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: List the data.
Resistance $R = 30\ \Omega$, conductivity $\kappa = 1.2\ \mathrm{S\,m^{-1}}$, and we want the cell constant $G^{*}$ in $\mathrm{cm^{-1}}$. The molarity is extra information not needed here.
Step 2: Recall the defining relations.
Conductance is $G = \dfrac{1}{R}$ and conductivity relates to it through the cell constant by \[ \kappa = G^{*} \cdot G = \frac{G^{*}}{R}. \]
Step 3: Solve for the cell constant.
Rearranging, $G^{*} = \kappa \cdot R$.
Step 4: Substitute in SI first.
\[ G^{*} = 1.2\ \mathrm{S\,m^{-1}} \times 30\ \Omega = 36\ \mathrm{m^{-1}}. \]
Step 5: Convert metres to centimetres.
Since $1\ \mathrm{m^{-1}} = 0.01\ \mathrm{cm^{-1}}$, \[ G^{*} = 36\ \mathrm{m^{-1}} \times \frac{1\ \mathrm{cm^{-1}}}{100\ \mathrm{m^{-1}}} = 0.36\ \mathrm{cm^{-1}}. \]
Step 6: Conclude.
The cell constant is $0.36\ \mathrm{cm^{-1}}$, option (C). Always watch the unit of $\kappa$ so the final answer lands in $\mathrm{cm^{-1}}$.
\[ \boxed{G^{*} = 0.36\ \mathrm{cm^{-1}}} \]