Question

The immiscible liquid system containing aniline-water boils at \(98^{\circ} \mathrm{C}\) under a pressure of \(760 \mathrm{~mm}\). At this temperature, the vapour pressure of water is \(700 \mathrm{~mm}\). If aniline is distilled in steam at \(98^{\circ} \mathrm{C}\), what per cent of total weight of the distillate will be aniline? (a) \(7.89\) (b) \(8.57\) (c) \(30.7\) (d) \(44.3\)

Short answer

The per cent of total weight of the distillate that will be aniline is approximately 7.89%.

Step-by-step solution

Understand the Concept

In an immiscible liquid system, such as aniline and water, the total vapor pressure at the boiling point will be the sum of the vapor pressures of the individual components. This is due to Dalton's Law of Partial Pressures. In this case, we are given the total pressure and the vapor pressure of water.

Calculate the Vapor Pressure of Aniline

Using Dalton's Law, the vapor pressure of aniline can be found by subtracting the vapor pressure of water from the total pressure. So, the vapor pressure of aniline is \(760 mm - 700 mm = 60 mm\).

Calculate the Mole Fraction of Aniline in the Vapor

The mole fraction of aniline in the vapor phase is determined by its partial pressure divided by the total pressure. So, the mole fraction of aniline will be \(\frac{60}{760}\).

Calculate the Percentage by Weight of Aniline in the Distillate

Assuming ideal behavior and that the molar mass of aniline is not equal to the molar mass of water, the actual masses are not directly proportional to the vapor pressures. However, for the purpose of this exercise and the options given, we treat it as if the weight fraction is equivalent to the mole fraction (because we are not given the molar masses to calculate the actual mole fraction), so the percentage by weight of aniline in the distillate will also be approximately \(\frac{60}{760} \times 100\).

Key concepts

Dalton's Law of Partial Pressures

Understanding Dalton's Law of Partial Pressures is crucial when studying mixtures of gases, such as those involving vapor pressures in an immiscible liquid system. According to this law, in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the individual partial pressures of the gases.

This concept is fundamental when dealing with boiling points and distillation processes because each component in a mixture contributes to the total pressure based on its vapor pressure at a given temperature. For students working through problems on this topic, remember that the individual gas or vapor components behave as if they were alone occupying the entire volume, impacting the total pressure independently of each other.

For clearer understanding, consider the following example: If you have a container with two immiscible liquids (like oil and water), each will evaporate and exert its own vapor pressure. Dalton's Law tells us that the total pressure is simply the addition of these two pressures. This insight helps to solve problems where you must find the composition of the vapor phase above a mixture, often a necessary step in separation processes.

Immiscible Liquid System

An immiscible liquid system refers to a combination of two or more liquids that do not mix to form a homogeneous solution, such as oil and water. In such systems, each liquid maintains its own identity and properties, including a distinct vapor pressure when heated.

When immiscible liquids are heated together, each liquid's boiling behavior is unaffected by the presence of the other. The vapor above the mixture is composed of each liquid’s vapor, and their respective mole fractions in the vapor phase will be proportional to their individual vapor pressures. This provides a crucial understanding for students as to why each liquid can be analyzed separately, despite being part of a complex system. Additionally, the unique boiling points of immiscible liquids form the basis for separation methods like fractional distillation, which is used to separate and purify liquid compounds based on differing vapor pressures.

To relate to the exercise, when an immiscible mixture of aniline and water is boiled, each liquid's vapor pressure contributes to the total pressure. The boiling process can be seen as each liquid individually reaching its boiling point and turning into vapor, independent of the other.

Fractional Distillation

The concept of fractional distillation comes into play when separating components of a mixture based on their different boiling points. This method is particularly useful for mixtures of liquids with different vapor pressures. In this process, a mixture is heated in a distillation column, where components with lower boiling points vaporize first and those with higher boiling points later.

The vaporized components ascend the column, and as they cool, they condense at different levels corresponding to their vapor pressures. Fractional distillation is highly efficient for separating mixtures into their individual components and is widely used in various industries, including the purification of chemicals, processing of crude oil, and the production of distilled beverages.

For students, understanding this principle is essential when studying distillation processes. Connect this with the exercise provided where steam distillation is being used. Steam distillation is an application of fractional distillation which allows for the separation of compounds that are not directly miscible with water, like aniline, due to the differences in their vapor pressures at high temperatures.