Problem 4 cm3 Consider this graph showing the molar volume in of a binary mixture at constant T and P. mol
Problem 4 cm3 Consider this graph showing the molar volume in of a binary mixture at constant T and P. mol
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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![**Problem 4**
Consider this graph showing the molar volume in \( \frac{\text{cm}^3}{\text{mol}} \) of a binary mixture at constant \( T \) and \( P \).
[Graph Description]
- The graph plots the molar volume \( V \) in \( \frac{\text{cm}^3}{\text{mol}} \) on the y-axis against the mole fraction \( x_1 \) on the x-axis.
- The x-axis is labeled \( x_1 \) and ranges from 0 to 1.
- The y-axis is labeled \( V \) in \( \frac{\text{cm}^3}{\text{mol}} \) and ranges from 80 to 140.
- The curve showing the molar volume is increasing and slightly concave upwards from around 90 at \( x_1 = 0 \) to approximately 130 at \( x_1 = 1 \).
**Questions:**
a) Estimate the pure species molar volumes, and the partial molar volumes at infinite-dilution \( \bar{V}_1^\infty \) and \( \bar{V}_2^\infty \).
b) Now consider the mixture with \( x_1 = 0.2 \). What is its molar volume of the mixture and the corresponding partial molar volumes \( \bar{V}_1 \) and \( \bar{V}_2 \). Make sure your answer satisfies the summability equation.
c) Derive an equation to describe the molar volume of the mixture as a function of \( x_1 \) assuming the two components would form an ideal mixture. And plot molar volume of ideal mixture with respect to \( x_1 \) using the Figure above.
**(Answers: a) 140 and 106 cm3/mole, respectively, b) 100, 130 and 92 cm3/mole respectively, c) Ideal mixture molar volume: 90+30x1; this should provide a straight line between 90 to 120 on the figure)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58e30080-5af3-43c1-bb19-7e2f27cfd9f6%2Fdc6652b0-891d-43cc-96aa-27cb0bae71e1%2F2oius0l_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 4**
Consider this graph showing the molar volume in \( \frac{\text{cm}^3}{\text{mol}} \) of a binary mixture at constant \( T \) and \( P \).
[Graph Description]
- The graph plots the molar volume \( V \) in \( \frac{\text{cm}^3}{\text{mol}} \) on the y-axis against the mole fraction \( x_1 \) on the x-axis.
- The x-axis is labeled \( x_1 \) and ranges from 0 to 1.
- The y-axis is labeled \( V \) in \( \frac{\text{cm}^3}{\text{mol}} \) and ranges from 80 to 140.
- The curve showing the molar volume is increasing and slightly concave upwards from around 90 at \( x_1 = 0 \) to approximately 130 at \( x_1 = 1 \).
**Questions:**
a) Estimate the pure species molar volumes, and the partial molar volumes at infinite-dilution \( \bar{V}_1^\infty \) and \( \bar{V}_2^\infty \).
b) Now consider the mixture with \( x_1 = 0.2 \). What is its molar volume of the mixture and the corresponding partial molar volumes \( \bar{V}_1 \) and \( \bar{V}_2 \). Make sure your answer satisfies the summability equation.
c) Derive an equation to describe the molar volume of the mixture as a function of \( x_1 \) assuming the two components would form an ideal mixture. And plot molar volume of ideal mixture with respect to \( x_1 \) using the Figure above.
**(Answers: a) 140 and 106 cm3/mole, respectively, b) 100, 130 and 92 cm3/mole respectively, c) Ideal mixture molar volume: 90+30x1; this should provide a straight line between 90 to 120 on the figure)**
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