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Chapter 10: Problem 25

Which of the following statements is(are) true? Correct the false statements. a. The vapor pressure of a solution is directly related to the mole fraction of solute. b. When a solute is added to water, the water in solution has a lower vapor pressure than that of pure ice at \(0^{\circ} \mathrm{C}\). c. Colligative properties depend only on the identity of the solute and not on the number of solute particles present. d. When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} \mathrm{C}\) because sugar has a higher boiling point than water.

Short Answer

Expert verified
a. False - The vapor pressure of a solution is directly related to the mole fraction of the solvent. b. True c. False - Colligative properties depend only on the number of solute particles present, not on the identity of the solute. d. True (with incorrect reasoning) - When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} C\) because of the boiling point elevation effect, a colligative property.

Step by step solution

01

Statement a

: a. The vapor pressure of a solution is directly related to the mole fraction of solute. This statement is false. The vapor pressure of a solution is directly related to the mole fraction of the solvent, not the solute. This relationship is described by Raoult's Law presented as: \(P_{solution} = x_{solvent} \cdot P_{solvent}^\circ\) Here, \(P_{solution}\) is the vapor pressure of the solution, \(x_{solvent}\) is the mole fraction of the solvent, and \(P_{solvent}^\circ\) is the vapor pressure of the pure solvent. Corrected Statement: The vapor pressure of a solution is directly related to the mole fraction of the solvent.
02

Statement b

: b. When a solute is added to water, the water in solution has a lower vapor pressure than that of pure ice at \(0^{\circ} C\). This statement is true. When a non-volatile solute is added to water, the vapor pressure of water in the solution decreases. It happens because the solute molecules occupy the surface of the solution, reducing the number of water molecules that can escape to the vapor phase.
03

Statement c

: c. Colligative properties depend only on the identity of the solute and not on the number of solute particles present. This statement is false. Colligative properties depend on the number of solute particles present in a solution, not on their identity. Examples of colligative properties include freezing point depression, boiling point elevation, osmotic pressure, and vapor pressure lowering. Corrected Statement: Colligative properties depend only on the number of solute particles present, not on the identity of the solute.
04

Statement d

: d. When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} C\) because sugar has a higher boiling point than water. This statement is true, but the reasoning is incorrect. When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} C\), but the reason is related to boiling point elevation, a colligative property. This increase in boiling point is proportional to the molality of the solute and does not depend on the boiling point of sugar. Corrected Statement: When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} C\) because of the boiling point elevation effect, a colligative property.

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Most popular questions from this chapter

Use the following data for three aqueous solutions of \(\mathrm{CaCl}_{2}\) to calculate the apparent value of the van't Hoff factor. $$\begin{array}{lc} \text { Molality } & \text { Freezing-Point Depression }\left(^{\circ} \mathrm{C}\right) \\ \hline 0.0225 & 0.110 \\ 0.0910 & 0.440 \\ 0.278 & 1.330 \end{array}$$

Pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}\right)\) and hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\) form an ideal solution. At \(25^{\circ} \mathrm{C}\) the vapor pressures of pentane and hexane are 511 and \(150 .\) torr, respectively. A solution is prepared by mixing \(25 \mathrm{mL} \text { pentane (density, } 0.63 \mathrm{g} / \mathrm{mL})\) with \(45 \mathrm{mL}\) hexane (density, 0.66 g/mL). a. What is the vapor pressure of the resulting solution? b. What is the composition by mole fraction of pentane in the vapor that is in equilibrium with this solution?

An aqueous solution containing 0.250 mole of Q, a strong electrolyte, in \(5.00 \times 10^{2} \mathrm{g}\) water freezes at \(-2.79^{\circ} \mathrm{C}\). What is the van't Hoff factor for Q? The molal freezing-point depression constant for water is \(1.86^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol} .\) What is the formula of \(\mathrm{Q}\) if it is \(38.68 \%\) chlorine by mass and there are twice as many anions as cations in one formula unit of Q?

An aqueous antifreeze solution is \(40.0 \%\) ethylene glycol \(\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{2}\right)\) by mass. The density of the solution is \(1.05 \mathrm{g} / \mathrm{cm}^{3}\) Calculate the molality, molarity, and mole fraction of the ethylene glycol.

Patients undergoing an upper gastrointestinal tract laboratory test are typically given an X-ray contrast agent that aids with the radiologic imaging of the anatomy. One such contrast agent is sodium diatrizoate, a nonvolatile water-soluble compound. A \(0.378-m\) solution is prepared by dissolving 38.4 g sodium diatrizoate (NaDTZ) in \(1.60 \times 10^{2} \mathrm{mL}\) water at \(31.2^{\circ} \mathrm{C}\) (the density of water at \(31.2^{\circ} \mathrm{C}\) is \(0.995 \mathrm{g} / \mathrm{cm}^{3}\) ). What is the molar mass of sodium diatrizoate? What is the vapor pressure of this solution if the vapor pressure of pure water at \(31.2^{\circ} \mathrm{C}\) is 34.1 torr?
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