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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 8 : Phase equilibria"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.6"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "P1 = 106.; \t\t\t#vapour pressure of n-heptane (kPa)\n",
      "P2 = 74.; \t\t\t#vapour pressure of toluene (kPa)\n",
      "P = 101.3; \t\t\t#total pressure (kPa)\n",
      "\n",
      "# Calculations\n",
      "x = (P-P2)/(P1-P2)\n",
      "y = x*(P1/P)\n",
      "\n",
      "# Results\n",
      "print 'Composition of liquid heptane is %f mol percent'%(x*100)\n",
      "print ' Composition of heptane in vapour form is %f mol percent'%(y*100)\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Composition of liquid heptane is 85.312500 mol percent\n",
        " Composition of heptane in vapour form is 89.270731 mol percent\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.7"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "P1 = 135.4; \t\t\t#vapour pressure of benzene (kPa)\n",
      "P2 = 54.; \t\t\t#vapour pressure of toluene (kPa)\n",
      "x =  0.5; \t\t\t#liquid phase composition\n",
      "\n",
      "# Calculations\n",
      "#Using eq. 8.51 (Page no. 332)\n",
      "P_beg = P2 + (P1-P2)*x;\n",
      "\n",
      "#At the end\n",
      "y = 0.5; \t\t\t#vapour phase composition\n",
      "#Using eq. 8.54 (Page no. 333) and rearranging\n",
      "P_end = (P1*P2)/(P1-y*(P1-P2))\n",
      "\n",
      "# Results\n",
      "print 'Pressure at the beginning of the process is %f kPa'%(P_beg)\n",
      "print ' Pressure at the end of the process is %f kPa'%(P_end)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Pressure at the beginning of the process is 94.700000 kPa\n",
        " Pressure at the end of the process is 77.208025 kPa\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.8"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math\n",
      "def P1(T):\n",
      "    y1 = math.e**(14.5463 - 2940.46/(T-35.93))  \t\t\t#vapour pressure of acetone\n",
      "    return y1\n",
      "\n",
      "def P2(T):\n",
      "    y2 = math.e**(14.2724 - 2945.47/(T-49.15))  \t\t\t#vapour pressure of acetonitrile\n",
      "    return y2\n",
      "\n",
      "# Variables\n",
      "T = 327.; \t\t\t#temperature in K\n",
      "P = 65.; \t\t\t#pressure in kPa\n",
      "\n",
      "# Calculations and Results\n",
      "P1_s = P1(T)\n",
      "P2_s = P2(T)\n",
      "\t\t\t#Using eq. 8.51 (Page no. 332)\n",
      "x1 = (P-P2_s)/(P1_s-P2_s)\n",
      "\t\t\t#Using eq. 8.54 (Page no. 333)\n",
      "y1 = x1*(P1_s/P)\n",
      "print '(a)'\n",
      "print ' x1 = %f'%x1\n",
      "print ' y1 = %f'%y1\n",
      "\n",
      "\t\t\t#(b). To calculate T and y1\n",
      "P = 65.; \t\t\t#pressure in kPa\n",
      "x1 = 0.4;\n",
      "\n",
      "flag = 1.;\n",
      "T2 = 340.; \t\t\t#temperatue (assumed)\n",
      "while(flag==1):\n",
      "    P1_s = P1(T2)\n",
      "    P2_s = P2(T2)\n",
      "    P_calc = P2_s + x1*(P1_s-P2_s)\n",
      "    if((P_calc-P)<=1):\n",
      "        flag = 0;\n",
      "    else:\n",
      "        T2 = T2-0.8;\n",
      "\n",
      "y1 = x1*(P1_s/P)\n",
      "print ' (b)'\n",
      "print ' Temperature is %f K'%T2\n",
      "print ' y1 = %f'%y1\n",
      "\n",
      "\t\t\t#(c). To calculate P and y1\n",
      "T3 = 327.; \t\t\t#temperature in K\n",
      "x1 = 0.4;\n",
      "\n",
      "P1_s = P1(T3)\n",
      "P2_s = P2(T3)\n",
      "P = P2_s + x1*(P1_s-P2_s)\n",
      "y1 = x1*(P1_s/P)\n",
      "print ' (c)'\n",
      "print ' Pressure is %f kPa'%P\n",
      "print ' y1 = %f'%y1\n",
      "\n",
      "\t\t\t#(d). To calculate T and x1\n",
      "P = 65.; \t\t\t#pressure in kPa\n",
      "y1 = 0.4;\n",
      "\n",
      "flag = 1.;\n",
      "T = 340.; \t\t\t#assumed temperature (K)\n",
      "while(flag==1):\n",
      "    P1_s = P1(T)\n",
      "    P2_s = P2(T)\n",
      "    y1_calc = (P1_s*(P-P2_s))/(P*(P1_s-P2_s))\n",
      "    if((y1_calc-y1)>=0.001):\n",
      "        flag = 0;\n",
      "    else:\n",
      "        T = T-2;\n",
      "\n",
      "x1 = y1*(P/P1_s)\n",
      "print ' (d)'\n",
      "print ' Temperature = %f K'%T\n",
      "print ' x1 = %f'%x1\n",
      "\n",
      "#(e). To calculate P and x1\n",
      "T = 327.; \t\t\t#temperature (K)\n",
      "y1 = 0.4;\n",
      "\n",
      "P1_s = P1(T)\n",
      "P2_s = P2(T)\n",
      "#Using eq. 8.54 and 8.51\n",
      "x1 = (y1*P2_s)/(P1_s-y1*(P1_s-P2_s))\n",
      "P = x1*(P1_s/y1)\n",
      "print ' (e)'\n",
      "print ' Pressure = %f kPa'%P\n",
      "print ' x1 = %f'%x1\n",
      "\n",
      "#(f). To calculate fraction of the system is liquid and vapour in equilibrium\n",
      "T = 327.; \t\t\t#temperature (K)\n",
      "P = 65.; \t\t\t#pressure (kPa)\n",
      "y1 = 0.7344;\n",
