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Chapter 16: Problem 17

For a dilute solution, Raoult's law states that : (a) the lowering of vapour pressure is equal to the mole fraction of solute. (b) the relative lowering of vapour pressure is equal to the mole fraction of solute. (c) the relative lowering of vapour pressure is proportional to the amount of solute in solution. (d) the vapour pressure of the solution is equal to the mole fraction of solvent.

Short Answer

Expert verified
(b) The relative lowering of vapour pressure is equal to the mole fraction of solute.

Step by step solution

01

Understanding Raoult's Law

Raoult's Law is a principle applied to ideal solutions. It states that in a dilute solution, each component of the solution exerts a partial vapor pressure proportional to its mole fraction. The total vapor pressure of the solution is the sum of these partial pressures.
02

Define Key Terms

Mole fraction of a component in a solution is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution. Relative lowering of vapor pressure means the change in vapor pressure relative to the original pressure, usually of the pure solvent.
03

Identify Relevant Concept

For a dilute solution, especially when considering the effects of a non-volatile solute, Raoult's Law tells us that the relative lowering of vapor pressure of the solvent is directly proportional to the mole fraction of the solute, which is the key concept in this exercise.
04

Analyze the Options

The exercise presents four statements. We must match these against what Raoult's Law asserts: (a) talks about lowering directly, (b) refers to relative lowering, (c) cites proportionality, and (d) focuses on solvent mole fraction against solution vapor pressure.
05

Select Correct Option

Option (b), stating the relative lowering of vapor pressure is equal to the mole fraction of solute, correctly represents Raoult's Law for dilute solutions. It captures the proportional relationship between the solute mole fraction and the change in vapor pressure compared to the pure solvent.

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Key Concepts

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

Vapor Pressure
Vapor pressure is the pressure exerted by the vapor of a liquid in equilibrium with its liquid phase at a given temperature. In a solution, vapor pressure changes depending on the composition. When you add a non-volatile solute, the solution's vapor pressure lowers compared to the pure solvent. This phenomenon occurs because the solute particles occupy space at the liquid surface, hindering solvent molecules from escaping into the vapor phase.
The measurement of vapor pressure is significant in determining the physical properties of solutions. For example:
  • It influences boiling points and freezing points.
  • It is crucial for understanding weather patterns and cooking at high altitudes.
Understanding vapor pressure helps predict how solutions will behave in different conditions, making it a core concept in chemistry and related fields.
Mole Fraction
Mole fraction is a way to express the concentration of a component in a mixture. It's defined as the number of moles of one component divided by the total number of moles of all components in the mixture. For a binary solution of solvent and a single solute, the mole fraction of the solute (denoted as \( x_2 \)) and of the solvent (denoted as \( x_1 \)) are very straightforward. They are calculated as follows:
  • \( x_1 = \frac{n_1}{n_1 + n_2} \), where \( n_1 \) is the moles of solvent and \( n_2 \) is the moles of solute.
  • \( x_2 = \frac{n_2}{n_1 + n_2} \).
The sum of the mole fractions in a solution is always 1. Mole fraction is significant because it remains constant regardless of temperature changes, unlike concentration units like molarity or molality.
Dilute Solution
A dilute solution is one where the amount of solute is relatively small compared to the solvent. In such solutions, the properties are almost identical to that of the pure solvent. Raoult's Law becomes particularly useful in dilute solutions for predicting how the vapor pressure is affected by solute addition. Here are some characteristics of dilute solutions:
  • They often lead to small changes in the physical properties, making calculations simpler.
  • Assumptions based on ideal behavior, like those used in Raoult's Law, tend to be more accurate.
When Raoult鈥檚 Law is applied to a dilute solution, it asserts that the relative lowering of vapor pressure is proportional to the mole fraction of the solute. This concept is central when studying solutions because it relates directly to essential phenomena such as boiling point elevation and freezing point depression.

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Most popular questions from this chapter

What is the molarity and molality of a \(13 \%\) solution (by weight) of sulphuric acid with a density of \(1.02 \mathrm{~g} / \mathrm{mL} ?\) To what volume should \(100 \mathrm{~mL}\) of this acid be diluted in order to prepare a \(1.5 \mathrm{~N}\) solution?

A solution at \(20^{\circ} \mathrm{C}\) is composed of \(1.5 \mathrm{~mol}\) of benzene and \(3.5 \mathrm{~mol}\) of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are \(74.7\) torr and \(22.3\) torr, respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively : (a) \(35.8\) torr and \(0.280\) (b) \(38.0\) torr and \(0.589\) (c) \(30.5\) torr and \(0.389\) (d) \(30.5\) torr and \(0.480\)

Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Application of colligative properties are very useful in day-to-day life. One of its example is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator of automobiles. A solution \(\mathrm{M}\) is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is \(0.9\) Given : Freezing point depression constant of water \(\left(K_{f}^{\text {water }}\right)\) $$ =1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} $$ Freezing point depression constant of ethanol ( \(\left.K_{f}{ }^{\text {ethanol }}\right)\) $$ =2.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} $$ Boiling point elevation constant of water \(\left(K_{b}^{\text {water }}\right)\) \(=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) Boiling point elevation constant of ethanol \(\left(K_{b}^{\text {ethanol }}\right)=1.2 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) Standard freezing point of water \(=273 \mathrm{~K}\) Standard freezing point of ethanol \(=155.7 \mathrm{~K}\) Standard boiling point of water \(=373 \mathrm{~K}\) Standard boiling point of ethanol \(=351.5 \mathrm{~K}\) Vapour pressure of pure water \(=32.8 \mathrm{~mm} \mathrm{Hg}\) Vapour pressure of pure ethanol \(=40 \mathrm{~mm} \mathrm{Hg}\) Molecular weight of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\) Molecular weight of ethanol \(=46 \mathrm{~g} \mathrm{~mol}^{-1}\) In answering the following questions, consider the solution to be ideal dilute solutions and solutes to be non-volatile and non-dissociative. The freezing point of the solution \(\mathrm{M}\) is (a) \(268.7 \mathrm{~K}\) (b) \(268.5 \mathrm{~K}\) (c) \(234.2 \mathrm{~K}\) (d) \(150.9 \mathrm{~K}\)

For an ideal solution of two components \(\mathrm{A}\) and \(\mathrm{B}\), which of the following is true? (a) \(\Delta \mathrm{H}_{\text {mixing }}<0\) (zero) (b) \(\Delta \mathrm{H}_{\text {mixing }}>0\) (zero) (c) \(\mathrm{A}-\mathrm{B}\) interaction is stronger than \(\mathrm{A}-\mathrm{A}\) and \(\mathrm{B}-\mathrm{B}\) interactions (d) \(\mathrm{A}-\mathrm{A}, \mathrm{B}-\mathrm{B}\) and \(\mathrm{A}-\mathrm{B}\) interactions are identical.

The vapour pressures of pure liquids \(\mathrm{A}\) and \(\mathrm{B}\) are 400 and \(600 \mathrm{mmHg}\), respectively at \(298 \mathrm{~K}\). On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid \(\mathrm{B}\) is \(0.5\) in the mixture. The vapour pressure of the final solution, the mole fractions of components \(\mathrm{A}\) and \(\mathrm{B}\) in vapour phase, respectively are: (a) \(450 \mathrm{mmHg}, 0.4,0.6\) (b) \(500 \mathrm{mmHg}, 0.5,0.5\) (c) \(450 \mathrm{mmHg}, 0.5,0.5\) (d) \(500 \mathrm{mmHg}, 0.4,06\)
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