2.00 g of an unknown compound is mixed to form a homogeneous solution with 75.00 g of benzene. This reduces the freezing point from 5.53 to 4.90 °C. What is the molar mass of the compound? AT;= – Kfx m; Kj= 5.12 for benzene

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**Freezing Point Depression and Molar Mass Calculation**

When 2.00 grams of an unknown compound is mixed with 75.00 grams of benzene, the freezing point of the solution drops from 5.53°C to 4.90°C. To determine the molar mass of the compound, we can use the equation for freezing point depression:

\[
\Delta T_f = -K_f \times m
\]

Where:
- \(\Delta T_f\) is the change in freezing point.
- \(K_f\) is the freezing point depression constant for benzene, given as 5.12°C kg/mol. 
- \(m\) is the molality of the solution.

**Steps to Calculate the Molar Mass:**

1. **Calculate \(\Delta T_f\):**
   \[
   \Delta T_f = 5.53°C - 4.90°C = 0.63°C
   \]

2. **Determine the molality (\(m\)):**
   Use the formula:
   \[
   m = \frac{\Delta T_f}{K_f} = \frac{0.63°C}{5.12°C \, \text{kg/mol}}
   \]

3. **Calculate moles of solute:**
   The molality (\(m\)) is moles of solute per kg of solvent. Use the mass of benzene (75.00 g = 0.075 kg) to find the moles of solute.

4. **Determine the molar mass of the compound:**
   Use the formula:
   \[
   \text{Molar mass} = \frac{\text{mass of solute (in grams)}}{\text{moles of solute}}
   \]

This process will yield the molar mass of the unknown compound.
Transcribed Image Text:**Freezing Point Depression and Molar Mass Calculation** When 2.00 grams of an unknown compound is mixed with 75.00 grams of benzene, the freezing point of the solution drops from 5.53°C to 4.90°C. To determine the molar mass of the compound, we can use the equation for freezing point depression: \[ \Delta T_f = -K_f \times m \] Where: - \(\Delta T_f\) is the change in freezing point. - \(K_f\) is the freezing point depression constant for benzene, given as 5.12°C kg/mol. - \(m\) is the molality of the solution. **Steps to Calculate the Molar Mass:** 1. **Calculate \(\Delta T_f\):** \[ \Delta T_f = 5.53°C - 4.90°C = 0.63°C \] 2. **Determine the molality (\(m\)):** Use the formula: \[ m = \frac{\Delta T_f}{K_f} = \frac{0.63°C}{5.12°C \, \text{kg/mol}} \] 3. **Calculate moles of solute:** The molality (\(m\)) is moles of solute per kg of solvent. Use the mass of benzene (75.00 g = 0.075 kg) to find the moles of solute. 4. **Determine the molar mass of the compound:** Use the formula: \[ \text{Molar mass} = \frac{\text{mass of solute (in grams)}}{\text{moles of solute}} \] This process will yield the molar mass of the unknown compound.
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