      "\n",
      "P1_s = P1(T)\n",
      "P2_s = P2(T)\n",
      "x1 = (P-P2_s)/(P1_s-P2_s)\n",
      "#Let f be the fraction of the mixture that is liquid\n",
      "#Applying acetone balance\n",
      "f = (0.7-y1)/(x1-y1)\n",
      "print ' (f)'\n",
      "print ' Fraction of mixture that is liquid is %f percent'%(f*100)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)\n",
        " x1 = 0.560806\n",
        " y1 = 0.734393\n",
        " (b)\n",
        " Temperature is 330.400000 K\n",
        " y1 = 0.588617\n",
        " (c)\n",
        " Pressure is 57.633467 kPa\n",
        " y1 = 0.590765\n",
        " (d)\n",
        " Temperature = 334.000000 K\n",
        " x1 = 0.240940\n",
        " (e)\n",
        " Pressure = 50.093199 kPa\n",
        " x1 = 0.235402\n",
        " (f)\n",
        " Fraction of mixture that is liquid is 19.816333 percent\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.9"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "%matplotlib inline\n",
      "\n",
      "# Variables\n",
      "P = 101.3; \t\t\t#total pressure over the system (kPa)\n",
      "T = [371.4, 378, 383, 388, 393, 398.6];\n",
      "Pa = [101.3 ,125.3, 140.0, 160.0 ,179.9, 205.3];\n",
      "Pb = [44.4 ,55.6 ,64.5, 74.8, 86.6 ,101.3];\n",
      "xa = [0,0,0,0,0,0]\n",
      "ya = [0,0,0,0,0,0]\n",
      "\n",
      "# Calculations\n",
      "#To construct boiling point and equilibrium point diagram\n",
      "for i in range(6):\n",
      "    xa[i] = (P-Pb[i])/(Pa[i]-Pb[i]) \t\t\t#Using eq. 8.51\n",
      "    ya[i] = xa[i]*(Pa[i]/P )\t\t\t#Using eq. 8.54\n",
      "\n",
      "from matplotlib.pyplot import *\n",
      "\t\t\t#(a).\n",
      "\t\t\t#To construct boiling point diagram\n",
      "plot(xa,T)\n",
      "plot(ya,T)\n",
      "\t\t\t#title(\"Boiling Point diagram xa and ya Temperature\"\n",
      "\t\t\t#(b).\n",
      "\t\t\t#To construct the equilibrium diagram\n",
      "plot(ya,xa)\n",
      "\t\t\t#title(\"Equilibrium Diagram\",\"xa\",\"ya\"\n",
      "show()\n",
      "#(c).\n",
      "\n",
      "# Results\n",
      "print '(c). The given subpart is theoretical and does not involve any numerical computation'\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['draw_if_interactive']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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obm4e12bPnj3GPffcYxiGYTQ3NxtutztZ3ZlXsYzFf/7zH6OgoMB477335qmX\ncyOWsbjQt7/9bWPv3r1z2MO5E8tYHD9+3Lj99tuNcDhsDAwMGIWFhcYHH3wwTz1OnljG4vHHHzdq\namoMwzCM9vZ2Y9myZZEvqc3m1KlTF/0yNt7cTNqpm+l+OHXukqhNmzZx7733cvjwYVwuF6mpqfzu\nd79LVnfmVSxj8cwzz/D5559Hzkvb7Xaamprms9tJEctYfFnEMhbFxcXccccduN1uhoeHefTRR1m5\ncuU89zzxYhmLp59+mqqqKgoLCxkZGeFnP/tZ5EtqM3nggQc4cuQInZ2d5OfnU1tby/DwMDDz3NQP\npkRETE63EhQRMTkFvYiIySnoRURMTkEvImJyCnoREZNT0IuImJyCXkTE5BT0IiIm9/8XDjZRk2RO\nAwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x226ec50>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(c). The given subpart is theoretical and does not involve any numerical computation\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.11"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "x1 = 46.1/100; \t\t\t#mole percent of A\n",
      "P = 101.3; \t\t\t#total pressure of system (kPa)\n",
      "P1_s = 84.8; \t\t\t#vapour pressure of component A (kPa)\n",
      "P2_s = 78.2; \t\t\t#vapour pressure of component B (kPa) \n",
      "\n",
      "# Calculations\n",
      "#To calculate van Laar constants\n",
      "gama1 = P/P1_s;\n",
      "gama2 = P/P2_s;\n",
      "x2 = 1-x1;\n",
      "import math\n",
      "#van Laar constants:\n",
      "#Using eq. 8.69 (Page no. 348)\n",
      "A = math.log (gama1)*(1 + (x2*math.log(gama2))/(x1*math.log(gama1)))**2;\n",
      "B = math.log (gama2)*(1 + (x1*math.log(gama1))/(x2*math.log(gama2)))**2;\n",
      "\n",
      "# Results\n",
      "print 'van Laar constants are:'\n",
      "print ' A = %f'%A\n",
      "print ' B = %f'%B\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "van Laar constants are:\n",
        " A = 1.298059\n",
        " B = 0.652282\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.12"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "x2 = 0.448; \t\t\t#mole fraction of ethanol\n",
      "P = 101.3; \t\t\t#total pressure (kPa)\n",
      "P1_s = 68.9; \t\t\t#Vapour pressure of benzene (kPa)\n",
      "P2_s = 67.4; \t\t\t#vapour pressure of ethanol (kPa)\n",
      "\n",
      "# Calculations\n",
      "#To calculate activity coeffecients in a solution containing 10% alcohol\n",
      "x1 = 1-x2;\n",
      "gama1 = P/P1_s;\n",
      "gama2 = P/P2_s;\n",
      "import math\n",
      "#Using eq. 8.69 (Page no. 348)\n",
      "#van Laar constants:\n",
      "A = math.log(gama1)*(1 + (x2*math.log(gama2))/(x1*math.log(gama1)))**2;\n",
      "B = math.log(gama2)*(1 + (x1*math.log(gama1))/(x2*math.log(gama2)))**2;\n",
