Calculate the boiling point of a solution containing 0.45g of camphor (mol. wt. 152) dissolved in 35.4g of acetone (b.p `56.3^@C`), `K_b` per 100 gm of acetone is `17.2^@C`

Options

A. `56.446^@C`
B. `52.401^@C`
C. `56.146^@C`
D. `50.464^@C`

Explanation

To calculate the boiling point of a solution containing camphor dissolved in acetone, we can follow these steps:

### Step 1: Calculate the number of moles of camphor (solute).
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given:
- Mass of camphor = 0.45 g
- Molar mass of camphor = 152 g/mol

Calculating the number of moles:
\[ \text{Number of moles of camphor} = \frac{0.45 \, \text{g}}{152 \, \text{g/mol}} \approx 0.00296 \, \text{mol} \]

### Step 2: Calculate the molality of the solution.
Molality (m) is defined as the number of moles of solute per kilogram of solvent.
Given:
- Mass of acetone (solvent) = 35.4 g = 0.0354 kg

Calculating molality:
\[ \text{Molality} = \frac{\text{Number of moles of solute}}{\text{mass of solvent (kg)}} = \frac{0.00296 \, \text{mol}}{0.0354 \, \text{kg}} \approx 0.0835 \, \text{mol/kg} \]

### Step 3: Calculate the boiling point elevation (\(\Delta T_b\)).
The formula for boiling point elevation is:
\[ \Delta T_b = K_b \times m \]
Where:
- \(K_b\) for acetone = 17.2 °C per 100 g of solvent = 17.2 °C per 0.1 kg of solvent = 172 °C/kg

Calculating the boiling point elevation:
\[ \Delta T_b = 172 \, \text{°C/kg} \times 0.0835 \, \text{mol/kg} \approx 0.143 \, \text{°C} \]

### Step 4: Calculate the new boiling point of the solution.
The boiling point of pure acetone is given as 56.3 °C. Therefore, the new boiling point of the solution is:
\[ \text{New boiling point} = \text{Boiling point of pure solvent} + \Delta T_b \]
\[ \text{New boiling point} = 56.3 \, \text{°C} + 0.143 \, \text{°C} \approx 56.443 \, \text{°C} \]

### Step 5: Round the final answer.
Rounding 56.443 °C gives us approximately 56.446 °C.

### Final Answer:
The boiling point of the solution is approximately **56.446 °C**.

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