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) \(4.19 \mathrm{mho} \mathrm{cm}^{2}\) (b) \(419 \mathrm{mh} \mathrm{cm}^{2}\) (c) \(0.0419 \mathrm{mho} \mathrm{cm}^{2}\) (d) \(0.209 \mathrm{mho} \mathrm{cm}^{2}\)

Step-by-Step Solution

Answer

The equivalent conductance of this solution is (b) 419 mho cm².

Step 1: Identify the Given Values

We are given that the specific conductance (also known as conductivity), \( k \), is \( 0.00419 \text{ mho cm}^{-1} \) and the concentration of the solution is \( 0.01 \text{ N} \).

Step 2: Use the Formula for Equivalent Conductance

The formula for equivalent conductance, \( \Lambda_{eq} \), is \( \Lambda_{eq} = \frac{k \times 1000}{c} \), where \( c \) is the concentration in normality (equivalents per liter).

Step 3: Substitute the Given Values into the Formula

Substitute \( k = 0.00419 \) and \( c = 0.01 \) into the formula: \[ \Lambda_{eq} = \frac{0.00419 \times 1000}{0.01} \].

Step 4: Calculate Equivalent Conductance

Perform the calculation: \[ \Lambda_{eq} = \frac{0.00419 \times 1000}{0.01} = 419 \text{ mho cm}^2 / \text{equiv} \].

Step 5: Choose the Correct Option

Comparing the calculated value with the options provided, the equivalent conductance is \( 419 \text{ mh cm}^2 \). This matches with option (b).

Key Concepts

Specific Conductance

Specific conductance, often just called conductivity, is a measure of how well a solution can conduct electricity. It gives us an idea of the number of ions available to carry electric charge. The more ions present, the higher the conductivity.Conductivity is expressed in units of \(\text{mho cm}^{-1}\) or \(\text{Siemens cm}^{-1}\). For example, if a solution has specific conductance of \(0.00419 \ \text{mho cm}^{-1}\), it tells us the solution’s ability to conduct electricity over a centimeter.In practice, specific conductance is vital for understanding the behavior of electrolyte solutions in various chemical processes and applications, from batteries to biochemistry.

Electrolyte Solution

An electrolyte solution is a liquid that contains ions and can conduct electricity. This concept is at the heart of many chemical and biological processes. Here are a few key points to understand about electrolyte solutions: - **Composition**: - Typically involves water as a solvent and dissolved ions like sodium, potassium, chloride and others. - Commonly formed by dissolving salts, acids, or bases in water. - **Functionality**: - In electrolyte solutions, the dissolved ions allow the solution to conduct electricity. - **Examples**: - Saline solution (common in medical use). - Seawater – naturally available electrolytic solution. Since ions carry electric current, the presence of electrolyte is crucial for any process that involves the flow of electric current through a liquid.

Conductivity Formula

The conductivity formula is a fundamental formula in electrochemistry that connects specific conductance, concentration, and equivalent conductance.The formula for equivalent conductance is given by:\[ \Lambda_{eq} = \frac{k \times 1000}{c} \]where:- \(\Lambda_{eq}\) is the equivalent conductance in \(\text{mho cm}^2/\text{equiv}\).- \(k\) is the specific conductance in \(\text{mho cm}^{-1}\).- \(c\) is the concentration in normality (N).This relation helps in transforming the specific conductance to a per unit measure for the ions, making it easier to compare different solutions regardless of their concentration. This is incredibly useful for figuring out how efficient an electrolyte solution is under different conditions.

Normality

Normality is a term used to describe the concentration of a solution in terms of equivalents per liter. An equivalent is the amount of substance that reacts with or replaces a standard quantity, like a hydrogen ion in an acid-base reaction.A few points to consider for a clearer understanding:- **Calculation**: - Normality (N) is calculated as \(\text{moles of solute} \times \text{valency factor}\).- **Uses**: - It is useful in redox reactions and acid-base equilibrium calculations. - Not as commonly used as molarity but when dealing with reactions involving ions or charge, it’s very helpful. - Allows direct use in measuring volumes for reactions due to one-to-one correspondence with reacting equivalents.Normality helps ensure precise and accurate measurements in titrations and chemical analysis where the reactivity of a solute is influenced by the amount of charge.