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Chapter 11: Problem 59

The vapor pressure of a solution containing 53.6 \(\mathrm{g}\) glycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\right)\) in 133.7 \(\mathrm{g}\) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is 113 torr at \(40^{\circ} \mathrm{C}\) . Calculate the vapor pressure of pure ethanol at \(40^{\circ} \mathrm{C}\) assuming that glycerin is a nonvolatile, nonelectrolyte solute in ethanol.

Short Answer

Expert verified
The vapor pressure of pure ethanol at \(40^{\circ}C\) is approximately 135.6 torr, calculated using the given vapor pressure of the solution (113 torr) and the mole fraction of ethanol in the solution (0.833) with Raoult's Law.

Step by step solution

01

Calculate the moles of glycerin and ethanol in the solution

First, let's determine the moles of glycerin and ethanol in the solution, using their molecular weights (glycerin: 92 g/mol and ethanol: 46 g/mol). Moles of glycerin = \( \frac{53.6 \text{ g}}{92 \text{ g/mol}} = 0.582 \text{ mol}\) Moles of ethanol = \( \frac{133.7 \text{ g}}{46 \text{ g/mol}} = 2.91 \text{ mol}\) Total moles = 3.492 mol
02

Calculate the mole fraction of ethanol in the solution

Next, we need to calculate the mole fraction of ethanol in the solution. Mole fraction is defined as the ratio of the moles of one component to the total moles of the solution. Mole fraction of ethanol (X_ethanol) = \( \frac{\text{moles of ethanol}}{\text{total moles}} = \frac{2.91 \text{ mol}}{3.492 \text{ mol}} = 0.833\)
03

Determine the relationship between vapor pressures using Raoult's Law

Raoult's Law states that the partial vapor pressure of each component in a solution is equal to the product of its mole fraction and the vapor pressure of the pure component. \( P_{solution} = X_{ethanol}P_{ethanol} \) We have the vapor pressure of the solution (P_solution = 113 torr) and the mole fraction of ethanol (X_ethanol = 0.833). We need to find the vapor pressure of pure ethanol (P_ethanol).
04

Calculate the vapor pressure of pure ethanol

To find the vapor pressure of pure ethanol, rearrange the equation from Step 3 to solve for P_ethanol, and then plug in the values for P_solution and X_ethanol to get the result. \( P_{ethanol} = \frac{P_{solution}}{X_{ethanol}} = \frac{113 \text{ torr}}{0.833} = 135.6 \text{ torr}\) Thus, the vapor pressure of pure ethanol at 40°C is approximately 135.6 torr.

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Most popular questions from this chapter

A 2.00 -g sample of a large biomolecule was dissolved in 15.0 \(\mathrm{g}\) carbon tetrachloride. The boiling point of this solution was determined to be \(77.85^{\circ} \mathrm{C}\) . Calculate the molar mass of the biomolecule. For carbon tetrachloride, the boiling-point constant is $5.03^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol},$ and the boiling point of pure carbon tetrachloride is \(76.50^{\circ} \mathrm{C} .\)

a. Calculate the freezing-point depression and osmotic pressure at $25^{\circ} \mathrm{C}\( of an aqueous solution containing 1.0 \)\mathrm{g} / \mathrm{L}$ of a protein (molar mass \(=9.0 \times 10^{4} \mathrm{g} / \mathrm{mol} )\) if the density of the solution is 1.0 \(\mathrm{g} / \mathrm{cm}^{3}\) b. Considering your answer to part a, which colligative property, freezing- point depression or osmotic pressure, would be better used to determine the molar masses of large molecules? Explain.

Plants that thrive in salt water must have internal solutions (inside the plant cells) that are isotonic with (have the same osmotic pressure as) the surrounding solution. A leaf of a saltwater plant is able to thrive in an aqueous salt solution (at \(25^{\circ} \mathrm{C} )\) that has a freezing point equal to \(-0.621^{\circ} \mathrm{C} .\) You would like to use this information to calculate the osmotic pressure of the solution in the cell. a. In order to use the freezing-point depression to calculate osmotic pressure, what assumption must you make (in addition to ideal behavior of the solutions, which we will assume)? b. Under what conditions is the assumption (in part a) reasonable? c. Solve for the osmotic pressure (at \(25^{\circ} \mathrm{C} )\) of the solution in the plant cell. d. The plant leaf is placed in an aqueous salt solution (at $25^{\circ} \mathrm{C}\( ) that has a boiling point of \)102.0^{\circ} \mathrm{C} .$ What will happen to the plant cells in the leaf?

What mass of sodium oxalate $\left(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\( is needed to prepare 0.250 \)\mathrm{L}\( of a \)0.100-M$ solution?

Explain the terms isotonic solution, crenation, and hemolysis.
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