What is the van’t Hoff factor for K2SO4 in an aqueous solution that is 5.00% K2SO4 by mass and freezes at -1.21 °C?

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Step 1: Understand the van't Hoff factor (i), which represents the number of particles a compound dissociates into in solution. For K2SO4, it dissociates into 2 K+ ions and 1 SO4^2- ion, so theoretically, i = 3.

Step 2: Use the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the change in freezing point, \( K_f \) is the cryoscopic constant of water (1.86 °C kg/mol), and \( m \) is the molality of the solution.

Step 3: Calculate the change in freezing point: \( \Delta T_f = 0 - (-1.21) = 1.21 \) °C.

Step 4: Determine the molality (m) of the solution. First, calculate the mass of K2SO4 in 100 g of solution (5.00 g), then convert this mass to moles using the molar mass of K2SO4 (174.26 g/mol). Finally, calculate molality by dividing moles of solute by the mass of solvent in kg (95 g of water = 0.095 kg).

Step 5: Rearrange the freezing point depression formula to solve for the van't Hoff factor (i): \( i = \frac{\Delta T_f}{K_f \cdot m} \). Substitute the values for \( \Delta T_f \), \( K_f \), and \( m \) to find the experimental van't Hoff factor.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

van't Hoff Factor (i)

The van't Hoff factor (i) is a measure of the number of particles into which a solute dissociates in solution. For ionic compounds, this factor is crucial for calculating colligative properties, such as freezing point depression and boiling point elevation. For K2SO4, which dissociates into two potassium ions (K+) and one sulfate ion (SO4^2-), the van't Hoff factor is 3.

Freezing Point Depression

Freezing point depression is a colligative property that describes how the freezing point of a solvent decreases when a solute is added. The extent of this depression is directly proportional to the molality of the solution and the van't Hoff factor. The formula ΔTf = i * Kf * m is used, where ΔTf is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution.

Mass Percent Concentration

Mass percent concentration is a way to express the concentration of a solution, defined as the mass of solute divided by the total mass of the solution, multiplied by 100. In this case, a 5.00% K2SO4 solution means that there are 5 grams of K2SO4 in 100 grams of solution. This information is essential for calculating the molality and subsequently the van't Hoff factor in the context of colligative properties.

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