The freezing-point depression for a given aqueous solution is0.32K. The freezing-point depression constant for water is 1.86 K/*m*. Calculate the molality of solutes in the solution.

The equation for freezing point depression is

Δ*Tf* = *Kf* · *m*
 
where Δ*Tf* is the freezing point depression, *Kf* is the freezing-point depression constant, and *m* is the total molality of all solutes in solution.

To calculate the molality of solutes in the solution, we can use the provided freezing point depression equation:

\[
\Delta T_f = K_f \cdot m
\]

Where:
- \(\Delta T_f\) is the freezing point depression,
- \(K_f\) is the freezing-point depression constant,
- \(m\) is the molality of the solution.

Given values:
- \(\Delta T_f = 0.32 \, \text{K}\),
- \(K_f = 1.86 \, \text{K/m}\).

Now, we can rearrange the equation to solve for molality (\(m\)):

\[
m = \frac{\Delta T_f}{K_f}
\]

Substituting the given values:

\[
m = \frac{0.32 \, \text{K}}{1.86 \, \text{K/m}}
\]

Let's calculate the molality: 

\[
m = \frac{0.32}{1.86}
\]The molality of the solutes in the solution is approximately \(0.172 \, \text{mol/kg}\).

Would you like further details or have any questions? Here are some related topics:

1. How does molality differ from molarity?
2. What factors affect freezing-point depression in a solution?
3. Can you explain why freezing-point depression occurs at the molecular level?
4. How would you calculate the mass of a solute needed to achieve a specific molality?
5. How does the presence of multiple solutes affect the freezing point of a solution?

**Tip:** Molality is temperature-independent because it's based on the mass of the solvent, not the volume, which makes it particularly useful in freezing-point depression and boiling-point elevation calculations.

Learn how to calculate the molality of solutes in a solution using freezing point depression. Understand the formula ΔTf = Kf * m and solve a specific problem with ΔTf = 0.32 K and Kf = 1.86 K/m. Detailed step-by-step solution and explanation.

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