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Ch.13 - Properties of Solutions
All textbooksBrown 14th EditionCh.13 - Properties of SolutionsProblem 102
Chapter 13, Problem 102

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?

Verified step by step guidance
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Step 1: Use Raoult's Law to determine the vapor pressure of pure ethanol. Raoult's Law states that the vapor pressure of the solution (P_solution) is equal to the mole fraction of the solvent (X_solvent) times the vapor pressure of the pure solvent (P_pure). Rearrange the equation to solve for P_pure: P_pure = P_solution / X_solvent.
Step 2: Calculate the mole fraction of ethanol in the solution. The mole fraction (X_solvent) is the ratio of the moles of ethanol to the total moles of the solution. First, calculate the moles of ethanol using its molar mass (46.07 g/mol).
Step 3: Calculate the moles of the solute. Use the given mass of the solute (9.15 g) and its unknown molar mass (M) to express the moles of solute as 9.15 g / M.
Step 4: Set up the equation for the mole fraction of ethanol: X_solvent = moles of ethanol / (moles of ethanol + moles of solute). Substitute the expressions for moles of ethanol and moles of solute into this equation.
Step 5: Solve the equation for the molar mass (M) of the solute. Use the known values for the vapor pressure of the solution and the calculated mole fraction to find the molar mass.
Related Practice
Textbook Question
A 'canned heat' product used to warm buffet dishes consists of a homogeneous mixture of ethanol 1C2H5OH2 and paraffin, which has an average formula of C24H50. What mass of C2H5OH should be added to 620 kg of the paraffin to produce 8 torr of ethanol vapor pressure at 35 °C? The vapor pressure of pure ethanol at 35 °C is 100 torr.
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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. (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
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).
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.