A solution of 0.640 g of azulene in 100.0 g of benzene is `80.23^(@)C`. The boilingpoint of benzeneis `80.10^(@)C`, and` K_(b)` is `2.53^(@)C`/molal What is the molecular mass of azulene?
(a)108
(b)99
(c)125
(d)134

Options

A. 108
B. 99
C. 125
D. 134

Answer

To find the molecular mass of azulene, we can follow these steps:

### Step 1: Calculate the elevation in boiling point (ΔT_b)
The elevation in boiling point is given by the formula:
\[ \Delta T_b = T_{\text{solution}} - T_{\text{solvent}} \]
Where:
- \( T_{\text{solution}} = 80.23^\circ C \) (boiling point of the solution)
- \( T_{\text{solvent}} = 80.10^\circ C \) (boiling point of benzene)

Calculating ΔT_b:
\[ \Delta T_b = 80.23 - 80.10 = 0.13^\circ C \]

### Step 2: Use the formula for boiling point elevation
The formula for boiling point elevation is:
\[ \Delta T_b = K_b \cdot m \]
Where:
- \( K_b = 2.53^\circ C/\text{molal} \) (boiling point elevation constant for benzene)
- \( m \) is the molality of the solution.

### Step 3: Rearrange the formula to find molality (m)
Rearranging the formula gives:
\[ m = \frac{\Delta T_b}{K_b} \]
Substituting the known values:
\[ m = \frac{0.13}{2.53} \approx 0.0514 \text{ molal} \]

### Step 4: Calculate the number of moles of solute (azulene)
Molality (m) is defined as the number of moles of solute per kilogram of solvent. We have 100 g of benzene, which is 0.1 kg. Therefore:
\[ m = \frac{\text{number of moles of solute}}{\text{mass of solvent in kg}} \]
Thus:
\[ \text{number of moles of azulene} = m \cdot \text{mass of solvent in kg} = 0.0514 \cdot 0.1 = 0.00514 \text{ moles} \]

### Step 5: Calculate the molecular mass of azulene
The molecular mass (M) can be calculated using the formula:
\[ \text{Molecular mass} = \frac{\text{mass of solute}}{\text{number of moles of solute}} \]
Substituting the values:
\[ \text{Molecular mass} = \frac{0.640 \text{ g}}{0.00514 \text{ moles}} \approx 124.9 \text{ g/mol} \]

### Conclusion
Rounding this value gives us approximately 125 g/mol. Therefore, the molecular mass of azulene is:
\[ \text{Molecular mass of azulene} \approx 125 \text{ g/mol} \]
Thus, the correct answer is (c) 125.

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