      "\n",
      "#For solution containing 10% alcohol\n",
      "x2 = 0.1;\n",
      "x1 = 1-x2;\n",
      "ln_g1 = (A*x2**2)/(((A/B)*x1+x2)**2)\n",
      "ln_g2 = (B*x1**2)/((x1+(B/A)*x2)**2)\n",
      "gama1 = math.e**ln_g1;\n",
      "gama2 = math.e**ln_g2;\n",
      "\n",
      "# Results\n",
      "print 'Activity coeffecients:'\n",
      "print ' For component 1: %f'%gama1\n",
      "print ' For component 2: %f'%gama2\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Activity coeffecients:\n",
        " For component 1: 1.025516\n",
        " For component 2: 4.141567\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.13"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "x2 = 0.585; \t\t\t#mol fraction of hydrazine\n",
      "P = 101.3; \t\t\t#total pressure of system (kPa)\n",
      "P2_s = 124.76; \t\t\t#vapour pressure of hydrazine (kPa)\n",
      "\n",
      "# Calculations\n",
      "#To calculate equilibrium vapour composition for solution containing 20% (mol) hydrazine\n",
      "x1 = 1-x2;\n",
      "P1_s = 1.6*P2_s; \t\t\t#vapour pressure of water (kPa)\n",
      "gama1 = P/P1_s;\n",
      "gama2 = P/P2_s;\n",
      "\n",
      "import math\n",
      "#Using eq. 8.69 (Page no. 348)\n",
      "#van Laar constants:\n",
      "A = math.log(gama1)*(1 + (x2*math.log(gama2))/(x1*math.log(gama1)))**2;\n",
      "B = math.log(gama2)*(1 + (x1*math.log(gama1))/(x2*math.log(gama2)))**2;\n",
      "\n",
      "#For solution containing 20% hydrazine\n",
      "x2 = 0.2;\n",
      "x1 = 1-x2;\n",
      "ln_g1 = (A*x2**2)/(((A/B)*x1+x2)**2)\n",
      "ln_g2 = (B*x1**2)/((x1+(B/A)*x2)**2)\n",
      "gama1 = math.e**ln_g1;\n",
      "gama2 = math.e**ln_g2;\n",
      "\n",
      "#Using eq. 8.47 (Page no. 325) for components 1 and 2 and rearranging\n",
      "alpha = 1.6; \t\t\t#alpha = P1_s/P2_s\n",
      "y1 = 1./(1 + (gama2*x2)/(gama1*x1*alpha))\n",
      "y2 = 1-y1;\n",
      "\n",
      "# Results\n",
      "print 'Equilibrium vapour composition for solution containing 20 mol percent hydrazine'\n",
      "print ' Hydrazine is %f percent'%(y2*100)\n",
      "print ' Water is %f percent'%(y1*100)\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Equilibrium vapour composition for solution containing 20 mol percent hydrazine\n",
        " Hydrazine is 5.279270 percent\n",
        " Water is 94.720730 percent\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.15"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "#Given:\n",
      "x1 = 0.047; \t\t\t#mol fraction of isopropanol\n",
      "P1 = 91.11; \t\t\t#vapour pessure of pure propanol (kPa)\n",
      "P = 91.2; \t\t\t#toatl pressure of system (kPa)\n",
      "P2 = 47.36; \t\t\t#vapour pressure of water (kPa)\n",
      "\n",
      "#van Laar consatnts:\n",
      "A = 2.470;\n",
      "B = 1.094;\n",
      "\n",
      "#To determine the total pressure:\n",
      "x2 = 1-x1;\n",
      "#Using eq. 8.68 (Page no. 348)\n",
      "ln_g1 = (A*x2**2)/(((A/B)*x1 + x2)**2);\n",
      "ln_g2 = (B*x1**2)/((x1 + (B/A)*x2)**2);\n",
      "gama1 = math.e**ln_g1;\n",
      "gama2 = math.e**ln_g2;\n",
      "#Total pressure:\n",
      "P_tot = (gama1*x1*P1) + (gama2*x2*P2);\n",
      "\n",
      "# Results\n",
      "if(P==P_tot):\n",
      "    print 'This is equal to total pressure'\n",
      "else:\n",
      "    print 'This is less than the total pressure. This error must have been caused by air leak'\n",
      "\n",
      "\n",
      " \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "This is less than the total pressure. This error must have been caused by air leak\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.16"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "P1 = 24.62; \t\t\t#vapour pressure of cyclohexane (kPa)\n",
      "P2 = 24.41; \t\t\t#vapour pressure of benzene (kPa)\n",
      "from numpy import array\n",
      "import math\n",
      "x1 = array([0, 0.2, 0.4, 0.6, 0.8, 1.0])\n",
      "x2 = 1-x1;\n",
      "g1 = [0,0,0,0,0,0]\n",
      "g2 = [0,0,0,0,0,0]\n",
      "P = [0,0,0,0,0,0]\n",
      "y1 = [0,0,0,0,0,0]\n",
      "\n",
      "# Calculations\n",
      "for i in range(6):\n",
      "    g1[i] = math.e**(0.458*x2[i]**2) \t\t\t#activity coeffecient for component 1\n",
      "    g2[i] = math.e**(0.458*x1[i]**2 )\t\t\t#activity coeffecient for component 2\n",
      "    P[i] = (g1[i]*x1[i]*P1) + (g2[i]*x2[i]*P2) \t\t\t#total pressure (kPa)\n",
      "    y1[i] = (g1[i]*x1[i]*P1)/P[i];\n",
      "\n",
      "\n",
      "from matplotlib.pyplot import *\n",
      "\n",
      "# Results\n",
      "#To construct P-x-y diagram\n",
      "plot(x1,P)\n",
      "plot(y1,P)\n",
      "\t\t\t#title(\"P-x-y Diagram\",\"x1 and y1\",\"Pressure\"\n",
