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Chapter 13: Problem 44

Write the equation representing Raoult's law, and express it in words.

Short Answer

Expert verified
Raoult's Law states that the vapor pressure of a component in a solution equals its vapor pressure when pure, multiplied by its mole fraction.

Step by step solution

01

Understand Raoult's Law

Raoult's Law is a fundamental principle in chemistry that relates to the vapor pressure of a solution and its individual components. It is applicable to ideal solutions, where the interactions between different molecules are similar to the interactions between the same type of molecules.
02

Write the Math Equation for Raoult's Law

Raoult's Law states that the partial vapor pressure of each component in an ideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.The equation is given by:\[ P_i = X_i imes P_i^0 \]where,- \( P_i \) is the partial vapor pressure of component \( i \) in the solution.- \( X_i \) is the mole fraction of component \( i \) in the solution.- \( P_i^0 \) is the vapor pressure of the pure component \( i \).
03

Express Raoult's Law in Words

In words, Raoult's Law can be described as follows: "The vapor pressure of a component in a solution is directly proportional to its mole fraction, with the proportionality factor being the vapor pressure of the pure component."

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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 a crucial concept in understanding Raoult's Law. It refers to the pressure exerted by a vapor in equilibrium with its liquid or solid form within a closed system. Many factors can affect this pressure, such as temperature and the nature of the liquid.
  • Higher temperatures generally increase vapor pressure because molecules move more energetically, escaping the liquid phase more readily.
  • Different substances have different inherent vapor pressures, based on molecular interactions within the liquid.

In the context of Raoult's Law, when a liquid forms part of a solution, its vapor pressure provides a basis to calculate how much of the liquid converts to vapor. The total vapor pressure of a solution can be seen as the sum of the partial pressures of all the components, each influenced by their individual vapor pressures and concentrations.
Ideal Solution
An ideal solution is a fundamental concept when applying Raoult's Law. It denotes a mixture where the interactions between different molecules are similar to the interactions between identical molecules.
  • This means that mixing the substances doesn't result in any significant change in temperature or volume.
  • The components mix uniformly at the molecular level, ensuring no preference for interaction with molecules of the same kind.

Understanding ideal solutions helps in simplifying the calculations and predictions related to Raoult's Law. This happens because the behavior of the molecules is predictable; they follow the law without deviations that are usually introduced by complex intermolecular forces in non-ideal solutions.
Mole Fraction
The mole fraction is an important concept in calculating vapor pressure using Raoult's Law. It is a way to express the concentration of a component in a mixture. The mole fraction of a component 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.
  • This is a dimensionless quantity; it has no units because it represents a ratio.
  • The mole fraction ranges from 0 to 1, with 1 meaning the component is present alone and 0 indicating it is entirely absent.

In Raoult's Law, the mole fraction directly impacts the partial vapor pressure of a component. Higher mole fractions result in higher partial pressures, reflecting a direct relationship wherein each component contributes to the total vapor pressure according to its concentration in the solution.

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Most popular questions from this chapter

What is osmosis? What is a semipermeable membrane?

Why is the discussion of the colligative properties of electrolyte solutions more involved than that of nonelectrolyte solutions?

Discuss the factors that influence the solubility of a gas in a liquid.

What are ion pairs? What effect does ion-pair formation have on the colligative properties of a solution? How does the ease of ion-pair formation depend on (a) charges on the ions, \((\mathrm{b})\) size of the ions, \((\mathrm{c})\) nature of the solvent (polar versus nonpolar), (d) concentration?

Give two examples of (a) a volatile liquid and (b) a nonvolatile liquid.
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