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Ch.13 - Properties of Solutions
All textbooksBrown 14th EditionCh.13 - Properties of SolutionsProblem 103
Chapter 13, Problem 103

Calculate the freezing point of a 0.100 m aqueous solution of K2SO4, (a) ignoring interionic attractions, and (b) taking interionic attractions into consideration by using the van’t Hoff factor (Table 13.4).

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Step 1: Identify the formula for freezing point depression, which is \( \Delta T_f = i \cdot K_f \cdot m \), where \( \Delta T_f \) is the freezing point depression, \( i \) is the van’t Hoff factor, \( K_f \) is the cryoscopic constant of the solvent (water in this case), and \( m \) is the molality of the solution.
Step 2: For part (a), calculate the freezing point depression ignoring interionic attractions. Assume \( i = 1 \) since interionic attractions are ignored. Use the given molality \( m = 0.100 \) m and the known \( K_f \) for water, which is approximately 1.86 °C/m.
Step 3: Calculate the freezing point depression \( \Delta T_f \) using the formula from Step 1 with \( i = 1 \). Substitute the values into the equation: \( \Delta T_f = 1 \cdot 1.86 \cdot 0.100 \).
Step 4: For part (b), consider interionic attractions by using the van’t Hoff factor for \( K_2SO_4 \). When \( K_2SO_4 \) dissociates in water, it forms 2 \( K^+ \) ions and 1 \( SO_4^{2-} \) ion, so \( i \) is approximately 3.
Step 5: Calculate the freezing point depression \( \Delta T_f \) using the formula from Step 1 with \( i = 3 \). Substitute the values into the equation: \( \Delta T_f = 3 \cdot 1.86 \cdot 0.100 \).
Related Practice
Textbook Question

Two beakers are placed in a sealed box at 25 °C. One beaker contains 30.0 mL of a 0.050 M aqueous solution of a nonvolatile nonelectrolyte. The other beaker contains 30.0 mL of a 0.035 M aqueous solution of NaCl. The water vapor from the two solutions reaches equilibrium. (a) In which beaker does the solution level rise, and in which one does it fall?

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Textbook Question

Two beakers are placed in a sealed box at 25 °C. One beaker contains 30.0 mL of a 0.050 M aqueous solution of a nonvolatile nonelectrolyte. The other beaker contains 30.0 mL of a 0.035 M aqueous solution of NaCl. The water vapor from the two solutions reaches equilibrium. (b) What are the volumes in the two beakers when equilibrium is attained, assuming ideal behavior?

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Open Question
The normal boiling point of ethanol, CH3CH2OH, is 78.4 °C. When 9.15 g of a soluble nonelectrolyte is dissolved in 100.0 g of ethanol at that temperature, the vapor pressure of the solution is 7.40 x 10^2 torr. What is the molar mass of the solute?
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?

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Open Question
A lithium salt used in lubricating grease has the formula LiC nH2n + 1O2. The salt is soluble in water to the extent of 0.036 g per 100 g of water at 25 °C. The osmotic pressure of this solution is found to be 57.1 torr. Assuming that molality and molarity in such a dilute solution are the same and that the lithium salt is completely dissociated in the solution, determine an appropriate value of n in the formula for the salt.
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.

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