      "show()\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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k2BF0tOiougAJqYZeZb+CYK0AB4ceRJdmXcosn53NbbRy5AjQvr0aAlQTaulX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\nRSjpE0KIFqGkTwghWuR/4t39YqZswywAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2f10390>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.17"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "P = 40.25; \t\t\t#total pressure (kPa)\n",
      "y1 = 0.566; \t\t\t#mol fraction of benzene in vapour phase\n",
      "x1 = 0.384; \t\t\t#mol fraction of benzene in liquid state\n",
      "P1 = 29.6; \t\t\t#vapour pressure of benzene (kPa)\n",
      "P2 = 22.9; \t\t\t#vapour pressure of ethanol (kPa)\n",
      "\n",
      "#To determine the composition and total pressure of azeotrope\n",
      "x2 = 1-x1;\n",
      "y2 = 1-y1;\n",
      "\n",
      "# Calculations\n",
      "#Using eq. 8.47 (Page no. 325)\n",
      "#Activity coeffecients:\n",
      "g1 = (y1*P)/(x1*P1)\n",
      "g2 = (y2*P)/(x2*P2)\n",
      "\n",
      "import math\n",
      "\t\t\t#Using eq. 8.69 (Page no. 348)\n",
      "\t\t\t#van Laar constants:\n",
      "A = math.log(g1)*((1 + (x2*math.log(g2))/(x1*math.log(g1)))**2)\n",
      "B = math.log(g2)*((1 + (x1*math.log(g1))/(x2*math.log(g2)))**2)\n",
      "\n",
      "\t\t\t#Assuming azeotropic comp. (for hit and trial method)\n",
      "x1 = 0.4;\n",
      "flag = 1.;\n",
      "while(flag==1):\n",
      "    x2 =1-x1;\n",
      "    ln_g1 = (A*x2**2)/(((A/B)*x1 + x2)**2)\n",
      "    ln_g2 = (B*x1**2)/((x1 + (B/A)*x2)**2)\n",
      "    g1 = math.e**ln_g1;\n",
      "    g2 = math.e**ln_g2;\n",
      "    P_1 = g1*P1;\n",
      "    P_2 = g2*P2;\n",
      "    if((P_1-P_2)<=1) and ((P_1-P_2)>=-1):\n",
      "        flag = 0;\n",
      "    else:\n",
      "        x1 = x1+0.1;\n",
      "\n",
      "# Results\n",
      "print 'Azeotropic compositon of benzene is %i percent'%(x1*100)\n",
      "print ' Total pressure of azeotrope is %f kPa'%((P_1+P_2)/2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Azeotropic compositon of benzene is 60 percent\n",
        " Total pressure of azeotrope is 40.858067 kPa\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.19"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "a12 = 1225.31; \t\t\t#(J/mol)\n",
      "a21 = 6051.01; \t\t\t#(J/mol)\n",
      "V1 = 74.05*10**-6; \t\t\t#(m**3/mol)\n",
      "V2 = 18.07*10**-6; \t\t\t#(m**3/mol)\n",
      "\n",
      "R = 8.314; \t\t\t#ideal gas constant\n",
      "T = 349; \t\t\t#temperature in K\n",
      "\n",
      "\n",
      "# Calculations\n",
      "#Antoine Equation:\n",
      "#Vapour pressure of 1st element\n",
      "def P1(T):\n",
      "    y1 = math.e**(14.39155-(2795.817/(T-43.198)))\n",
      "    return y1\n",
      "\n",
      "\t\t\t#Vapour pressure of 2nd element\n",
      "def P2(T):\n",
      "    y2 = math.e**(16.26205-(3799.887/(T-46.854)))\n",
      "    return y2\n",
      "\n",
      "\t\t\t#To calculate equilibrium pressure and composition\n",
      "\t\t\t#Using eq. 8.73 (Page no. 350)\n",
      "\t\t\t#Wilson Parameters:\n",
      "W12 = (V2/V1)*math.e**(-a12/(R*T));\n",
      "W21 = (V1/V2)*math.e**(-a21/(R*T));\n",
      "import math\n",
      "\t\t\t#Using Antoine equation\n",
      "P1_s = P1(T);\n",
      "P2_s = P2(T);\n",
      "\n",
      "\t\t\t#(a). Composition of vapour in equilibrium\n",
      "x1 = 0.43;\n",
      "x2 = 1-x1;\n",
      "\n",
      "\t\t\t#Using eq. 8.72 (Page no. 350)\n",
      "\t\t\t#Wilson equations:\n",
      "\t\t\t#Activity coeffecient of 1st component\n",
      "def g_1(n1,n2): \t\t\t#n1 is mol fraction of 1 and n2 is for 2\n",
      "    y3 = math.e**(-math.log(n1 + W12*n2) + n2*((W12/(n1+W12*n2))-(W21/(W21*n1+n2))));\n",
      "    return y3\n",
      "\n",
      "\t\t\t#Activity coeffecint of 2nd component\n",
      "def g_2(n1,n2):\n",
      "    y4 = math.e**(-math.log(n2 + W21*n1) - n1*((W12/(n1+W12*n2))-(W21/(W21*n1+n2))));\n",
      "    return y4\n",
      "    \n",
      "\t\t\t#Activity coeffecients:\n",
      "g1 = g_1(x1,x2);\n",
      "g2 = g_2(x1,x2);\n",
      "\n",
      "P = (g1*x1*P1_s) + (g2*x2*P2_s);\n",
      "y1 = (g1*x1*P1_s)/P;\n",
      "\n",
      "# Results\n",
      "print '(a).'\n",
      "print ' Equilibrium pressure is %f kPa'%P\n",
      "print ' Composition of acetone vapour in equilibrium is %f'%y1\n",
      "\n",
      "\n",
      "#(b). Composition of liquid in equilibrium\n",
      "y1 = 0.8;\n",
      "y2 = 1-y1;\n",
      "g1 = 1; g2 = 1; \t\t\t#assumed activity coeffecients\n",
      "P_as = 1/((y1/(g1*P1_s)) + (y2/(g2*P2_s)));\n",
      "\n",
      "\t\t\t#Hit and trial method:\n",
      "flag = 1;\n",
      "while(flag==1):\n",
      "    x1 = (y1*P_as)/(g1*P1_s);\n",
      "    x2 = 1-x1;\n",
      "    g1 = g_1(x1,x2);\n",
      "    g2 = g_2(x1,x2);\n",
