Ch.13 - Properties of Solutions

Problem 104b

Chapter 13, Problem 104b

Carbon disulfide (CS₂) boils at 46.30 °C and has a density of 1.261 g/mL. (b) When 5.39 g of a nondissociating unknown is dissolved in 50.0 mL of CS₂, the solution boils at 47.08 °C. What is the molar mass of the unknown?

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First, identify the boiling point elevation formula: ΔT_b = i * K_b * m, where ΔT_b is the boiling point elevation, i is the van't Hoff factor (which is 1 for a nondissociating solute), K_b is the ebullioscopic constant of the solvent, and m is the molality of the solution.

Calculate the boiling point elevation (ΔT_b) by subtracting the boiling point of pure CS2 from the boiling point of the solution: ΔT_b = 47.08 °C - 46.30 °C.

Determine the molality (m) of the solution using the formula: m = moles of solute / kg of solvent. First, convert the volume of CS2 to mass using its density: mass of CS2 = 50.0 mL * 1.261 g/mL.

Rearrange the boiling point elevation formula to solve for the molality: m = ΔT_b / (i * K_b). Use the calculated ΔT_b and the known K_b for CS2 to find the molality.

Finally, calculate the molar mass of the unknown solute using the formula: molar mass = mass of solute / moles of solute. Use the mass of the solute (5.39 g) and the moles of solute obtained from the molality calculation.

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Key Concepts

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

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. This phenomenon occurs because the presence of solute particles disrupts the formation of vapor above the liquid, requiring a higher temperature to reach the boiling point. 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.

Molality

Molality (m) is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. It is particularly useful in colligative property calculations because it is independent of temperature and volume changes. To calculate molality, one must first determine the number of moles of the solute and the mass of the solvent in kilograms, which allows for accurate determination of the solution's properties.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of an unknown solute, one can use the relationship between the mass of the solute, the change in boiling point, and the molality of the solution. By rearranging the boiling point elevation formula and substituting known values, one can solve for the molar mass, which is essential for identifying the unknown substance.

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Molar Mass Calculation Example

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Textbook Question

Carbon disulfide (CS₂) boils at 46.30 °C and has a density of 1.261 g/mL. (a) When 0.250 mol of a nondissociating solute is dissolved in 400.0 mL of CS₂, the solution boils at 47.46 °C. What is the molal boiling-point-elevation constant for CS₂?

Textbook Question

Fluorocarbons (compounds that contain both carbon and fluorine) were, until recently, used as refrigerants. The compounds listed in the following table are all gases at 25 °C, and their solubilities in water at 25 °C and 1 atm fluorocarbon pressure are given as mass percentages. (a) For each fluorocarbon, calculate the molality of a saturated solution.

Textbook Question

Fluorocarbons (compounds that contain both carbon and fluorine) were, until recently, used as refrigerants. The compounds listed in the following table are all gases at 25 °C, and their solubilities in water at 25 °C and 1 atm fluorocarbon pressure are given as mass percentages. (b) Which molecular property best predicts the solubility of these gases in water: molar mass, dipole moment, or ability to hydrogen-bond to water?

Fluorocarbon Solubility (mass %)

CF₄ 0.0015

CClF₃ 0.009

CCl₂F₂ 0.028

CHClF₂ 0.30

Carbon disulfide (CS2) boils at 46.30 °C and has a density of 1.261 g/mL. (b) When 5.39 g of a nondissociating unknown is dissolved in 50.0 mL of CS2, the solution boils at 47.08 °C. What is the molar mass of the unknown?

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Key Concepts

Boiling Point Elevation

Molality

Molar Mass Calculation

Carbon disulfide (CS₂) boils at 46.30 °C and has a density of 1.261 g/mL. (b) When 5.39 g of a nondissociating unknown is dissolved in 50.0 mL of CS₂, the solution boils at 47.08 °C. What is the molar mass of the unknown?