Question

Challenge A 0.045 \(\mathrm{m}\) solution (consisting of a nonvolatile, nonelectrolyte solute) is experimentally found to have a freezing point depression of \(0.08^{\circ} \mathrm{C}\) What is the freezing point depression constant \(\left(K_{f}\right) .\) Which is most likely to be the solvent: water, ethanol, or chloroform?

Short answer

The freezing point depression constant (Kf) can be calculated using the formula Kf = ΔTf / molality, where ΔTf is the freezing point depression and molality is the molality of the solution. Using the given values, Kf ≈ 1.78 \( \frac{^{\circ}C}{m} \). Comparing this to the known Kf values for water, ethanol, and chloroform, we find that the most likely solvent is water as the calculated Kf value is closest to the Kf value for water (1.86 \( \frac{^{\circ}C}{m} \)).

Step-by-step solution

Identify given values

The given values are: 1. molality of the solution: 0.045 m 2. freezing point depression: 0.08 °C 3. nature of solute: nonelectrolyte and nonvolatile

Calculate Kf

Using the formula, we can calculate the freezing point depression constant (Kf): Kf = ΔTf / molality Kf = \( \frac{0.08 \, ^{\circ}C}{0.045 \, m} \) Kf ≈ 1.78 \( \frac{^{\circ}C}{m} \) Step 2: Identify the most likely solvent

Compare Kf values

Now we'll compare the calculated Kf value to the known Kf values for water, ethanol, and chloroform. Kf values of the solvents: 1. Water: 1.86 \( \frac{^{\circ}C}{m} \) 2. Ethanol: 2.00 \( \frac{^{\circ}C}{m} \) 3. Chloroform: 4.68 \( \frac{^{\circ}C}{m} \) Our calculated Kf value is 1.78 \( \frac{^{\circ}C}{m} \)

Determine the most likely solvent

Based on the comparison, the Kf value of 1.78 \( \frac{^{\circ}C}{m} \) is closest to the Kf value for water (1.86 \( \frac{^{\circ}C}{m} \)). So, the most likely solvent is water.

Key concepts

Molality

Molality is a concentration term that is crucial when dealing with solutions. It measures the number of moles of solute per kilogram of solvent. Different from molarity, which depends on the total volume of the solution, molality is only concerned with the mass of the solvent.

Using molality is highly beneficial in scenarios involving temperature changes, such as freezing point depression, because it does not vary with temperature like volume-based concentrations can. It's represented by a lowercase "m" after the numeric concentration (e.g., 0.045 m).

Understanding the concept of molality is key when working with freezing point depression, because it directly affects how much the freezing point of a solution lowers with the addition of a solute.

Nonelectrolyte Solute

A nonelectrolyte solute is a substance that, when dissolved in a solvent, does not dissociate into ions. This means it does not conduct electricity. In the context of freezing point depression, it's important because nonelectrolytes exhibit predictable behavior according to colligative properties.

Colligative properties are characteristics that depend on the number of solute particles but not their identity. Therefore, when you're dealing with nonelectrolyte solutions, calculations for freezing point depression become straightforward, as the ions or particles in solution are of no consequence in affecting these properties beyond their quantity.

In this exercise, understanding that the solute doesn't dissociate was crucial in calculating an accurate molality and subsequently an accurate freezing point depression constant, since the number of particles directly affects the degree of freezing point depression.

Kf Values

The "Kf" value, or the freezing point depression constant, is a specific property of solvents. It indicates how much the presence of a solute will lower the freezing point of the solvent. Thus, it's vital for determining which solvent you're dealing with when faced with a freezing point depression problem.

Each solvent has a unique Kf value, which combines with the molality of a solution to quantify the freezing point depression using the formula:

• \[ K_f = \frac{\Delta T_f}{\text{molality}} \]

This formula is used to solve the given exercise, where calculating the Kf allows us to identify the solvent. Comparing our calculated value with known Kf values for water, ethanol, and chloroform, we can determine that water is the likely solvent because its Kf is closest to our calculated Kf.