Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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**Title: Determining the Freezing Point Depression of a Solution**

**Introduction:**
The freezing point of pure benzene, \( \text{C}_6\text{H}_6 \), is \( 5.50 \, ^\circ\text{C} \) at 1 atmosphere. When a nonvolatile, nonelectrolyte solute such as DDT (dichlorodiphenyltrichloroethane) dissolves in benzene, it causes the freezing point of the solution to lower. The task is to determine the molality and new freezing point of a benzene solution with DDT.

**Problem Statement:**
A student dissolves 11.78 grams of DDT (\( \text{C}_{14}\text{H}_9\text{Cl}_5 \); molar mass = 354.5 g/mol) in 252.1 grams of benzene. Using the provided table of boiling and freezing point constants, calculate:

1. The molality of the solution.
2. The freezing point of the solution.

**Data:**

| Solvent       | Formula           | \( K_b \, (^\circ\text{C/m}) \) | \( K_f \, (^\circ\text{C/m}) \) |
|---------------|-------------------|-------------------------------|-------------------------------|
| Water         | \( \text{H}_2\text{O} \)    | 0.512                         | 1.86                          |
| Ethanol       | \( \text{CH}_3\text{CH}_2\text{OH} \) | 1.22                          | 1.99                          |
| Chloroform    | \( \text{CHCl}_3 \)        | 3.67                          | 3.62                          |
| Benzene       | \( \text{C}_6\text{H}_6 \)        | 2.53                          | 5.12                          |
| Diethyl ether | \( \text{CH}_3\text{CH}_2\text{OCH}_2\text{CH}_3 \) | 2.02                          | —                             |

**Instructions:**

1. **Calculate the Molality (\( m \)) of the Solution:**
   - Use the formula:
     \[
     \text{molality} \, (
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Transcribed Image Text:**Title: Determining the Freezing Point Depression of a Solution** **Introduction:** The freezing point of pure benzene, \( \text{C}_6\text{H}_6 \), is \( 5.50 \, ^\circ\text{C} \) at 1 atmosphere. When a nonvolatile, nonelectrolyte solute such as DDT (dichlorodiphenyltrichloroethane) dissolves in benzene, it causes the freezing point of the solution to lower. The task is to determine the molality and new freezing point of a benzene solution with DDT. **Problem Statement:** A student dissolves 11.78 grams of DDT (\( \text{C}_{14}\text{H}_9\text{Cl}_5 \); molar mass = 354.5 g/mol) in 252.1 grams of benzene. Using the provided table of boiling and freezing point constants, calculate: 1. The molality of the solution. 2. The freezing point of the solution. **Data:** | Solvent | Formula | \( K_b \, (^\circ\text{C/m}) \) | \( K_f \, (^\circ\text{C/m}) \) | |---------------|-------------------|-------------------------------|-------------------------------| | Water | \( \text{H}_2\text{O} \) | 0.512 | 1.86 | | Ethanol | \( \text{CH}_3\text{CH}_2\text{OH} \) | 1.22 | 1.99 | | Chloroform | \( \text{CHCl}_3 \) | 3.67 | 3.62 | | Benzene | \( \text{C}_6\text{H}_6 \) | 2.53 | 5.12 | | Diethyl ether | \( \text{CH}_3\text{CH}_2\text{OCH}_2\text{CH}_3 \) | 2.02 | — | **Instructions:** 1. **Calculate the Molality (\( m \)) of the Solution:** - Use the formula: \[ \text{molality} \, (
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