Question

The resistance of $0.2\ \mathrm{M}$ solution of an electrolyte is $30\ \Omega$ and conductivity is $1.2\ \mathrm{S\ m^{-1}}$. What is the value of cell constant?

• A. $0.47\ \mathrm{cm^{-1}}$
• B. $0.1\ \mathrm{cm^{-1}}$
• C. $0.36\ \mathrm{cm^{-1}}$
• D. $0.2\ \mathrm{cm^{-1}}$

Hint:

Be very careful with units in electrochemistry! If $\kappa$ is in $\mathrm{m^{-1}}$, dividing the final product by 100 converts it directly to $\mathrm{cm^{-1}}$ because $1\ \mathrm{cm} = 10^{-2}\ \mathrm{m}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We are given the molarity ($0.2\ \mathrm{M}$), resistance ($R = 30\ \Omega$), and conductivity ($\kappa = 1.2\ \mathrm{S\ m^{-1}}$) of an electrolytic solution. We need to determine its cell constant ($G^*$) in units of $\mathrm{cm^{-1}}$.

Step 2: Key Formula or Approach:
The relationship between conductivity ($\kappa$), resistance ($R$), and cell constant ($G^*$) is given by: $$\kappa = \frac{G^*}{R} \implies G^* = \kappa \times R$$ Since the options are provided in $\mathrm{cm^{-1}}$ and the given conductivity is in $\mathrm{S\ m^{-1}}$, we must properly convert the unit from $\mathrm{m^{-1}}$ to $\mathrm{cm^{-1}}$ using $1\ \mathrm{m^{-1}} = \frac{1}{100}\ \mathrm{cm^{-1}}$.

Step 3: Detailed Explanation:
Substitute the given values into the cell constant formula: $$G^* = 1.2\ \mathrm{S\ m^{-1}} \times 30\ \Omega$$ $$G^* = 36\ \mathrm{m^{-1}}$$ Now, perform the unit conversion to match the options: $$G^* = 36 \times \frac{1}{100}\ \mathrm{cm^{-1}}$$ $$G^* = 0.36\ \mathrm{cm^{-1}}$$

Step 4: Final Answer:
The cell constant of the given cell is $0.36\ \mathrm{cm^{-1}}$, which corresponds to option (C).