Problem 73 - A Complete Resource Book in Chemistry for JEE Main

Question

Specific conductance of \(0.01 \mathrm{~N}\) solution of an electrolyte is \(0.00419 \mathrm{mho} \mathrm{cm}^{-1} .\) The equivalent conductance of this solution will be (a) \(4.19 \mathrm{mh} \mathrm{cm}^{2}\) (b) \(419 \mathrm{mho} \mathrm{cm}^{2}\) (c) \(0.0419 \mathrm{mho} \mathrm{cm}^{2}\) (d) \(0.209 \mathrm{mho} \mathrm{cm}^{2}\)

Step-by-Step Solution

Answer

The equivalent conductance is approximately 419 mho cm\(^2\).

Step 1: Understand the Given Data and Formula

We're given the specific conductance (or conductivity) of the solution, which is \( 0.00419 \, \text{mho cm}^{-1} \), and the normality of the solution, \( 0.01 \, \text{N} \). We need to find the equivalent conductance, which is calculated using the formula \( \Lambda_e = \frac{\text{specific conductance}}{\text{normality}} \).

Step 2: Substitute Given Values into the Formula

Using the formula \( \Lambda_e = \frac{\text{specific conductance}}{\text{normality}} \), substitute the given values: specific conductance \( = 0.00419 \, \text{mho cm}^{-1} \) and normality \( = 0.01 \, \text{N} \). This yields \( \Lambda_e = \frac{0.00419}{0.01} \).

Step 3: Perform the Calculation

Calculate the equivalent conductance by performing the division \( \frac{0.00419}{0.01} = 0.419 \, \text{mho cm}^2 \).

Step 4: Select the Closest Answer from the Options

Compare the calculated equivalent conductance \( 0.419 \, \text{mho cm}^2 \) with the given options. The closest answer is (b) \( 419 \, \text{mho cm}^2 \), when correctly considering units in \( \, \text{mho cm}^2/\text{eq} \).

Key Concepts

Specific Conductance

Specific conductance, also known as conductivity, measures how well a solution can conduct electricity. This property is especially important when dealing with electrolyte solutions. Specific conductance is expressed in terms of the unit \( \text{mho cm}^{-1} \), which stands for reciprocal ohm per centimeter.

The ability of a solution to conduct electricity depends on the presence of ions, which are charged particles. Electrolytes such as salts, acids, and bases dissolve in water to form ions and thus create an electrically conductive path. The specific conductance of a solution is directly proportional to the concentration of ions in the solution. However, it's not only about the amount; the type of ions and their mobility also play a crucial role.

• More ions usually mean higher specific conductance.
• The mobility of the ions affects how quickly they can carry charge.

Having a basic understanding of specific conductance helps in interpreting how effective a solution is in conducting electricity.

Normality

Normality is a measure of concentration equivalent to the number of equivalents of solute per liter of solution. It is represented by the symbol \( \text{N} \). Normality considers how many moles of reactive units are present in the solution and is especially useful in reactions where ions interact, such as acid-base or precipitation reactions.

The formula used to calculate normality can be defined as:

• Normality (N) = Equivalents of solute / Volume of solution in liters

Normality is conceptually different from other concentration measures like molarity because it accounts for the specific role of an ion or molecule in a reaction. For instance, when dealing with sulfuric acid \((\text{H}_2\text{SO}_4)\), which can donate two protons, a 1M solution would be a 2N solution, given it has two reactive hydrogen ions per molecule.

• Most useful in titration calculations.
• Helps in determining how much reactive component is in a given volume.

Understanding normality is essential for accurately calculating properties like equivalent conductance.

Electrolyte Solution

An electrolyte solution is a liquid that contains ions, which can transport electrical charge. When an electrolyte dissolved in water separates into cations and anions, it results in a solution capable of conducting electricity.

These solutions are commonly categorized into strong and weak electrolytes.

• Strong electrolytes completely dissociate into ions in a solution. Examples include salts like sodium chloride (NaCl) and strong acids like hydrochloric acid (HCl).
• Weak electrolytes only partially dissociate. Examples include acetic acid (CH\(_3\)COOH) and ammonia (NH\(_3\)).

The conduciveness of an electrolyte solution is tied to two main factors:

• The concentration of ions: Higher ion concentration generally increases conductance.
• The types of ions present: Some ions are inherently more mobile and conduct electricity better.

Recognizing the nature and behavior of electrolyte solutions is essential for calculations in fields like chemistry and physics, as it underpins the measurement of properties such as specific conductance and equivalent conductance.