When 9.12 g of HCl was dissolved in 190 g of water, the freezing point of the solution was - 4.65 °C. What is the value of the van't Hoff factor for HCl?

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Identify the formula for freezing point depression: \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the change in freezing point, \( i \) is the van't Hoff factor, \( K_f \) is the cryoscopic constant of the solvent, and \( m \) is the molality of the solution.

Calculate the change in freezing point \( \Delta T_f \) by subtracting the freezing point of pure water (0 °C) from the freezing point of the solution (-4.65 °C).

Determine the molality \( m \) of the solution by dividing the moles of solute (HCl) by the mass of the solvent (water) in kilograms. First, calculate the moles of HCl using its molar mass.

Use the known value of the cryoscopic constant \( K_f \) for water, which is 1.86 °C kg/mol.

Rearrange the freezing point depression formula to solve for the van't Hoff factor \( i \): \( i = \frac{\Delta T_f}{K_f \cdot m} \).

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Key Concepts

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

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 calculating changes in freezing point when a solute is added to a solvent.

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 can be calculated using the formula ΔTf = i * Kf * m, where ΔTf is the change in freezing point, i is the van't Hoff factor, Kf is the freezing point depression constant of the solvent, and m is the molality of the solution. This concept is crucial for determining the van't Hoff factor in the given problem.

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 non-electrolytes, i is typically 1, while for electrolytes, it corresponds to the number of ions produced. In the case of HCl, which dissociates into H⁺ and Cl⁻ ions, the van't Hoff factor is 2. This factor is vital for accurately calculating colligative properties like freezing point depression.