S.I. unit of molar conductivity is `ohm^(-1) cm ^(2) mol ^(-1)`

Options

A. `S m^(2) mol^(-1)`
B. `S m^(-1) mol^(-1)`
C. `S m ^(-2) mol `
D. ` S m^(2) mol ^(-1)`

Answer

To determine the S.I. unit of molar conductivity, we can follow these steps:

### Step 1: Understand Molar Conductivity
Molar conductivity (Λ) is defined as the conductivity (κ) of an electrolyte solution divided by the concentration (C) of the electrolyte in moles per liter (mol/L).

### Step 2: Write the Formula
The formula for molar conductivity is given by:
\[ Λ = \frac{κ}{C} \]

### Step 3: Identify Units
- The unit of conductivity (κ) is Siemens per meter (S/m), which can also be expressed as ohm\(^{-1}\)m\(^{-1}\).
- The concentration (C) is expressed in moles per cubic meter (mol/m³).

### Step 4: Substitute the Units
Substituting the units into the formula for molar conductivity:
\[ Λ = \frac{S/m}{mol/m^3} \]

### Step 5: Simplify the Units
When we simplify the units, we get:
\[ Λ = S \cdot m^3 \cdot mol^{-1} \cdot m^{-1} = S \cdot m^2 \cdot mol^{-1} \]

### Step 6: Convert Siemens to Ohm
Since 1 S (Siemens) is equivalent to ohm\(^{-1}\), we can express the unit of molar conductivity as:
\[ Λ = ohm^{-1} \cdot m^2 \cdot mol^{-1} \]

### Step 7: Convert Meters to Centimeters
To express this in terms of centimeters, we note that:
1 m = 100 cm, hence:
\[ m^2 = (100 \, cm)^2 = 10,000 \, cm^2 \]

### Step 8: Final Unit of Molar Conductivity
Thus, substituting back, we have:
\[ Λ = ohm^{-1} \cdot cm^2 \cdot mol^{-1} \]

### Conclusion
The S.I. unit of molar conductivity is:
\[ ohm^{-1} \cdot cm^2 \cdot mol^{-1} \]