A 0.95 m aqueous solution of an ionic compound with the formula MX has a freezing point of -3.0 °C. Calculate the van’t Hoff factor (i) for MX at this concentration.

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insert step 1> Determine the freezing point depression (\( \Delta T_f \)) using the formula \( \Delta T_f = T_f^0 - T_f \), where \( T_f^0 \) is the freezing point of pure water (0 °C) and \( T_f \) is the freezing point of the solution (-3.0 °C).

insert step 2> Use the formula for freezing point depression: \( \Delta T_f = i \cdot K_f \cdot m \), where \( K_f \) is the cryoscopic constant for water (1.86 °C/m) and \( m \) is the molality of the solution (0.95 m).

insert step 3> Rearrange the formula to solve for the van’t Hoff factor \( i \): \( i = \frac{\Delta T_f}{K_f \cdot m} \).

insert step 4> Substitute the known values into the equation: \( i = \frac{3.0}{1.86 \times 0.95} \).

insert step 5> Calculate the value of \( i \) to determine the van’t Hoff factor for the ionic compound MX.

Key Concepts

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

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 number of solute particles in the solution. The formula used to calculate the change in freezing point is ΔTf = i * Kf * m, where ΔTf is the change in freezing point, Kf is the freezing point depression constant, and m is the molality of the solution.

Van't Hoff Factor (i)

The van't Hoff factor (i) represents the number of particles into which a solute dissociates in solution. For ionic compounds, this factor is crucial as it affects colligative properties like freezing point depression and boiling point elevation. For example, if an ionic compound MX dissociates into M⁺ and X⁻, the van't Hoff factor would be 2, indicating that two particles are produced per formula unit of the solute.

Molality (m)

Molality (m) is a measure of concentration defined as the number of moles of solute per kilogram of solvent. It is particularly useful in colligative property calculations because it remains unaffected by temperature changes, unlike molarity. In the context of freezing point depression, knowing the molality of the solution allows for accurate calculations of how much the freezing point will decrease based on the number of solute particles present.

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