A 1.2 m aqueous solution of an ionic compound with the formula MX 2 has a boiling point of 101.4 °C. Calculate the van't Hoff factor (i) for MX 2 at this concentration.

Hi everyone here we have a question telling us that the boiling point of a 2.4 morality solution of an ionic compound MX three is 103.9°C. And our question is, what is the van Hoff factor I for M X three? So we know that the change in the boiling point equals the boiling point of our solution minus the boiling point of our solvent. The change in boiling point equals the van Hoff factor times the boiling point constant times the morality. So the change in boiling point Equals 103 .9° C -100°C, Which equals 3.9 degrees Celsius. Our boiling point constant equals 0.512 degrees Celsius per morality. So R. I equals R. Change in boiling point divided by our Van Hoff factor times our boiling point constant times our morality, So I equals 3.9°C divided by 0. degrees Celsius per morality Times 2.4 Morality, Which equals 3.2. And that is our final answer. Thank you for watching. Bye.

Ch.14 - Solutions

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Tro 6th Edition

Ch.14 - Solutions

Problem 99

Chapter 14, Problem 99

A 1.2 m aqueous solution of an ionic compound with the formula MX₂ has a boiling point of 101.4 °C. Calculate the van't Hoff factor (i) for MX₂ at this concentration.

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insert step 1> Determine the boiling point elevation (ΔT_b) using the formula: ΔT_b = T_b(solution) - T_b(pure solvent). Here, T_b(solution) is 101.4 °C and T_b(pure solvent) for water is 100.0 °C.

insert step 2> Use the boiling point elevation formula: ΔT_b = i * K_b * m, where i is the van't Hoff factor, K_b is the ebullioscopic constant for water (0.512 °C kg/mol), and m is the molality of the solution (1.2 m).

insert step 3> Rearrange the formula to solve for the van't Hoff factor (i): i = ΔT_b / (K_b * m).

insert step 4> Substitute the known values into the equation: i = (101.4 °C - 100.0 °C) / (0.512 °C kg/mol * 1.2 m).

insert step 5> Calculate the value of i to determine the van't Hoff factor for the ionic compound MX2.

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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. In this context, the boiling point elevation of the solution is used to determine the van't Hoff factor.

Boiling Point Elevation

Boiling point elevation is a colligative property that describes how the boiling point of a solvent increases when a solute is dissolved in it. The change in boiling point can be calculated using the formula ΔT_b = i * K_b * m, where ΔT_b is the boiling point elevation, i is the van't Hoff factor, K_b is the ebullioscopic constant of the solvent, and m is the molality of the solution. This concept is crucial for solving the given problem.

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 typically greater than one, as they dissociate into multiple ions. For the compound MX2, which dissociates into one M ion and two X ions, the expected van't Hoff factor would be 3. Calculating i involves using the observed boiling point elevation to find the effective number of particles in solution.