The correct expression in SI system relating the equivalent conductance `(wedge_(aq))` , specific conductance (K) and equivalent concentration (C) is (where C is the number of gram equivalents in one litre of the solution).

Options

A. `wedge_(aq)=K/C`
B. `wedge_(aq)=(Kxx1000)/C`
C. `wedge_(aq)=(Kxx1000^(-3))/C`
D. `wedge_(aq)=(Kxx1000^(-6))/C`

Answer

To derive the correct expression relating equivalent conductance (Λ), specific conductance (κ), and equivalent concentration (C), we can follow these steps:

### Step 1: Understand the definitions
- **Equivalent Conductance (Λ)**: It is defined as the conductance of a solution containing one gram equivalent of solute when placed between two parallel electrodes that are 1 cm apart.
- **Specific Conductance (κ)**: This is the conductance of a solution per unit volume and is measured in S/m (Siemens per meter).
- **Equivalent Concentration (C)**: This is the number of gram equivalents of solute per liter of solution, expressed in eq/L.

### Step 2: Relate Equivalent Conductance to Specific Conductance and Volume
The formula for equivalent conductance is given by:
\[ Λ = κ \times V \]
where V is the volume of the solution in liters that contains one gram equivalent of the solute.

### Step 3: Express Volume in terms of Concentration
Since we are considering one gram equivalent of solute, we can express the volume V in terms of the equivalent concentration C:
\[ V = \frac{1 \text{ eq}}{C \text{ (eq/L)}} = \frac{1}{C} \text{ L} \]

### Step 4: Substitute Volume into the Equivalent Conductance Formula
Substituting the expression for volume into the equation for equivalent conductance:
\[ Λ = κ \times \left(\frac{1}{C}\right) \]
However, since we need to express this in SI units, we need to account for the conversion from liters to milliliters (1 L = 1000 mL). Therefore, we multiply by 1000:
\[ Λ = κ \times \left(\frac{1000}{C}\right) \]

### Step 5: Final Expression
Thus, the final expression relating equivalent conductance (Λ), specific conductance (κ), and equivalent concentration (C) is:
\[ Λ = \frac{1000 \cdot κ}{C} \]

### Conclusion
The correct expression in SI system relating equivalent conductance, specific conductance, and equivalent concentration is:
\[ Λ = \frac{1000 \cdot κ}{C} \]