      "    P_calc = 1/((y1/(g1*P1_s)) + (y2/(g2*P2_s)));\n",
      "    if((P_calc-P_as)<=1) and ((P_calc-P_as)>=-1):\n",
      "        flag = 0;\n",
      "    else:\n",
      "        P_as = P_calc;\n",
      "\n",
      "print ' (b).'\n",
      "print ' Equilibrium Pressure is %f kPa'%P_calc\n",
      "print ' Composition of acetone in liquid in equilibrium is %f'%x1\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a).\n",
        " Equilibrium pressure is 162.828251 kPa\n",
        " Composition of acetone vapour in equilibrium is 0.795360\n",
        " (b).\n",
        " Equilibrium Pressure is 164.488565 kPa\n",
        " Composition of acetone in liquid in equilibrium is 0.456817\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.20"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "P = 101.3; \t\t\t#total pressure of system (kPa)\n",
      "T = 337.5; \t\t\t#temperature in K\n",
      "x1 = 0.842;\n",
      "\n",
      "#Antoine constants\n",
      "#For methanol(1)\n",
      "A1 = 16.12609;\n",
      "B1 = 3394.286;\n",
      "C1 = 43.2;\n",
      "\n",
      "#For methyl ethyl ketone (2)\n",
      "A2 = 14.04357;\n",
      "B2 = 2785.225;\n",
      "C2 = 57.2;\n",
      "import math\n",
      "\n",
      "# Calculations\n",
      "#To determine parameters in Wilson's equation\n",
      "P1_s = math.e**(A1-(B1/(T-C1)))\n",
      "P2_s = math.e**(A2-(B2/(T-C2)))\n",
      "x2 = 1-x1;\n",
      "g1 = P/P1_s;\n",
      "g2 = P/P2_s;\n",
      "\n",
      "#Using eq. 8.72 and rearranging:\n",
      "def Wils(n): \t\t\t#n is the Wilson's parameter W12\n",
      "    y1 = (((g1*x2)/(1-(n*x1/(x1+n*x2))+(x1/x2)*math.log(g1*(x1+n*x2))))**(x2/x1))*(g1*(x1+n*x2))\n",
      "    return y1\n",
      "\n",
      "flag = 1;\n",
      "W12 = 0.5; \t\t\t#assumed value\n",
      "while(flag==1):\n",
      "    res = Wils(W12)\n",
      "    if ((res-1)>=-0.09):\n",
      "        flag = 0;\n",
      "    else:\n",
      "        W12 = W12+0.087;\n",
      "\n",
      "\t\t\t#For 2nd Wilson parameter:\n",
      "\t\t\t#Using eq. 8.72 and rearranging:\n",
      "k = math.log(g1*(x1+W12*x2))/x2 - (W12/(x1+W12*x2))\n",
      "W21 = (-k*x2)/(1+k*x1)\n",
      "\n",
      "# Results\n",
      "print \"wilson parameters are: %f, %f\"%(W12,W21)\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "wilson parameters are: 0.935000, 0.470758\n"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.21"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\t\t\n",
      "from numpy import *\n",
      "\n",
      "# Variables\n",
      "P = 101.3; \t\t\t#total pressure in kPa\n",
      "T = [333, 343, 353, 363]; \t\t\t#temperatures(K)\n",
      "Pa = [81.97 ,133.29 ,186.61, 266.58]; \t\t\t#Partial pressure of component A (kPa)\n",
      "Pb = [49.32 ,73.31, 106.63, 166.61]; \t\t\t#Partial pressure of component B (kPa)\n",
      "Pc = [39.32 ,62.65, 93.30, 133.29]; \t\t\t#Partial pressure of component C (kPa)\n",
      "xa = 0.45; \t\t\t#mole fraction of methanol\n",
      "xb = 0.3; \t\t\t#mole fraction of ethanol\n",
      "\n",
      "# Calculations and Results\n",
      "xc = 1-xa-xb; \t\t\t#mole fraction of propanol\n",
      "\n",
      "#To calculate bubble and dew point and the composition \n",
      "#(a). To calculate bubble point and vapour composition\n",
      "from matplotlib.pyplot import *\n",
      "plot(T,Pa);\n",
      "plot(T,Pb);\n",
      "plot(T,Pc);\n",
      "\t\t\t#title(\" \",\"Temperature\",\"Vapour pressures\");\n",
      "\t\t\t#legend(\"Pa\",\"Pb\",\"Pc\");\n",
      "\n",
      "\t\t\t#Using eq. 8.84 (Page no. 362)\n",
      "\t\t\t#At bubble temperature, sum(yi) = sum((xi*Pi)/P) = 1\n",
      "sum_y = [0,0,0,0]\n",
      "for i in range(4):\n",
      "    sum_y[i] = (xa*Pa[i])/P + (xb*Pb[i])/P + (xc*Pc[i])/P;\n",
      "\n",
      "Tb = interp(1,sum_y,T); \t\t\t#obtaining temperature at which sum (yi) = 1\n",
      "\n",
      "\t\t\t#Obtaining vapour pressures at bubble temperature\n",
      "Pb1 = interp(Tb,T,Pa);\n",
      "Pb2 = interp(Tb,T,Pb);\n",
      "Pb3 = interp(Tb,T,Pc);\n",
      "\n",
      "\t\t\t#Calculating equilibrium vapour composition\n",
      "ya = (xa*Pb1*100)/P;\n",
      "yb = (xb*Pb2*100)/P;\n",
      "yc = (xc*Pb3*100)/P;\n",
      "\n",
      "print '(a).'\n",
      "print ' The bubble temperature is %f K'%Tb\n",
      "print ' The equilibrium vapour contains %f methanol, %f ethanol and %f propanol'%(ya,yb,yc)\n",
      "\n",
      "#(b). The dew point and liquid composition\n",
      "#Vapour phase compositions at dew point\n",
      "ya = 0.45; \t\t\t#methanol\n",
      "yb = 0.30; \t\t\t#ethanol\n",
      "yc = 0.25; \t\t\t#propanol\n",
      "\n",
      "sum_x = zeros(4)\n",
      "#At dew point, sum(xi) = sum ((yi*P)/Pi) = 1\n",
      "for i in range(4):\n",
      "    sum_x[i] = (ya*P)/Pa[i] + (yb*P)/Pb[i] + (yc*P)/Pc[i];\n",
