0.05 M NaOH solution offered a resistance of 31.6 ohm in a conductivity cell at 298 K. If the cell constant of the conductivity cell is 0.367 cm -1,calculate molar conductivity of NaOH solution

To find the molar conductivity of the NaOH solution, we can use the relationship between conductivity, cell constant, and molar conductivity. The formula we will use is:

Understanding the Key Concepts

First, let's break down the terms involved:

• Conductivity (κ): This is a measure of a solution's ability to conduct electricity, expressed in siemens per meter (S/m).
• Cell Constant (K): This is a characteristic of the conductivity cell, given in cm^-1. It relates the geometry of the cell to the measurement of conductivity.
• Molar Conductivity (Λ_m): This indicates how well a particular concentration of an electrolyte conducts electricity, expressed in S m² mol^-1.

Step-by-Step Calculation

1. **Calculate the conductivity (κ)**: The conductivity can be calculated using the formula:

κ = 1 / R

Where R is the resistance of the solution. Given that R = 31.6 ohms, we can calculate κ:

κ = 1 / 31.6 = 0.031645 S/m

2. **Convert the cell constant to meters**: Since the cell constant is given in cm^-1, we need to convert it to m^-1 for consistency in units:

K = 0.367 cm^-1 = 0.367 / 100 = 0.00367 m^-1

3. **Calculate the molar conductivity (Λ_m)**: The molar conductivity can be calculated using the formula:

Λ_m = κ / C

Where C is the concentration of the solution in moles per liter (mol/L). Given that the concentration is 0.05 M, we can substitute the values:

Λ_m = κ × K

Now substituting the values:

Λ_m = 0.031645 S/m × 0.367 m^-1

Λ_m = 0.0116 S m² mol^-1

Final Result

The molar conductivity of the 0.05 M NaOH solution at 298 K is approximately 0.0116 S m² mol^-1.

This calculation illustrates how conductivity, cell constant, and concentration interact to determine the molar conductivity of an electrolyte solution. Understanding these relationships is crucial in fields like analytical chemistry and electrochemistry, where conductivity measurements are frequently used to analyze solutions.