductances of their individual ions

Use the limiting conductance of KBr to calculate the conductance of K+

To find the limiting equivalent ionic conductance of Na+, we can use the value given for Br-. Since the value for KBr (total) is 151.5 and for Br- is 78, the conductance of K+ can be calculated by subtracting the conductance of Br- from the total conductance for KBr: Conductance of K+ = 151.5 - 78 = 73.5 S cm^2 eq^-1.

Use the conductance of K+ to find the conductance of Na+

Since the limiting equivalent conductance is an intensive property, it does not vary with the nature of the other ion in the salt. Therefore, the conductance of K+ in KCl can be used to find the conductance of Na+ in NaCl by subtraction: Conductance of Na+ = Conductance of NaCl - Conductance of K+ = 126.5 - 73.5 = 53 S cm^2 eq^-1.

Key concepts

Ionic Conductance

Understanding ionic conductance is crucial when diving into the properties of electrolyte solutions. It's a measure of an ion's ability to conduct electricity in a solution. Each type of ion has a characteristic conductance value, which depends on factors such as the charge of the ion, its size, and how it interacts with the solvent. When ions are in a solution, they help carry the electric current by moving towards the electrodes when a potential is applied. This movement is essential for processes like electroplating, batteries, and even biological functions such as nerve signal transmission.

To grasp this concept better, it helps to think of an ion as a swimmer in a large pool; the better the swimmer, the faster they can move through the water, which in our analogy represents the ion's ability to conduct electricity through the solution. Their speed in the pool would resemble their ionic conductance in a solution.

Infinite Dilution

The term infinite dilution might sound a bit abstract, but it's an important hypothetical state used to understand the properties of ions in a solution without the complication of interactions between them. At infinite dilution, an electrolyte is diluted to the point where its ions are so far apart that they essentially do not influence each other's behavior. This means they are free to move in the solution without being affected by the electrostatic forces of nearby ions. This is a key concept because it allows scientists to measure the limiting equivalent conductance, which is the conductance value when the concentration approaches zero.

Imagine being in a crowded room where it's difficult to move because you keep bumping into people. Now, imagine the people gradually disappearing until you're the only one left – you're free to move as you please. This situation resembles the condition of ions at infinite dilution and helps to illustrate why interaction between ions is negligible at this state.

Electrolyte Solution

An electrolyte solution is simply a solution that contains ions and can conduct electricity. When an electrolyte dissolves in a solvent, such as water, it dissociates into positively and negatively charged ions. This process is essential for conduction because ions are the carriers of electric current in solutions. Common examples include solutions of salts, acids, or bases in water.

Every time you drink a sports drink, you're replenishing your body's electrolytes—compounds like sodium chloride or potassium chloride that are vital for many physiological processes. These dissolved ions conduct electric signals in your body, helping to regulate nerve and muscle function. In the classroom or lab, understanding the behavior of electrolyte solutions underpins much of physical chemistry, including aspects of chemical equilibrium, pH, and electrochemical reactions.

Conductivity in Physical Chemistry

When we talk about conductivity in physical chemistry, we're looking at a material's ability to conduct an electric current. Conductivity is an intrinsic property that tells us how well charges move through a given substance, be it a solution, solid, or gas. In the context of electrolyte solutions, conductivity is usually expressed in terms of equivalents per unit volume and depends on the concentration of ions and their individual conductive abilities.

The conductivity of a solution provides essential information about the solution's composition and the concentration of ions. For example, by measuring the conductivity of an unknown solution, chemists can infer the type and quantity of ions present. Moreover, conductivity measurements serve as an invaluable tool for monitoring reactions in real-time, particularly in industrial processes, where maintaining proper ionic concentration is crucial for quality control.