      "\n",
      "Td = interp(1,sum_x,T); \t\t\t#obtaining temperature at which sum (xi) = 1\n",
      "\n",
      "#Obtaining vapour pressures at dew temperature\n",
      "Pd1 = interp(Td,T,Pa);\n",
      "Pd2 = interp(Td,T,Pb);\n",
      "Pd3 = interp(Td,T,Pc);\n",
      "\n",
      "#Calculating liquid composition\n",
      "xa = (ya*P*100)/Pd1;\n",
      "xb = (yb*P*100)/Pd2;\n",
      "xc = (yc*P*100)/Pd3;\n",
      "\n",
      "print ' (c).'\n",
      "print ' The dew point is %f K'%Td\n",
      "print ' At dew point liquid contains %f methanol, %f ethanol and %f propanol'%(xa,xb,xc)\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a).\n",
        " The bubble temperature is 343.879659 K\n",
        " The equilibrium vapour contains 61.294328 methanol, 22.578783 ethanol and 16.126889 propanol\n",
        " (c).\n",
        " The dew point is 363.000000 K\n",
        " At dew point liquid contains 17.099932 methanol, 18.240202 ethanol and 18.999925 propanol\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gwIHYtWuXbunlO++8g7i4ONja2mLdunUIDQ1t+qKdaIK2vl7sE79tm5i7iowU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\n7ImIrMD/A7UqI330WejFAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2f23e50>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.22"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Given:\n",
      "\n",
      "P = 1447.14; \t\t\t#pressure of the system (kPa)\n",
      "x = [0.25 ,0.4, 0.35]; \t\t\t#composition of the components\n",
      "T = [355.4 ,366.5]; \t\t\t#assumed temperatures (K)\n",
      "K1 = [2.00, 0.78 ,0.33]; \t\t\t#value of Ki at 355.4 K \n",
      "K2 = [2.30, 0.90 ,0.40]; \t\t\t#value of Ki at 366.5 K\n",
      "\n",
      "\n",
      "# Calculation and Result\n",
      "\n",
      "Kx = [0, 0];\n",
      "for i in range(3):\n",
      "    Kx[0] = Kx[0]+K1[i]*x[i];\n",
      "    Kx[1] = Kx[1]+K2[i]*x[i];\n",
      "\n",
      "Tb = interp(1,Kx,T);\n",
      "\n",
      "#At Tb K, from Fig. 13.6 of Chemical Engineer's Handbook\n",
      "Kb = [2.12 ,0.85 ,0.37]\n",
      "\n",
      "#Calculation of vapour composition\n",
      "y1 = Kb[0]*x[0]*100;\n",
      "y2 = Kb[1]*x[1]*100;\n",
      "y3 = Kb[2]*x[2]*100;\n",
      "\n",
      "print '(a).'\n",
      "print ' The bubble point temperature is %f K'%Tb\n",
      "print ' At bubble point vapour contains %f percent propane, %f percent butane and %f percent pentane'%(y1,y2,y3)\n",
      "\n",
      "#(b). The dew point temperature and composition of the liquid\n",
      "T = [377.6 ,388.8]; \t\t\t#assumed temperatures (K)\n",
      "y = [0.25, 0.40, 0.35]; \t\t\t#vapour composition at dew point\n",
      "K1 = [2.6, 1.1, 0.5]; \t\t\t#at 377.6 K\n",
      "K2 = [2.9, 1.3, 0.61]; \t\t\t#at 388.8 K\n",
      "\n",
      "#At dew point, sum(yi/Ki) = 1\n",
      "Ky = [0, 0];\n",
      "for i in range(3):\n",
      "    Ky[0] = Ky[0] + y[i]/K1[i];\n",
      "    Ky[1] = Ky[1] + y[i]/K2[i];\n",
      "\n",
      "Td = interp(1,Ky,T);\n",
      "\n",
      "#At Td K,\n",
      "Kd = [2.85, 1.25, 0.59];\n",
      "\n",
      "#Calculation of liquid composition\n",
      "x1 = y[0]*100/Kd[0];\n",
      "x2 = y[1]*100/Kd[1];\n",
      "x3 = y[2]*100/Kd[2];\n",
      "\n",
      "print ' (b).'\n",
      "print ' The dew point temperature is %f K'%Td\n",
      "print ' Liquid at dew point contains %f percent propane, %f percent butane and %f percent pentane'%(x1,x2,x3)\n",
      "\n",
      "#(c). Temperature and composition when 45% of initial mixture is vaporised\n",
      "#Basis: \n",
      "F = 100; \n",
      "V = 45; \n",
      "L = 55;\n",
      "\n",
      "#For the given condition eq. 8.91 (Page no. 364) is to be satisfied\n",
      "#sum(zi/(1+ L/(VKi))) = 0.45\n",
      "\n",
      "z = [0.25, 0.4, 0.35];\n",
      "T = [366.5 ,377.6]; \t\t\t#assumed temperatures\n",
      "K1 = [2.3 ,0.9 ,0.4]; \t\t\t#at 366.5 K\n",
      "K2 = [2.6 ,1.1 ,0.5]; \t\t\t#at 377.6 K\n",
      "\n",
      "Kz = [0 ,0];\n",
      "for i in range(3):\n",
      "    Kz[0] = Kz[0] + z[i]/(1 + L/(V*K1[i]));\n",
      "    Kz[1] = Kz[1] + z[i]/(1 + L/(V*K2[i]));\n",
      "\n",
      "#The required temperature is T3\n",
      "T3 = interp(.45,Kz,T);\n",
      "\n",
      "#At T3 K\n",
      "K3 = [2.5, 1.08, 0.48];\n",
      "\n",
      "#Calculating liquid and vapour compositions\n",
      "for i in range(3):\n",
      "    y[i] = (z[i]/(1 + L/(V*K3[i])))/0.45;\n",
      "    x[i] = ((F*z[i]) - (V*y[i]))/L;\n",
      "    print (x[i]);\n",
      "\n",
      "\n",
      "print ' (c).'\n",
      "print ' The equilibrium temperature is %f K'%T3\n",
      "print ' Liquid composition in equilibrium is %f percent propane, %f percent butane \\\n",
      "and %f percent pentane'%(x[0]*100,x[1]*100,x[2]*100)\n",
