The molal boiling point constant for water is`0.513^(@)C kgmol^(-1)`. When `0.1`mole of sugar is dissolved in `200`ml of water , the solution boils under a pressure of one atmosphere at

Options

A. `100.513^(@)C`
B. `100.0513^(@)C`
C. `100.256^(@)C`
D. `101.025^(@)C`

Explanation

To solve the problem, we need to find the boiling point of the solution when 0.1 mole of sugar is dissolved in 200 ml of water. We will use the formula for boiling point elevation:

\[ \Delta T_b = i \cdot K_b \cdot m \]

Where:
- \(\Delta T_b\) = boiling point elevation
- \(i\) = van 't Hoff factor (for sugar, a non-electrolyte, \(i = 1\))
- \(K_b\) = molal boiling point constant (for water, \(K_b = 0.513 \, °C \, kg \, mol^{-1}\))
- \(m\) = molality of the solution

### Step 1: Calculate the molality of the solution
Molality (\(m\)) is defined as the number of moles of solute per kilogram of solvent.

Given:
- Number of moles of sugar = 0.1 moles
- Volume of water = 200 ml

First, we need to convert the volume of water to mass. The density of water is approximately \(1 \, g/ml\), so:

\[ \text{Mass of water} = \text{Volume} \times \text{Density} = 200 \, ml \times 1 \, g/ml = 200 \, g \]

Now, convert grams to kilograms:

\[ \text{Mass of water in kg} = \frac{200 \, g}{1000} = 0.2 \, kg \]

Now, we can calculate molality:

\[ m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} = \frac{0.1 \, moles}{0.2 \, kg} = 0.5 \, mol/kg \]

### Step 2: Calculate the boiling point elevation
Now we can substitute the values into the boiling point elevation formula:

\[ \Delta T_b = i \cdot K_b \cdot m \]

Substituting the values:

\[ \Delta T_b = 1 \cdot 0.513 \, °C \, kg \, mol^{-1} \cdot 0.5 \, mol/kg = 0.2565 \, °C \]

### Step 3: Calculate the new boiling point of the solution
The boiling point of pure water is \(100 \, °C\). Therefore, the boiling point of the solution (\(T_b\)) is:

\[ T_b = 100 \, °C + \Delta T_b = 100 \, °C + 0.2565 \, °C = 100.2565 \, °C \]

### Final Answer
The solution boils at approximately \(100.26 \, °C\).

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