{ "cells": [ { "cell_type": "markdown", "id": "9a4b7dc9-f027-4be6-a4e9-43baa4e470ff", "metadata": { "tags": [] }, "source": [ "# Week 2 Exercise: Liquid Vapour Equilibria\n", "\n", "## Bubble and Dew points\n", "\n", "Compute the bubble and dew pressure for a chloroform-methanol mixture at 50$^\\circ$ C for all possible molar compositions. \n", "\n", "### Data and useful information\n", "\n", "The Equilibrium vapour pressure in bar is given by the following Antoine equation: \n", "\n", "$$\n", "\\log_{10}{P^\\circ(T)}= A-\\frac{B}{T+C} - \\log_{10}750\n", "$$\n", "\n", "with (chloroform=1, methanol=2): \n", "\n", "$A=[6.95465, 8.08097]$\n", "\n", "$B=[1170.966, 1582.271]$\n", "\n", "$C=[226.232, 239.726]$\n", "\n", "\n", "The activity of the components of the mixture (chloroform=1, methanol=2) can be described by the Van Laar model i.e.: \n", "\n", "$$\n", "\\ln{\\gamma_1}=\\frac{A_{12}}{1+\\frac{A_{12}x_1}{A_{21}x_2}}\n", "$$\n", "\n", "\n", "$$\n", "\\ln{\\gamma_2}=\\frac{A_{21}}{1+\\frac{A_{21}x_2}{A_{12}x_1}}\n", "$$\n", "\n", "with $A_{12}=0.9726$ and $A_{21}=1.9210$.\n", "\n", "### Problem definitions: \n", "\n", "When computing the __Bubble__ pressure, we are estimating the pressure (and the composition) of the very first bubble of vapour formed in a liquid at known composition ($\\mathbf{x}$ is known). \n", "The equations we can use to solve the problem are the equilibrium statements N-1 species in the system (i.e. the Raoult equation in the case of an ideal mixture of ideal gases) and the stoichiometric constraint on the composition of the __vapour__ phase. \n", "\n", "When computing the __Dew__ pressure, we are estimating the pressure (and the composition) of the very first droplet of liquid formed in a vapour at known composition ($\\mathbf{y}$ is known). \n", "The equations we can use to solve the problem are the equilibrium statements N-1 species in the system (i.e. the Raoult equation in the case of an ideal mixture of ideal gases) and the stoichiometric constraint on the composition of the __liquid__ phase. \n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "b1795d92", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "
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