Choroform , `CHCl_(3)`, boils at `61.7^(@)`C. If the `K_(b)` for choroform is `3.63^(@)C//"molal"`, what is the boiling point of a solution of 15.0 kg of` CH_(3)` and 0.616 kg of acenaphthalene, `C_(12)H_(10)` ?
(a)61.9
(b)62
(c)52.2
(d)62.67

Options

A. 61.9
B. 62
C. 52.2
D. 62.67

Answer

To find the boiling point of the solution of chloroform with acenaphthalene, we will follow these steps:

### Step 1: Identify the Given Data
- Boiling point of pure chloroform, \( T_b^0 = 61.7^\circ C \)
- Boiling point elevation constant, \( K_b = 3.63^\circ C/\text{molal} \)
- Mass of acenaphthalene, \( m_B = 0.616 \, \text{kg} = 616 \, \text{g} \)
- Mass of chloroform, \( m_A = 15.0 \, \text{kg} = 15000 \, \text{g} \)

### Step 2: Calculate the Molar Mass of Acenaphthalene
The molecular formula of acenaphthalene is \( C_{12}H_{10} \).
- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Hydrogen (H) = 1 g/mol

Calculating the molar mass:
\[ \text{Molar mass of } C_{12}H_{10} = (12 \times 12) + (10 \times 1) = 144 + 10 = 154 \, \text{g/mol} \]

### Step 3: Calculate the Molality of the Solution
Molality (\( m \)) is defined as the number of moles of solute per kilogram of solvent.

First, we need to find the number of moles of acenaphthalene:
\[ \text{Moles of acenaphthalene} = \frac{\text{mass}}{\text{molar mass}} = \frac{616 \, \text{g}}{154 \, \text{g/mol}} \approx 4.0 \, \text{mol} \]

Next, calculate the molality:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} = \frac{4.0 \, \text{mol}}{15.0 \, \text{kg}} \approx 0.267 \, \text{molal} \]

### Step 4: Calculate the Boiling Point Elevation
Using the formula for boiling point elevation:
\[ \Delta T_b = K_b \times m \]
Substituting the values:
\[ \Delta T_b = 3.63^\circ C/\text{molal} \times 0.267 \, \text{molal} \approx 0.97^\circ C \]

### Step 5: Calculate the New Boiling Point of the Solution
Now, we can find the boiling point of the solution:
\[ T_b = T_b^0 + \Delta T_b = 61.7^\circ C + 0.97^\circ C \approx 62.67^\circ C \]

### Final Answer
The boiling point of the solution is approximately \( 62.67^\circ C \).

### Conclusion
The correct answer is (d) 62.67.

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