The unit of ebullioscopic constant is

Options

A. `Kg " mol"^(-1)`
B. K kg mol
C. K kg `"mol"^(-1)`
D. K g mol

Explanation

To determine the unit of the ebullioscopic constant (Kb), we can follow these steps:

### Step 1: Understand the Definition
The ebullioscopic constant (Kb) is defined as the elevation in boiling point produced when one mole of a solute is dissolved in one kilogram (kg) of solvent.

### Step 2: Write the Formula
The relationship between the elevation in boiling point (ΔTb), the ebullioscopic constant (Kb), and the molality (m) of the solution is given by the formula:
\[ \Delta T_b = K_b \times m \]

### Step 3: Identify the Units
- ΔTb (elevation in boiling point) is measured in degrees Celsius (°C) or Kelvin (K).
- Molality (m) is defined as moles of solute per kilogram of solvent, which has the unit:
\[ \text{mol/kg} \]

### Step 4: Rearrange the Formula to Solve for Kb
To find the unit of Kb, we can rearrange the formula:
\[ K_b = \frac{\Delta T_b}{m} \]

### Step 5: Substitute the Units
Substituting the units into the rearranged formula:
- The unit of ΔTb is K (or °C).
- The unit of molality (m) is mol/kg.

Thus, the unit of Kb becomes:
\[ K_b = \frac{K}{\text{mol/kg}} \]

### Step 6: Simplify the Units
This can be expressed as:
\[ K_b = \frac{K \cdot \text{kg}}{\text{mol}} \]

Thus, the unit of the ebullioscopic constant (Kb) is:
\[ K \cdot \text{kg/mol} \]

### Final Answer
The unit of the ebullioscopic constant (Kb) is:
\[ \text{K kg}^{-1} \text{mol}^{-1} \]

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