The distance between two electrodes of a cell is 2.5 cm and area of each electrode is 5 cm^2. The ce — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Understand the Definition and Formula for Cell Constant ($G^*$) The **cell constant** ($G^*$) of a conductivity cell is a characteristic geometric property of the cell. It is defined as the ratio of the distance ($l$) between the two parallel electrodes to the cross-sectional area ($A$) of each electrode: $$G^* = \frac{l}{A}$$ The SI unit of cell constant is $\text{m}^{-1}$, although it is also commonly expressed in CGS units as $\text{cm}^{-1}$. Step 2 - Substitute the Given Values into the Formula We are given the following geometric parameters of the cell: * Distance between the electrodes ($l$) = $2.5\text{ cm}$ * Cross-sectional area of each electrode ($A$) = $5\text{ cm}^2$ Substituting these values into the formula: $$G^* = \frac{2.5\text{ cm}}{5\text{ cm}^2}$$ $$G^* = 0.5\text{ cm}^{-1}$$ Step 3 - Convert the Cell Constant to SI Units ($\text{m}^{-1}$) To compare our calculated value with the options provided in the question, we need to convert the unit from $\text{cm}^{-1}$ to $\text{m}^{-1}$. We know that: $$1\text{ cm} = 10^{-2}\text{ m}$$ Therefore, the conversion factor for the inverse unit is: $$1\text{ cm}^{-1} = \frac{1}{1\text{ cm}} = \frac{1}{10^{-2}\text{ m}} = 10^2\text{ m}^{-1} = 100\text{ m}^{-1}$$ Now, multiply our calculated cell constant by this conversion factor: $$G^* = 0.5 \times 100\text{ m}^{-1}$$ $$G^* = \boxed{50\text{ m}^{-1}}$$ Step 4 - Evaluate the Options * **Option (A) is incorrect:** This option ($0.5\text{ m}^{-1}$) has the correct numerical value from the CGS calculation ($0.5\text{ cm}^{-1}$), but the unit has been incorrectly written as $\text{m}^{-1}$ without performing the required unit conversion. * **Option (B) is incorrect:** This value ($12.5\text{ cm}^3$) is obtained by multiplying the length and area ($2.5\text{ cm} \times 5\text{ cm}^2$), which yields a volume ($\text{cm}^3$) rather than a cell constant. * **Option (C) is incorrect:** This value ($2.0\text{ cm}$) is obtained by taking the reciprocal ratio ($\frac{A}{l} = \frac{5}{2.5}$), which is the inverse of the cell constant and carries incorrect units. * **Option (D) is correct:** As shown by the mathematical conversion, $0.5\text{ cm}^{-1}$ is exactly equal to $50\text{ m}^{-1}$. $$\text{Correct Option: } \boxed{\text{D}}$$