The freezing point of water is 0.00 °C at 1 atmosphere.

A student dissolves 14.38 grams of chromium(II) iodide,  (305.8 g/mol), in 264.4 grams of water

The freezing point of a solution can be determined using **freezing point depression**, a colligative property that depends on the number of solute particles in a solution. The formula for freezing point depression is:

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

Where:
- \(\Delta T_f\) is the freezing point depression (how much the freezing point is lowered).
- \(i\) is the van't Hoff factor (the number of particles the solute dissociates into).
- \(K_f\) is the cryoscopic constant of the solvent (for water, \(K_f = 1.86 \,^\circ\text{C}/\text{m}\)).
- \(m\) is the molality of the solution (moles of solute per kilogram of solvent).

### Step 1: Calculate molality (m)
First, calculate the number of moles of chromium(II) iodide (CrI₂).

\[
\text{Moles of CrI}_2 = \frac{\text{mass of CrI}_2}{\text{molar mass of CrI}_2} = \frac{14.38 \, \text{g}}{305.8 \, \text{g/mol}} \approx 0.047 \, \text{mol}
\]

Now, calculate the molality (\(m\)) of the solution:

\[
m = \frac{\text{moles of CrI}_2}{\text{mass of solvent in kg}} = \frac{0.047 \, \text{mol}}{0.2644 \, \text{kg}} \approx 0.178 \, \text{mol/kg}
\]

### Step 2: Determine van't Hoff factor (i)
Chromium(II) iodide (CrI₂) dissociates into 3 ions (1 Cr²⁺ ion and 2 I⁻ ions):

\[
i = 3
\]

### Step 3: Calculate freezing point depression (\(\Delta T_f\))

\[
\Delta T_f = i \cdot K_f \cdot m = 3 \cdot 1.86 \,^\circ\text{C}/\text{m} \cdot 0.178 \, \text{mol/kg} \approx 0.995 \,^\circ\text{C}
\]

### Step 4: Find the new freezing point
The freezing point of water is 0.00 °C, so the freezing point of the solution is:

\[
\text{Freezing point} = 0.00 \,^\circ\text{C} - \Delta T_f = 0.00 \,^\circ\text{C} - 0.995 \,^\circ\text{C} \approx -0.995 \,^\circ\text{C}
\]

### Final Answer:
The freezing point of the solution is approximately **-0.995°C**.

---

Would you like further details or have any questions? Here are 5 related questions to consider:

1. How would the freezing point change if more solute is added?
2. What is the significance of the van't Hoff factor in freezing point depression?
3. How does freezing point depression differ for ionic vs. non-ionic compounds?
4. What would happen to the freezing point if the solvent was something other than water?
5. How is freezing point depression applied in real-world scenarios, such as road deicing?

**Tip:** Freezing point depression is proportional to the number of dissolved particles, so ionic compounds tend to have a larger effect than non-electrolytes.

A student dissolves 14.38 grams of chromium(II) iodide, (305.8 g/mol), in 264.4 grams of water. What is the freezing point of the solution?

Learn how to calculate the freezing point depression for a solution of chromium(II) iodide (CrI₂) in water. This detailed guide walks through key concepts like molality, the van't Hoff factor, and colligative properties, perfect for high school chemistry students.

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