Question

The unit of equivalent conductivity is

• A. $\mathrm{S}{\mathrm{cm}}^{-2}$
• B. $\mathrm{ohm}·{\mathrm{cm}}^2(\mathrm{g}-\mathrm{equivalent})$
• C. $\mathrm{ohm}-\mathrm{cm}$
• D. ${\mathrm{ohm}}^{-1}·{\mathrm{cm}}^2{(\mathrm{g}-\mathrm{equivalent})}^{-1}$

Answer 1

The correct option is D

${\mathrm{ohm}}^{-1}·{\mathrm{cm}}^2{(\mathrm{g}-\mathrm{equivalent})}^{-1}$

Step 1: Formulas used

1. $\begin{array}{l}\mathrm{Equivalent}\mathrm{conductivity}=\frac{\mathrm{Conductivity}}{\mathrm{Gram}\mathrm{equivalent}}\end{array}$
2. $\begin{array}{l}\mathrm{Gram}\mathrm{equivalent}=\frac{\mathrm{Number}\mathrm{of}\mathrm{gram}\mathrm{equivalent}}{\mathrm{Volume}}\end{array}$

Step 2: Calculation for SI unit

$\begin{array}{l}\mathrm{Gram}\mathrm{equivalent}=\frac{\mathrm{Number}\mathrm{of}\mathrm{gram}\mathrm{equivalent}}{\mathrm{Volume}}\end{array}$

SI unit of volume is ${\mathrm{m}}^3$

$\begin{array}{l}\mathrm{Gram}\mathrm{equivalent}=\frac{\mathrm{g}-\mathrm{equivalent}}{{\mathrm{m}}^3}\end{array}$

Now, $\begin{array}{l}\mathrm{Equivalent}\mathrm{conductivity}=\frac{\mathrm{Conductivity}}{\mathrm{Gram}\mathrm{equivalent}}\end{array}$

When the potential gradient is unity, electrical conductivity is the amount of electricity that flows through a comparable slab every second.

$\begin{array}{l}\mathrm{Conductivity}=\frac{1}{\mathrm{Resistivity}}\end{array}$

The SI unit of Conductivity is $\frac{\mathrm{S}}{\mathrm{m}}$.

$$\begin{gathered} \begin{array}{l}\mathrm{Equivalent}\mathrm{conductivity}=\frac{\frac{\mathrm{S}}{\mathrm{m}}}{\frac{\mathrm{g}-\mathrm{equivalent}}{{\mathrm{m}}^3}}\end{array} \\ \begin{array}{l}\mathrm{Equivalent}\mathrm{conductivity}=\frac{\mathrm{S}}{\mathrm{m}}\times \frac{{\mathrm{m}}^3}{\mathrm{g}-\mathrm{equivalent}}\end{array} \\ \begin{array}{l}\mathrm{Equivalent}\mathrm{conductivity}=\frac{{\mathrm{Sm}}^2}{\mathrm{g}-\mathrm{equivalent}}\end{array} \end{gathered}$$

Converting m² to cm²

Then, ${\mathrm{Sm}}^2={\mathrm{ohm}}^{-1}{\mathrm{cm}}^2$.

Hence, the final SI unit of equivalent conductivity will be ${\mathrm{ohm}}^{-1}·{\mathrm{cm}}^2{(\mathrm{g}-\mathrm{equivalent})}^{-1}$.

Therefore, the correct option is (D) ${\mathrm{ohm}}^{-1}·{\mathrm{cm}}^2{(\mathrm{g}-\mathrm{equivalent})}^{-1}$.