      "print ' Vapour composition in equilibrium is %f percent propane, %f percent butane \\\n",
      "and %f percent pentane'%(y[0]*100,y[1]*100,y[2]*100);\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a).\n",
        " The bubble point temperature is 360.855932 K\n",
        " At bubble point vapour contains 53.000000 percent propane, 34.000000 percent butane and 12.950000 percent pentane\n",
        " (b).\n",
        " The dew point temperature is 388.800000 K\n",
        " Liquid at dew point contains 8.771930 percent propane, 32.000000 percent butane and 59.322034 percent pentane\n",
        "0.149253731343\n",
        "0.3861003861\n",
        "0.456919060052\n",
        " (c).\n",
        " The equilibrium temperature is 374.651845 K\n",
        " Liquid composition in equilibrium is 14.925373 percent propane, 38.610039 percent butane and 45.691906 percent pentane\n",
        " Vapour composition in equilibrium is 37.313433 percent propane, 41.698842 percent butane and 21.932115 percent pentane\n"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.23"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "from numpy import array\n",
      "\n",
      "# Variables\n",
      "P = 101.3; \t\t\t#total pressure (kPa)\n",
      "x1 = array([0.003, 0.449, 0.700, 0.900])\n",
      "y1 = array([0.432, 0.449, 0.520, 0.719])\n",
      "P1 = [65.31 ,63.98, 66.64, 81.31]; \t\t\t#(kPa)\n",
      "P2 = [68.64 ,68.64, 69.31, 72.24]; \t\t\t#(kPa)\n",
      "\n",
      "import math\n",
      "\n",
      "# Calculations\n",
      "#To test whether the given data are thermodynamically consistent or not\n",
      "x2 = 1-x1;\n",
      "y2 = 1-y1;\n",
      "g1= [0,0,0,0]\n",
      "g2 = [0,0,0,0]\n",
      "c=[0,0,0,0]\n",
      "import math\n",
      "for i in range(4):\n",
      "    g1[i] = (y1[i]*P)/(x1[i]*P1[i])\n",
      "    g2[i] = (y2[i]*P)/(x2[i]*P2[i])\n",
      "    c[i] = math.log(g1[i]/g2[i]) \t\t\t#k = ln (g1/g2)\n",
      "from matplotlib.pyplot import *\n",
      "plot(x1,c)\n",
      "\t\t\t#a = get(\"current_axes\"\n",
      "\t\t\t#set(a,\"x_location\",\"origin\"\n",
      "\n",
      "# Results\n",
      "show()\n",
      "\t\t\t#As seen from the graph net area is not zero\n",
      "print 'The given math.experimental data do not satisfy the Redlich-Kistern criterion'\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HverDR9ay9g/UL69gHPkH0Rl/yDuqI5lMJhNeffVV7N6924GJrM+Uk5ODnJwc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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x227f050>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The given math.experimental data do not satisfy the Redlich-Kistern criterion\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.25"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "x1 = [0.0331, 0.9652]; \t\t\t#composition of chloroform\n",
      "P = [40.84 ,84.88]; \t\t\t#total pressure for system (kPa)\n",
      "P1 = 82.35; \t\t\t#vapour pressure of chloroform at 328 K (kPa)\n",
      "P2 = 37.30; \t\t\t#vapour pressure of acetone at 328 K (kPa) \n",
      "\n",
      "\n",
      "# Calculations\n",
      "#To estimate the constants in Margules equation\n",
      "#Using eq. 8.103 and 8.104 (Page no. 375)\n",
      "g1_inf = (P[0]-(1-x1[0])*P2)/(x1[0]*P1)\n",
      "g2_inf = (P[1]-(x1[1]*P1))/((1-x1[1])*P2)\n",
      "\n",
      "import math\n",
      "A = math.log(g1_inf)\n",
      "B = math.log(g2_inf)\n",
      "\n",
      "# Results\n",
      "print 'Margules constants are:'\n",
      "print ' A = %f'%A\n",
      "print ' B = %f'%B\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Margules constants are:\n",
        " A = 0.560560\n",
        " B = 1.424762\n"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.26"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "x1 = [0., 0.033, 0.117, 0.318, 0.554, 0.736, 1.000]; \t\t\t#liquid composition of acetone\n",
      "pp1 = [0.,25.33, 59.05, 78.37, 89.58,94.77, 114.63]; \t\t\t#partial pressure of acetone (kPa)\n",
      "Pw = 19.91; \t\t\t#vapour pressure of water at 333 K (kPa)\n",
      "k = [0,0,0,0,0,0,0]\n",
      "\n",
      "# Calculations\n",
      "for i in range(1,6):\n",
      "    k[i] = x1[i]/((1.-x1[i])*pp1[i])\n",
      "\n",
      "k[6] = 0.1; \t\t\t#k(7) should tend to infinity\n",
      "from matplotlib.pyplot import *\n",
      "plot(pp1,k)\n",
      "show()\n",
      "\t\t\t#From graph% area gives the integration and hence partiaal pressure of water is calculated\n",
      "pp2 = [19.91, 19.31, 18.27, 16.99, 15.42, 13.90, 0];\n",
      "\n",
      "# Results\n",
      "print \"The results are:\"\n",
      "print '  Acetone composition      Partial pressure of water'\n",
      "for i in range(7):\n",
