The correct answer is (4) \(ohm^{-1}\text{ cm }^2\text{ mol}^{-1}\).
Molar conductivity (\(\Lambda_m\)) is a measure of the ability of a solution to carry an electric current. It is defined as the conductivity of a solution divided by the molarity of the electrolyte in that solution. The unit of molar conductivity is typically expressed as siemens per meter squared per mole (S m² mol⁻¹) or ohm⁻¹ cm² mol⁻¹.
The formula for molar conductivity is:
\[ \Lambda_m = \frac{\kappa}{c} \]
where:
- \(\Lambda_m\) is the molar conductivity,
- \(\kappa\) is the conductivity of the solution in siemens per centimeter (S cm⁻¹),
- \(c\) is the molarity of the electrolyte in mol L⁻¹.
Now, let's look at the units in more detail:
1. Siemens (S) is the unit of electrical conductance. It is equivalent to ampere per volt (A V⁻¹).
2. The unit of molarity (mol L⁻¹) is used for the concentration term in the denominator.
Combining these units, we get the molar conductivity in siemens per meter squared per mole (S m² mol⁻¹) or ohm⁻¹ cm² mol⁻¹.
Now, let's examine the options:
1. \(\text{ ohm cm}^{-2}\text{ mol}^{-1}\) - Incorrect, as it is missing the squared unit for area.
2. \( ohm^{-1}\text{ cm }\text{ mol}^{-2}\) - Incorrect, as the order of units is not consistent with the definition of molar conductivity.
3. \(\text{ohm cm}^2\text{ mol}^{-1}\) - Incorrect, as it has the squared unit for area but is missing the reciprocal of the unit for conductivity.
4. \( ohm^{-1}\text{ cm }^2\text{ mol}^{-1}\) - This is the correct unit, with the reciprocal of ohms for conductivity and the squared unit for area.
Therefore, the correct answer is option 4: \( ohm^{-1}\text{ cm }^2\text{ mol}^{-1}\). |
