The boiling of a solution containing 1.5 g of dichlorobenzene in 100 g of benzene was higher by `0.268^(@)C` . Calculate the molar mass of dichlorobenzene (`k_(b)` for benzene 2.62 degree/molal)

Explanation

To solve the problem of calculating the molar mass of dichlorobenzene based on the boiling point elevation, we can follow these steps:

### Step 1: Identify the given data
- Mass of dichlorobenzene (solute, \( W_B \)) = 1.5 g
- Mass of benzene (solvent, \( W_A \)) = 100 g
- Elevation in boiling point (\( \Delta T_b \)) = 0.268 °C
- Boiling point elevation constant for benzene (\( K_b \)) = 2.62 °C/m

### Step 2: Write the formula for boiling point elevation
The formula for boiling point elevation is given by:
\[ \Delta T_b = K_b \times m \]
Where \( m \) is the molality of the solution. The molality can be calculated using:
\[ m = \frac{W_B}{M_B \times W_A} \]
Where:
- \( W_B \) = mass of solute (dichlorobenzene)
- \( M_B \) = molar mass of solute (dichlorobenzene, which we need to find)
- \( W_A \) = mass of solvent (benzene)

### Step 3: Substitute the expression for molality into the boiling point elevation formula
Substituting the expression for molality into the boiling point elevation formula gives:
\[ \Delta T_b = K_b \times \frac{W_B}{M_B \times W_A} \]

### Step 4: Rearrange the formula to solve for \( M_B \)
Rearranging the equation to isolate \( M_B \):
\[ M_B = \frac{K_b \times W_B \times 1000}{\Delta T_b \times W_A} \]

### Step 5: Substitute the known values into the equation
Now we substitute the values we have:
- \( K_b = 2.62 \, \text{°C/m} \)
- \( W_B = 1.5 \, \text{g} \)
- \( \Delta T_b = 0.268 \, \text{°C} \)
- \( W_A = 100 \, \text{g} \)

Substituting these values:
\[ M_B = \frac{2.62 \times 1.5 \times 1000}{0.268 \times 100} \]

### Step 6: Perform the calculations
Calculating the numerator:
\[ 2.62 \times 1.5 \times 1000 = 3930 \]
Calculating the denominator:
\[ 0.268 \times 100 = 26.8 \]
Now, divide the numerator by the denominator:
\[ M_B = \frac{3930}{26.8} \approx 146.6 \, \text{g/mol} \]

### Conclusion
Thus, the molar mass of dichlorobenzene is approximately **146.6 g/mol**.

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