Problem 29 - A Complete Resource Book in Chemistry for JEE Main

Question

The cell constant of a solution, whose specific conductance and observed conductance are same, is equal to (a) 1 (b) 0 (c) 10 (d) 100

Step-by-Step Solution

Answer

The cell constant is 1.

Step 1: Understanding the Concepts

To solve this problem, we need to understand the relationship between cell constant, specific conductance (also known as conductivity), and observed conductance. The cell constant is given by \( K = \frac{G}{ ext{Specific Conductance}} \), where \( K \) is the cell constant and \( G \) is the conductance.

Step 2: Analyzing the Given Information

According to the problem, the specific conductance and the observed conductance are the same. Mathematically, this means \( ext{Specific Conductance} = G \).

Step 3: Applying the Formula

Using the formula for cell constant \( K = \frac{G}{ ext{Specific Conductance}} \), and since \( G = ext{Specific Conductance} \), substituting this gives us \( K = \frac{G}{G} = 1 \).

Step 4: Determining the Correct Answer

From the calculation in the previous step, we find that the cell constant \( K \) is equal to 1.

Key Concepts

Cell Constant

The cell constant is a crucial factor in electrochemistry, particularly when measuring conductance in a solution. It is essentially a conversion factor that relates the measured conductance to specific conductance.
The formula for the cell constant (\( K \)) is:

• \(K = \frac{G}{\text{Specific Conductance}}\)

Understanding the role of the cell constant is key in electrochemical measurements. It can be thought of like the calibration of a measuring device, adjusting measurements to account for geometric factors. When both specific conductance and observed conductance are the same, the cell constant simplifies to 1. This indicates a precise and effective measurement setup.
This condition clearly reflects a balanced system where the measurement setup does not introduce any discrepancies or variances.

Specific Conductance

In electrochemistry, specific conductance, also known as conductivity, is a measure of a solution's ability to conduct an electric current. It is typically expressed in units of \( Siemens/cm \) and is an intrinsic property of the solution.
Its value depends primarily on the nature of the ions present, the concentration of ions, and the temperature of the solution.

• Intrinsic property of solutions.
• Depends on the ion concentration and type.
• Influenced by temperature.

Specific conductance is important because it tells us how well ions move through the solution, which directly affects the ability to conduct electricity. This measurement is vital in applications such as water quality testing and chemical analysis.
Correspondingly, when designing experiments or interpreting data, it's crucial to ensure that the solutions are properly configured and measured at controlled conditions to obtain accurate results.

Conductance Formula

The conductance formula is at the heart of understanding how solutions conduct electricity. Conductance is denoted \( G \) and measured in Siemens. It quantitatively reflects the ease with which an electric current passes through a conductor. The simple formula connecting observed conductance and specific conductance through the cell constant is:

• \(G = K \times \text{Specific Conductance}\)

In the exercise in question, we saw that when observed conductance equals specific conductance, the formula \( K = \frac{G}{\text{Specific Conductance}} \) simplifies to \( K = 1 \). This simple mathematical relationship illustrates how the cell constant aids in converting between these two measurements.
Studying conductance formulas helps in understanding the properties of solutions and their ionic characteristics, paving the way for better industrial processes and analytical methodologies.