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A fixed volume tank has water in vapor-liquid equilibrium. A mole of methane is added to the system. All gases are ideal. The amount of water in the vapor phase [_ а. stays the same vapor b. increases 1 mỏl CH, С. decreases liquid

A fixed volume tank has water in vapor-liquid equilibrium. A mole of methane is added to the system. All gases are ideal. The amount of water in the vapor phase [_ а. stays the same vapor b. increases 1 mỏl CH, С. decreases liquid

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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**Understanding Vapor-Liquid Equilibrium** In this scenario, we have a fixed volume tank with water in a state of vapor-liquid equilibrium. This means that the rate at which the water molecules evaporate (transition from liquid to vapor) is equal to the rate at which the vapor molecules condense back into the liquid. The system has reached a stable equilibrium. **Effect of Adding Methane (CH₄)** The system is subjected to a change by adding 1 mole of methane gas. Methane is an ideal gas, meaning it follows the ideal gas law where gases do not interact with each other except through elastic collisions and have the same average kinetic energy at a given temperature. **Analyzing the Impact on Water Vapor** The question posed is: How does the addition of 1 mole of methane affect the amount of water in the vapor phase? **Choices:** a. stays the same b. increases c. decreases **Diagram Explanation** The provided diagram illustrates the tank with two distinct layers: - The bottom portion is labeled "liquid," representing the liquid water in the tank. - The top portion is labeled "vapor," indicating the water vapor in equilibrium with the liquid. To the right of the tank, there is a depiction of methane being added. An arrow shows the introduction of 1 mole of CH₄ into the tank. **Key Concepts to Consider:** 1. **Partial Pressure**: Adding methane will increase the total pressure in the tank but the partial pressure of water vapor remains the same at equilibrium. 2. **Raoult's Law**: In an ideal mixture, the partial pressure of each component in the vapor phase depends on its mole fraction and vapor pressure. 3. **Dalton's Law of Partial Pressures**: Total pressure is the sum of the partial pressures of all gases present. In conclusion, when a mole of methane is introduced to the system, the total pressure in the tank increases, yet the partial pressure of water remains unchanged. The vapor phase of water can only hold a specific partial pressure at a given temperature according to Raoult's Law and thus will condense back to the liquid phase to maintain equilibrium. **Correct Answer:** c. decreases With the increase in total pressure from the addition of methane, the water molecules in the vapor phase condense to maintain the equilibrium, leading to a decrease in the amount of water vapor.
Transcribed Image Text:**Understanding Vapor-Liquid Equilibrium** In this scenario, we have a fixed volume tank with water in a state of vapor-liquid equilibrium. This means that the rate at which the water molecules evaporate (transition from liquid to vapor) is equal to the rate at which the vapor molecules condense back into the liquid. The system has reached a stable equilibrium. **Effect of Adding Methane (CH₄)** The system is subjected to a change by adding 1 mole of methane gas. Methane is an ideal gas, meaning it follows the ideal gas law where gases do not interact with each other except through elastic collisions and have the same average kinetic energy at a given temperature. **Analyzing the Impact on Water Vapor** The question posed is: How does the addition of 1 mole of methane affect the amount of water in the vapor phase? **Choices:** a. stays the same b. increases c. decreases **Diagram Explanation** The provided diagram illustrates the tank with two distinct layers: - The bottom portion is labeled "liquid," representing the liquid water in the tank. - The top portion is labeled "vapor," indicating the water vapor in equilibrium with the liquid. To the right of the tank, there is a depiction of methane being added. An arrow shows the introduction of 1 mole of CH₄ into the tank. **Key Concepts to Consider:** 1. **Partial Pressure**: Adding methane will increase the total pressure in the tank but the partial pressure of water vapor remains the same at equilibrium. 2. **Raoult's Law**: In an ideal mixture, the partial pressure of each component in the vapor phase depends on its mole fraction and vapor pressure. 3. **Dalton's Law of Partial Pressures**: Total pressure is the sum of the partial pressures of all gases present. In conclusion, when a mole of methane is introduced to the system, the total pressure in the tank increases, yet the partial pressure of water remains unchanged. The vapor phase of water can only hold a specific partial pressure at a given temperature according to Raoult's Law and thus will condense back to the liquid phase to maintain equilibrium. **Correct Answer:** c. decreases With the increase in total pressure from the addition of methane, the water molecules in the vapor phase condense to maintain the equilibrium, leading to a decrease in the amount of water vapor.
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