A 1.0 m solution of K2SO4 in water has a freezing point of -4.3 °C. What is the value of the van’t Hoff factor i for K2SO4?

Verified step by step guidance

1. Step 1: Understand the concept of 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, theoretically giving i = 3.
2. 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.
3. Step 3: Calculate the change in freezing point \( \Delta T_f \) by subtracting the observed freezing point from the normal freezing point of water (0 °C).
4. Step 4: Rearrange the freezing point depression formula to solve for the van’t Hoff factor \( i \): \( i = \frac{\Delta T_f}{K_f \cdot m} \).
5. Step 5: Substitute the known values into the rearranged formula to calculate the van’t Hoff factor \( i \).

Key Concepts

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. Understanding colligative properties is essential for determining how solute concentration affects the physical state of a solution.

Freezing Point Depression

Freezing point depression is a colligative property that describes the decrease in the freezing point of a solvent when a solute is added. The extent of freezing point depression is directly proportional to the molality of the solution and the van’t Hoff factor (i), which accounts for the number of particles the solute dissociates into. This concept is crucial for calculating the freezing point of solutions.

van’t Hoff Factor (i)

The van’t Hoff factor (i) is a dimensionless number that represents the number of particles into which a solute dissociates in solution. For ionic compounds like K2SO4, which dissociates into multiple ions (2 K+ and 1 SO4^2-), the van’t Hoff factor is greater than 1. Calculating i is vital for accurately applying colligative property equations, such as those used to determine freezing point depression.