The resistance of a conductivity cell containing 0.001 M KCl solution at 298 K is 1500 O. What is the cell constant if the conductivity of 0.001 M KCl solution at 298 K is 0.146 × 10-3 S cm-1?

To find the cell constant of a conductivity cell, we can use the relationship between conductivity, resistance, and the cell constant. The formula that connects these variables is:

Understanding the Relationship

The cell constant (K) can be defined as:

K = σ × R

Where:

• K is the cell constant (in cm^-1),
• σ is the conductivity of the solution (in S cm^-1), and
• R is the resistance of the cell (in ohms, Ω).

Given Values

From the problem, we have:

• Resistance (R) = 1500 Ω
• Conductivity (σ) = 0.146 × 10^-3 S cm^-1

Calculating the Cell Constant

Now, we can rearrange the formula to find the cell constant:

K = σ × R

Substituting the given values:

K = (0.146 × 10^-3 S cm^-1) × (1500 Ω)

Performing the Calculation

Now, let's do the multiplication:

K = 0.146 × 10^-3 × 1500

Calculating this gives:

K = 0.146 × 1.5 = 0.219

Since we are multiplying by 10^-3, we need to adjust the final result:

K = 0.219 cm^-1

Final Result

The cell constant for the conductivity cell containing a 0.001 M KCl solution at 298 K is approximately 0.219 cm^-1.

This calculation illustrates how conductivity and resistance are interrelated in electrochemistry, providing insight into the properties of solutions and their behavior in an electric field. Understanding these concepts is crucial for applications in analytical chemistry, environmental monitoring, and various industrial processes.