{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains course material from [CBE20255](https://jckantor.github.io/CBE20255)\n", "by Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE20255.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Operating Limits for a Methanol Lighter](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/07.03-Operating-Limits-for-a-Methanol-Lighter.ipynb) | [Contents](toc.ipynb) | [Henry Law Constants](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/07.05-Henry-Law-Constants.ipynb) >
"
]
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"source": [
"# Raoult Law for Ideal Mixtures"
]
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"source": [
"## Summary\n",
"\n",
"This notebook illustrates the use of Raoult's Law to calculate vapor pressure, and compares the results to experimental data for a non-ideal system. The video is used with permission from [learnCheme.com](http://learncheme.ning.com/), a project at the University of Colorado funded by the National Science Foundation and the Shell Corporation."
]
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"source": [
"## Introduction\n",
"\n",
"Thermally based chemical separations, such as distillation and flash units, [account for about 10 to 15 percent of the world's energy use](https://phys.org/news/2016-04-chemical-world.html). Raoult's law provides an idealized but nonetheless insightful understanding of how the vapor-liquid equilibrieum of mixtures is exploited for industrial separations. \n",
"\n",
"**Dalton's law**, in turn, says the total pressure $P$ is equal to the sum of the partial pressures, i.e.,\n",
"\n",
"\\begin{equation}\n",
"P = \\sum_{n=1}^N p_n\n",
"\\end{equation}\n",
"\n",
"\n",
"**Raoult's law** says the partial pressure $p_n$ of each component in a mixture of liquids is equal to the product of the mole fraction $x_n$ and the saturation pressure $P^{sat}_n(T)$ of the pure component. That is,\n",
"\n",
"\\begin{equation}\n",
"p_n = x_n P^{sat}_n(T)\n",
"\\end{equation}\n",
"\n",
"For an **ideal gas**, the partial pressure of an component in a mixture of gases is equal to the mole fraction $y_n$ and total pressure $P$\n",
"\n",
"\\begin{equation}\n",
"p_n = y_n P\n",
"\\end{equation}\n",
"\n",
"Subject to the assumptions of ideal liquid and gas mixtures, these three equations can be combined to provide a useful theory for vapor-liquid equilibrium and separations of ideal mixtures."
]
},
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"source": [
"## Vapor Pressure of Pure Components"
]
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"id": "GPnyjjeTXz05"
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"source": [
"The calculations in this notebook are for a representative system of two components, [acetone and ethanol for which experimental data](http://www.ddbst.com/en/EED/VLE/VLE%20Acetone%3BEthanol.php) is available from the [Dortmund Data Bank](http://www.ddbst.com/ddbst.html). \n",
"\n",
"We start by creating two functions to estimate vapor pressure for the individual species using Antoine's equation."
]
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"# Antoine's equations\n",
"A = 'acetone'\n",
"B = 'ethanol'\n",
"\n",
"def PsatA(T):\n",
" return 10**(7.02447 - 1161.0/(T + 224))\n",
"\n",
"def PsatB(T):\n",
" return 10**(8.04494 - 1554.3/(T + 222.65))"
]
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"source": [
"In particular, let's compute the saturation pressure at 32 $^\\circ$C can compare to [experimental data](http://www.ddbst.com/en/EED/VLE/VLE%20Acetone%3BEthanol.php)."
]
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