Question

A conductivity cell containing 0.001 M AgNO$_3$ solution develops resistance 6530ohm at 25$^{\circ}$C. Calculate the electrical conductivity of solution at same temperature if the cell constant is 0.653 cm$^{-1}$.

• A. 1.0 x 10$^{-4}$ S cm$^{-1}$
• B. 1.0 x 10$^{-3}$ S cm$^{-1}$
• C. 1.0 x 10$^{-5}$ S cm$^{-1}$
• D. 1.0 x 10$^{-2}$ S cm$^{-1}$

Hint:

Remember the relationship between conductivity ($\kappa$), resistance (R), and cell constant (G$^*$): $\kappa = G^*/R$. The unit of conductivity is Siemens per centimeter (S cm$^{-1}$) or ohm$^{-1}$ cm$^{-1}$. The cell constant (G$^*$) has units of inverse length (e.g., cm$^{-1}$).

Answer 1

The Correct Option is C

Step 1: Identify the given values.\nResistance (R) = 6530 $\Omega$\nCell constant (G$^*$) = 0.653 cm$^{-1}$\n\n
Step 2: Recall the formula for electrical conductivity.\nElectrical conductivity ($\kappa$) is related to resistance (R) and cell constant (G$^*$) by the formula:\n\[\kappa = \frac{\text{G}^*}{\text{R\]\n
Step 3: Substitute the given values into the formula.\n\[\kappa = \frac{0.653 \text{ cm}^{-1{6530 \text{ }\Omega}\]\n
Step 4: Calculate the electrical conductivity.\n\[\kappa = 0.0001 \text{ }\Omega^{-1}\text{ cm}^{-1}\]\nSince 1 $\Omega^{-1}$ is equal to 1 Siemens (S), the conductivity can be expressed as:\n\[\kappa = 1 \times 10^{-4} \text{ S cm}^{-1}\]\n
Step 5: Compare the calculated value with the options.\nThe calculated conductivity is $1 \times 10^{-4}$ S cm$^{-1}$.\n