Equivalent conductivity can be expressed in terms of specific conductance (k) and concentration (N) in gram equivalent `dm^(-3)` as:

Options

A. `kxxN`
B. `(kxx1000)/N`
C. `(kxxN)/1000`
D. `kxxNxx1000`

Answer

To express equivalent conductivity in terms of specific conductance (k) and concentration (N) in gram equivalent per decimeter cube, we can follow these steps:

### Step 1: Understand the Definitions
- **Specific Conductance (k)**: This is the conductivity of a solution per unit volume.
- **Equivalent Conductivity (Λ)**: This is defined as the conductivity of a solution containing one gram equivalent of the electrolyte.
- **Concentration (N)**: This is the number of gram equivalents of solute per liter of solution.

### Step 2: Relate Equivalent Conductivity to Specific Conductance
The equivalent conductivity (Λ) can be expressed in terms of specific conductance (k) and the volume of the solution (V) that contains one gram equivalent of the electrolyte:
\[ \Lambda = k \times V \]

### Step 3: Express Volume in Terms of Concentration
Since concentration (N) is defined as the number of gram equivalents per volume in liters, we can express the volume (V) in terms of concentration:
\[ N = \frac{1 \text{ gram equivalent}}{V} \implies V = \frac{1}{N} \]

### Step 4: Substitute Volume into the Equivalent Conductivity Equation
Substituting the expression for volume (V) into the equation for equivalent conductivity:
\[ \Lambda = k \times \left(\frac{1}{N}\right) \]

### Step 5: Adjust for Units
Since we want the equivalent conductivity in terms of decimeters cubed (dm³), we need to convert the volume from milliliters to liters. We know that:
\[ 1 \text{ mL} = 0.001 \text{ L} \implies 1000 \text{ mL} = 1 \text{ L} \]
Thus, we multiply by 1000 to convert:
\[ \Lambda = k \times \frac{1000}{N} \]

### Final Expression
The final expression for equivalent conductivity in terms of specific conductance and concentration is:
\[ \Lambda = \frac{k \times 1000}{N} \]