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 (option a).

Step 1: Understand the Problem

The problem asks for the cell constant of a solution where the specific conductance (also known as conductivity) is equal to the observed conductance. The cell constant connects the cell's resistance and conductivity to the observed conductance.

Step 2: Recall the Formula

The formula for calculating the conductance using the cell constant is given by: \( G = K \times L \), where \( G \) is the observed conductance, \( K \) is the specific conductance, and \( L \) is the cell constant.

Step 3: Solve for Cell Constant

Given that the specific conductance \( K \) is equal to the observed conductance \( G \), we can set \( K = G \). Substituting into the formula gives \( G = G \times L \).

Step 4: Simplify the Equation

By simplifying the equation \( G = G \times L \), we divide both sides by \( G \) (assuming \( G \) is not zero), resulting in \( 1 = L \).

Step 5: Conclusion

Since the equation simplifies to \( L = 1 \), the cell constant is 1.

Key Concepts

Cell Constant

In the study of electrochemistry, the cell constant plays a crucial role. It is a factor that links the physical dimensions of an electrolyte solution's container or cell to its ability to conduct electricity. The formula used to determine this is \( G = K \times L \), where \( G \) is the observed conductance, \( K \) represents the specific conductance, and \( L \) is the cell constant.

• The cell constant, \( L \), accounts for the geometry of the electrodes and the distance between them in a conductivity cell.
• It is dimensionless and quantifies how the container influences the measurement of conductivity.

When you have a solution where the specific conductance is equal to the observed conductance, the simplified equation \( 1 = L \) suggests a cell constant of 1. This indicates that the physical setup of the cell doesn't alter the measurement, making the dimensions standard or neutral in effect.

Specific Conductance

Specific conductance, or conductivity, measures how well a solution can conduct an electric current. It's expressed in Siemens per meter (S/m) and depends on the concentration of ions in a solution as well as the nature of the ionic species present.

• Higher ion concentrations generally lead to higher specific conductance.
• The types of ions and their mobility also affect this measure.

Specific conductance is intrinsic to the material, meaning it's a property of the material itself. In electrochemical cells, it tells us about the effectiveness of the solution in carrying current independent of cell geometry. Thus, a solution with high specific conductance is better at facilitating electric flow.

Observed Conductance

Observed conductance is the actual measurement of a current passing through a cell containing an electrolyte solution. It's the practical application of theoretical concepts in real-world settings. This value depends not only on the ionic nature and concentration of the solution (specific conductance) but also on the physical setup of the cell.

• If the specific conductance and observed conductance are the same, it indicates that the cell constant is neutral, commonly \( L = 1 \).
• Practical measurements can be affected by factors such as electrode shape, arrangement, and the solution's homogeneity.

Thus, observed conductance is dependent on how well the cell geometry complements the intrinsic properties of the solution.