In the lab, a student needs to determine the van't Hoff factor for a deicer in water. Using the same deicer, he prepares six solutions at different concentrations. The freezing point depression constant for water is 1.86 K/m.

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**Freezing Point Depression versus Molality**

**Graph and Equation Analysis**

The above image depicts a graph titled "Freezing point depression versus molality." The graph is a linear plot that shows the relationship between the freezing point depression (ΔTf) of a solution and its molality (m). 

- **X-axis (horizontal):** It represents the molality (m) of the solution, ranging from 0 to 5.
- **Y-axis (vertical):** It indicates the freezing point depression (in Kelvin, K), ranging from 0 to 30.

The data points on the graph form a linear pattern, indicating a direct proportionality between the freezing point depression and the molality. The equation of the line, given as y = 6x, represents this relationship where:

- **y:** Freezing point depression (ΔTf)
- **x:** Molality (m)
- **Slope:** 6, meaning for each unit increase in molality, the freezing point depression increases by 6 K.

**Lab Exercise**

In this scenario, a student is required to determine the van't Hoff factor (i) for a deicer dissolved in water. To achieve this, the student prepares six solutions with different molalities.

- **Freezing point depression constant for water (Kf):** 1.86 K·m^-1

**Task:**
Calculate the van’t Hoff factor (i) using the provided data and the freezing point depression equation.

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

Given that the slope of the line (represented by 6 in the equation y = 6x) is equal to the product \( i \cdot K_f \), solve for \( i \):

\[ 6 = i \cdot 1.86 \]
\[ i = \frac{6}{1.86} \]

**Determine the van't Hoff factor (i):**

\[ i = \boxed{\_\_\_\_} \]
Transcribed Image Text:**Freezing Point Depression versus Molality** **Graph and Equation Analysis** The above image depicts a graph titled "Freezing point depression versus molality." The graph is a linear plot that shows the relationship between the freezing point depression (ΔTf) of a solution and its molality (m). - **X-axis (horizontal):** It represents the molality (m) of the solution, ranging from 0 to 5. - **Y-axis (vertical):** It indicates the freezing point depression (in Kelvin, K), ranging from 0 to 30. The data points on the graph form a linear pattern, indicating a direct proportionality between the freezing point depression and the molality. The equation of the line, given as y = 6x, represents this relationship where: - **y:** Freezing point depression (ΔTf) - **x:** Molality (m) - **Slope:** 6, meaning for each unit increase in molality, the freezing point depression increases by 6 K. **Lab Exercise** In this scenario, a student is required to determine the van't Hoff factor (i) for a deicer dissolved in water. To achieve this, the student prepares six solutions with different molalities. - **Freezing point depression constant for water (Kf):** 1.86 K·m^-1 **Task:** Calculate the van’t Hoff factor (i) using the provided data and the freezing point depression equation. \[ \Delta T_f = i \cdot K_f \cdot m \] Given that the slope of the line (represented by 6 in the equation y = 6x) is equal to the product \( i \cdot K_f \), solve for \( i \): \[ 6 = i \cdot 1.86 \] \[ i = \frac{6}{1.86} \] **Determine the van't Hoff factor (i):** \[ i = \boxed{\_\_\_\_} \]
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