The boiling point of solution obtained by dissolving 0.51 g
anthracene in 35 g chloroform increases by `0.32^(@)`C then what
will be the molar mass of anthracene if for chloroform `K_(b)=3.9K Kg mol^(-1)` :-

Options

A. 175.2
B. 177.6
C. 178.6
D. 182.3

Explanation

To find the molar mass of anthracene based on the boiling point elevation of the solution, we can follow these steps:

### Step 1: Write the formula for boiling point elevation
The boiling point elevation (\( \Delta T_b \)) is given by the formula:
\[ \Delta T_b = K_b \times m \]
where:
- \( \Delta T_b \) is the boiling point elevation,
- \( K_b \) is the ebullioscopic constant of the solvent (chloroform in this case),
- \( m \) is the molality of the solution.

### Step 2: Identify the known values
From the problem, we have:
- \( \Delta T_b = 0.32 \, ^\circ C \)
- \( K_b = 3.9 \, K \cdot kg \cdot mol^{-1} \)
- Mass of anthracene (solute) = 0.51 g
- Mass of chloroform (solvent) = 35 g

### Step 3: Convert the mass of the solvent to kilograms
Since molality is defined as moles of solute per kilogram of solvent, we convert the mass of chloroform from grams to kilograms:
\[ \text{Mass of solvent in kg} = \frac{35 \, g}{1000} = 0.035 \, kg \]

### Step 4: Rearrange the boiling point elevation formula to find molality
We can rearrange the formula to solve for molality (\( m \)):
\[ m = \frac{\Delta T_b}{K_b} \]

### Step 5: Substitute the known values into the molality formula
Substituting the known values:
\[ m = \frac{0.32}{3.9} \approx 0.08205 \, mol/kg \]

### Step 6: Use the definition of molality to find moles of solute
Molality is defined as:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]
Thus, we can express moles of solute as:
\[ \text{moles of solute} = m \times \text{mass of solvent in kg} = 0.08205 \times 0.035 \approx 0.00287175 \, mol \]

### Step 7: Calculate the molar mass of anthracene
The molar mass (M) can be calculated using the formula:
\[ M = \frac{\text{mass of solute}}{\text{moles of solute}} \]
Substituting the values we have:
\[ M = \frac{0.51 \, g}{0.00287175 \, mol} \approx 177.6 \, g/mol \]

### Final Answer
The molar mass of anthracene is approximately **177.6 g/mol**.

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