      "    print '       %f                       %f'%(x1[i],pp2[i])\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vez1Y5nf58mUxYcIEceXKFWGz2cScOXPEvn37An5+Z8+e7RaOvc1n7dq1YtOm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\nDH4iIoVh8BMRKcz/Axc5FnWtf/T6AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x30fad10>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The results are:\n",
        "  Acetone composition      Partial pressure of water\n",
        "       0.000000                       19.910000\n",
        "       0.033000                       19.310000\n",
        "       0.117000                       18.270000\n",
        "       0.318000                       16.990000\n",
        "       0.554000                       15.420000\n",
        "       0.736000                       13.900000\n",
        "       1.000000                       0.000000\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.27 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "P = 93.30; \t\t\t#total pressure in kPa\n",
      "T1 = 353.; \t\t\t#(K)\n",
      "T2 = 373.; \t\t\t#(K)\n",
      "Pa1 = 47.98; \t\t\t#Vapour pressure of water at 353 K (kPa)\n",
      "Pb1 = 2.67; \t\t\t#Vapour pressure of liquid at 353 K (kPa)\n",
      "Pa2 = 101.3; \t\t\t#Vapour pressure of water at 373 K (kPa)\n",
      "Pb2 = 5.33; \t\t\t#Vapour pressure of liquid at 373 K (kPa)\n",
      "\n",
      "# Calculations and Results\n",
      "#To calculate under three phase equilibrium:\n",
      "#(a). The equilibrium temperature\n",
      "P1 = Pa1+Pb1; \t\t\t#sum of vapour pressures at 353 K\n",
      "P2 = Pa2+Pb2; \t\t\t#at 373 K\n",
      "\n",
      "#Since vapour pressure vary linearly with temperature% so T at which P = 93.30 kPa\n",
      "T = T1 + ((T2-T1)/(P2-P1))*(P-P1)\n",
      "print '(a). The equilibrium temperature is %f K'%T\n",
      "\n",
      "#(b). The composition of resulting vapour\n",
      "#At equilibrium temp:\n",
      "Pa = 88.5; \t\t\t#vapour pressure of water (kPa)\n",
      "Pb = 4.80; \t\t\t#vapour pressure of liquid (kPa)\n",
      "\n",
      "#At 3-phase equilibrium% ratio of mol fractions of components is same as the ratio of vapour pressures\n",
      "P = Pa+Pb; \t\t\t#sum of vapour pressures\n",
      "y = Pa/P; \t\t\t#mole fraction of water\n",
      "print ' The vapour contains %f mol percent water vapour'%(y*100)\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a). The equilibrium temperature is 368.237585 K\n",
        " The vapour contains 94.855305 mol percent water vapour\n"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 8.28"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "T = [323 ,333, 343, 348, 353, 363, 373]; \t\t\t#temperatures (K)\n",
      "P2 = [12.40 ,19.86, 31.06, 37.99, 47.32, 70.11, 101.3]; \t\t\t#vapour pressure for benzene (kPa)\n",
      "P1 = [35.85 ,51.85, 72.91, 85.31, 100.50, 135.42, 179.14]; \t\t\t#vapour pressure for water (kPa)\n",
      "Tb = 353.1; \t\t\t#boiling temperature (K)\n",
      "Pb = 101.3; \t\t\t#boiling pressure (kPa)\n",
      "\n",
      "\n",
      "# Calculations and Results\n",
      "#To prepare temperature composition diagram\n",
      "#To find three phase temperature\n",
      "P = [0,0,0,0,0,0,0]\n",
      "for i in range(7):\n",
      "    P[i] = P1[i] + P2[i];\n",
      "from matplotlib.pyplot import *\n",
      "plot(P,T)\n",
      "\t\t\t#From graph, at P = 101.3 kPa..\n",
      "T_ = 340.; \t\t\t#three phase temperature\n",
      "\n",
      "\t\t\t#At three phase temperature\n",
      "P1_ = 71.18; \t\t\t#(kPa)\n",
      "P2_ = 30.12; \t\t\t#(kPa)\n",
      "xb_ = P1_/Pb; \t\t\t#mol fraction of benzene at triple point\n",
      "\n",
      "\t\t\t#For the dew point curve\n",
      "\t\t\t#For curve BE in temp range from 342 to 373 K\n",
      "y1 = [0,0,0,0,0,0,0]\n",
      "for i in range(2,7):\n",
      "    y1[i] = 1-(P2[i]/Pb )\n",
      "\n",
      "\t\t\t#xset('window',1\n",
      "T1 = [0,0,0,0,0,0,0]\n",
      "y1_ = [0,0,0,0,0,0,0]\n",
      "T1[0] = 342\n",
      "y1_[0] = 0.7;\n",
      "for i in range(1,6):\n",
      "    T1[i] = T[i+1];\n",
      "    y1_[i] = y1[i+1];\n",
      "\n",
      "plot(y1_,T1)\n",
      "y2 = [0,0,0,0,0,0,0]\n",
      "\t\t\t#For the curve Ae in the temp range of 342 K to 353.1 K\n",
      "for i in range(2,5):\n",
      "    y2[i] = P1[i]/Pb;\n",
      "\n",
      "T2 = [0,0,0,0,0,0,0]\n",
      "y2_ = [0,0,0,0,0,0,0]\n",
      "T2[0] = 342.;\n",
      "y2_[0] = 0.7;\n",
      "for i in range(1,4):\n",
      "    T2[i] = T[i+1]\n",
      "    y2_[i] = y2[i+1]\n",
      "\n",
      "plot(y2_,T2)\n",
      "\t\t\t#axhspan(0.25,0.75,facecolor='0.5'\n",
      "\t\t\t#title(\"Temperature Composition diagram\",\"xa,ya\",\"Temperature\"\n",
      "show()\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x2cc5c50>"
       ]
      }
     ],
     "prompt_number": 47
    }
   ],
   "metadata": {}
  }
 ]
}