Problem 5 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Consider the statements S1 and S2: S1 : Conductivity always increases with decrease in the concentration of electrolyte. S2 : Molar conductivity always increases with decrease in the concentration of electrolyte. The correct option among the following is : [Main April 10, 2019 (I)] (a) Both S1 and \(\mathrm{S} 2\) are wrong (b) \(\mathrm{S} 1\) is wrong and \(\mathrm{S} 2\) is correct (c) Both S1 and S2 are correct (d) \(\mathrm{S} 1\) is correct and \(\mathrm{S} 2\) is wrong

Step-by-Step Solution

Answer

(b) S1 is wrong and S2 is correct.

Step 1: Understanding Conductivity

Conductivity of a solution refers to its ability to conduct electric current. It depends on the number of ions present in the solution. As the concentration of electrolyte decreases, the number of ions decreases, reducing the overall conductivity. Hence, the statement S1 'Conductivity always increases with decrease in the concentration of electrolyte' is incorrect.

Step 2: Understanding Molar Conductivity

Molar conductivity is defined as the conductivity of a solution divided by its molar concentration. It usually increases when the concentration of electrolyte decreases because the ions are more dissociated and are free to move, leading to higher mobility at lower concentrations, i.e., less crowding of ions. Thus, statement S2 'Molar conductivity always increases with decrease in the concentration of the electrolyte' is correct.

Step 3: Comparing Statements to Options

Given that S1 is false and S2 is true, we compare these findings with the given options. Option (b) 'S1 is wrong and S2 is correct' matches the analysis of the statements.

Key Concepts

Molar Conductivity

Molar conductivity is an important concept when discussing the electrical properties of electrolytes. In simple terms, it describes how well a solution can conduct electricity based on the concentration of ions present. Molar conductivity is calculated by dividing the conductivity of the solution by its molar concentration. This detail is crucial: as the concentration of an electrolyte decreases, the molar conductivity typically increases. The reason for this increase is twofold.

• When the electrolyte is more diluted, the ions are less crowded.
• This reduced crowding allows ions to move more freely, enhancing the solution's conductive capability.

The impact of increased mobility of ions at lower concentrations becomes evident in the rise of molar conductivity. Therefore, in many cases, when you see electrolyte solutions, diluted ones often display higher molar conductivities.

Concentration of Electrolytes

The concentration of electrolytes in a solution is a measure of how much solute is present relative to the solvent. This concentration affects many chemical and physical properties, including the solution's conductivity. When dealing with conductivity, it's important to note that increasing the concentration usually increases the number of ions available. However, it's a bit of a double-edged sword.

• At higher concentrations, although there are more ions, they tend to crowd each other.
• This crowding can hinder their movement, thus decreasing overall ion mobility.

These factors lead to a common misconception that conductivity increases with decreasing concentration, which is not typical. In reality, with less crowding at lower concentrations, while the overall number of ions may decrease, the individual ion's ability to contribute to conductivity often enhances at very low concentrations.

Ionic Mobility

Ionic mobility refers to the speed at which ions move through a solution when an electrical field is applied. It's a critical factor affecting both conductivity and molar conductivity of a solution. Several factors influence ionic mobility:

• The size and charge of the ion: Smaller ions with higher charges tend to be more mobile.
• The viscosity of the solvent: More viscous solvents hinder ion movement.
• The concentration of the solution: Generally, lower concentrations reduce the hindrance caused by ion crowding.

As concentration decreases, ions experience less resistance from each other, leading to increased mobility. This is why we often observe higher molar conductivity as dilution occurs. As a result, the enhanced movement amplifies the conductivity of each ion, making the solution more effective in conducting electricity.