Bromoform has a normal has freezing point of `7.734^(@)C` and `K_(f)=14.4^(@)C// m`.a solution of 2.60 g of an unknown substance in 100 g of freezes at `5.43^(@)C`. What is the molecules mass of the unkniwn substance ?

Options

A. 16.25
B. 162.5
C. 100
D. none of these

Answer

To find the molecular mass of the unknown substance dissolved in bromoform, we can follow these steps:

### Step 1: Determine the Depression in Freezing Point (ΔTf)
The depression in freezing point can be calculated using the formula:
\[ \Delta T_f = T_f^0 - T_f \]
Where:
- \(T_f^0\) is the normal freezing point of bromoform (7.734 °C).
- \(T_f\) is the freezing point of the solution (5.43 °C).

Calculating:
\[ \Delta T_f = 7.734 °C - 5.43 °C = 2.304 °C \]

### Step 2: Use the Freezing Point Depression Formula
The relationship between the depression in freezing point and the molality of the solution is given by:
\[ \Delta T_f = K_f \cdot m \]
Where:
- \(K_f\) is the freezing point depression constant (14.4 °C/m).
- \(m\) is the molality of the solution.

Rearranging the formula to find molality:
\[ m = \frac{\Delta T_f}{K_f} \]

Substituting the values:
\[ m = \frac{2.304 °C}{14.4 °C/m} = 0.1592 \, \text{mol/kg} \]

### Step 3: Calculate the Number of Moles of Solute
Molality (m) is defined as the number of moles of solute per kilogram of solvent:
\[ m = \frac{n}{W_{solvent}} \quad \text{(where \(W_{solvent}\) is in kg)} \]
Given that we have 100 g of bromoform, we convert this to kilograms:
\[ W_{solvent} = 100 \, \text{g} = 0.1 \, \text{kg} \]

Now we can find the number of moles of the unknown substance (n):
\[ n = m \cdot W_{solvent} = 0.1592 \, \text{mol/kg} \cdot 0.1 \, \text{kg} = 0.01592 \, \text{mol} \]

### Step 4: Calculate the Molecular Mass of the Unknown Substance
The molecular mass (M) can be calculated using the formula:
\[ M = \frac{W_{solute}}{n} \]
Where:
- \(W_{solute}\) is the mass of the unknown substance (2.60 g).

Substituting the values:
\[ M = \frac{2.60 \, \text{g}}{0.01592 \, \text{mol}} \approx 163.1 \, \text{g/mol} \]

### Conclusion
The molecular mass of the unknown substance is approximately **163.1 g/mol**.

---