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Lowering of vapour pressure, \(\Delta \mathrm{p}\); elevation in boiling point \(\Delta \mathrm{T}_{\mathrm{b}}\); and depression freezing point \(\Delta \mathrm{T}_{\mathrm{f}}\) of a solvent for the same molar concentration of each of the three solutes: (A) sugar, (B) \(\mathrm{NaCl}\) and \((\mathrm{C})\) \(\mathrm{BaCl}_{2}\) following the sequence (a) \(\Delta \mathrm{T}_{\mathrm{b}}: \mathrm{C}>\mathrm{B}>\mathrm{A}\) (b) \(\Delta \mathrm{T}_{\mathrm{f}}: \mathrm{A}<\mathrm{B}<\mathrm{C}\) (c) \(\Delta p: A

Short Answer

Expert verified
Option (d) "All the above" is correct as all given sequences are satisfied.

Step by step solution

01

Understanding the Effect of Solutes

When a non-volatile solute is added to a solvent, it causes a lowering of vapor pressure (9p), elevation in boiling point (9T_b), and depression in freezing point (9T_f). These colligative properties depend on the number of particles of solute present in the solution.
02

Analyzing the Solutes

Solute A (sugar) does not dissociate in a solution, thus gives 1 particle per molecule. Solute B (NaCl) dissociates into 2 ions (Na^+ and Cl^-), and solute C (BaCl_2) dissociates into 3 ions (Ba^{2+} and 2 Cl^-). The number of particles determines the magnitude of the colligative properties' effect.
03

Applying the Colligative Property Effects

For colligative properties, the impact on 9T_b, 9T_f, and 9p is proportional to the number of solute particles. Hence for elevation of boiling point and depression of freezing point, the order of effect will be: C (3 particles) > B (2 particles) > A (1 particle).
04

Evaluating the Given Options

From our analysis: - 9T_b: C > B > A corresponds to sequence (a). - 9T_f: A < B < C also corresponds to (b) as the effect is greater with more particles. - 9p: A < B < C matches the impact as well, corresponding to (c). Thus, given that all three collated sequences are satisfied, option (d) "All the above" is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vapor Pressure Lowering
When a non-volatile solute is added to a solvent, it disrupts the evaporation rate, resulting in vapor pressure lowering. Imagine adding sugar to water. The sugar molecules don't evaporate, but they take up space at the surface, reducing the number of water molecules able to escape into the vapor phase. This leads to lower vapor pressure. The decrease in vapor pressure is one of the colligative properties, which depends on the number of solute particles. Crucially, it does not matter what type of particle is added but how many there are. For instance: - Sugar (A) doesn't dissociate, contributing just 1 particle. - Salt, NaCl (B), splits into 2 particles: Na鈦 and Cl鈦. - BaCl鈧 (C) generates 3 particles: one Ba虏鈦 and two Cl鈦. Thus, more particles lead to more significant lowering of vapor pressure. For the same molar concentration, BaCl鈧 with the most particles will exhibit the greatest reduction in vapor pressure.
Boiling Point Elevation
Boiling point elevation occurs when the boiling point of a solvent increases after adding a solute. The additional solute particles disrupt the escape of solvent molecules into the vapor phase, requiring more heat to achieve the boiling point. This process is also an example of a colligative property, being reliant on solute particles' quantity rather than their type. Consider: - Sugar (A) provides only 1 particle per molecule, having the least effect. - NaCl (B) splits into 2 particles (Na鈦 and Cl鈦), leading to a moderate increase. - BaCl鈧 (C) dissociates into 3 particles: one Ba虏鈦 and two Cl鈦, causing the most elevation. So, with more dissociated particles, BaCl鈧 raises the boiling point the most, followed by NaCl and then sugar.
Freezing Point Depression
Freezing point depression refers to the lowering of a solvent's freezing point due to solute presence. When a solute is added, it disturbs the orderly arrangement needed for the solvent to freeze, thus requiring a lower temperature to achieve the solid state. As with vapor pressure and boiling point, this phenomenon is a colligative property. It hinges on how many particles are formed: - Sugar (A) remains as a single entity, offering the weakest effect. - NaCl (B) dissociates into two ions, amplifying the depression. - BaCl鈧 (C), creating three particles, manifests the most substantial impact. In summary, with more solute particles preventing solid formation, the freezing point decreases more significantly for BaCl鈧, then NaCl, and least for sugar.

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Most popular questions from this chapter

Which one of the following statements is/are true? a. two sucrose solutions of same molality prepared in different solvents will have the same freezing point depression b. the osmotic pressure ( \(\pi\) ) of a solution is given by the equation \(\pi=\) MRT, where \(M\) is the molarity of the solution c. Raoult's law states that the vapour pressure of a component over a solution is proportional to its mole fraction d. the correct order of osmotic pressure for \(0.01\) M aqueous solution of each compound is \(\mathrm{BaCl}_{2}>\mathrm{KCl}<\mathrm{CH}_{3} \mathrm{COOH}>\) Sucrose

Match the following: Column I A. \(01 \mathrm{M} \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) B. \(0.1 \mathrm{M} \mathrm{AlPO}_{4}\) C. 0.1 M Glucose D. \(0.1 \mathrm{M} \mathrm{CaCl}_{2}\) Column II (p) Solution with highest boiling point (q) Van't Hoff factor is greater than 1 (r) Solution with lowest osmotic pressure (s) Solution with lowest freezing point

Which of the following statement is/are correct? a. Maximum boiling azeotropic mixture boils at temperature higher than either of the two pure components b. Minimum boiling azeotropic mixture boils at temperature lower than either of the two pure components c. Maximum boiling azeotropic mixture shows negative deviation d. Minimum boiling azeotropic mixture shows no deviation

To \(500 \mathrm{~cm}^{3}\) of water, \(3.0 \times 10^{-3} \mathrm{~kg}\) of acetic acid is added. If \(23 \%\) of acetic acid is dissociated, what will be the depression in freezing point? \(\mathrm{K}_{\mathrm{f}}\) and density of water at \(1.86 \mathrm{~K} \mathrm{~kg}-1\) and \(0.0997 \mathrm{~g} \mathrm{~cm}^{-3}\) respectively. a. \(0.186 \mathrm{~K}\) b. \(0.228 \mathrm{~K}\) c. \(0.371 \mathrm{~K}\) d. \(0.555 \mathrm{~K}\) [IIT 2000]

Which of the following can not form(s) ideal solution? a. Ethyl alcohol + water b. Ethyl bromide \(+\) ethyl iodide c. Benzene \(+\) Toluene d. Chloroform + benzene

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