A' gram of non-volatile, non-electrolyte (molar mass M) is dissolved in 200 ml of unknown solvent (density`=1.25 gm//ml` molal elevation constant is `K_(b)`) .Elevation in boiling point of this solution can be given by

Options

A. `(M)/(K_(b))`
B. `(4K_(b)A)/(M)`
C. `(K_(b)A)/(4M)`
D. `(K_(b)M)/(4A)`

Answer

To solve the problem of determining the elevation in boiling point (\( \Delta T_b \)) of a solution made by dissolving \( A \) grams of a non-volatile, non-electrolyte solute with molar mass \( M \) in 200 ml of an unknown solvent (with a density of 1.25 g/ml), we can follow these steps:

### Step 1: Calculate the mass of the solvent
The mass of the solvent can be calculated using the formula:
\[ \text{Mass of solvent} = \text{Volume} \times \text{Density} \]
Given that the volume of the solvent is 200 ml and the density is 1.25 g/ml, we can substitute these values:
\[ \text{Mass of solvent} = 200 \, \text{ml} \times 1.25 \, \text{g/ml} = 250 \, \text{g} \]

### Step 2: Convert the mass of the solvent to kilograms
Since molality is defined in terms of kilograms of solvent, we convert the mass of the solvent from grams to kilograms:
\[ \text{Mass of solvent in kg} = \frac{250 \, \text{g}}{1000} = 0.25 \, \text{kg} \]

### Step 3: Calculate the number of moles of solute
The number of moles of solute can be calculated using the formula:
\[ \text{Moles of solute} = \frac{\text{Mass of solute}}{\text{Molar mass of solute}} = \frac{A}{M} \]

### Step 4: Calculate the molality of the solution
Molality (\( m \)) is defined as the number of moles of solute per kilogram of solvent:
\[ m = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}} = \frac{A/M}{0.25} \]
This simplifies to:
\[ m = \frac{4A}{M} \]

### Step 5: Use the formula for elevation in boiling point
The elevation in boiling point can be calculated using the formula:
\[ \Delta T_b = K_b \times m \]
Substituting the expression for molality:
\[ \Delta T_b = K_b \times \frac{4A}{M} \]

### Final Answer
Thus, the elevation in boiling point of the solution can be given by:
\[ \Delta T_b = \frac{4K_b A}{M} \]