path: root/Introduction_To_Chemical_Engineering_Thermodynamics_by_G._Halder/Ch9.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 9 - Solutoin thermodynamic properties"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.1 Page: 338"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.1 - Page: 338\n",
      "\n",
      "\n",
      "Partial molar volume of water is 2.76e-05 cubic m/mol\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from __future__ import division\n",
    "print \"Example: 9.1 - Page: 338\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "V1_bar = 52.37*10**(-6)## [partial molar volume of ethanol, cubic m/mol]\n",
    "y1 = 0.5## [mole fraction of ethanol]\n",
    "Density = 800.21## [kg/cubic m]\n",
    "M1 = 46*10**(-3)## #[Molecular wt. of ethanol,kg/mol]\n",
    "M2 = 18*10**(-3)## [Molecular wt. of water,kg/cmol]\n",
    "#*************#\n",
    "\n",
    "y2 = 1 - y1## [mole fraction of water]\n",
    "M = y1*M1 + y2*M2## [Molecular wt. of mixture, kg/mol]\n",
    "V = M/Density## [Volume of mixture, cubic m/mol]\n",
    "# From Eqn. 9.9:\n",
    "V2_bar = (V - y1*V1_bar)/y2## [partial molar volume of water, cubic m/mol]\n",
    "print \"Partial molar volume of water is %.2e cubic m/mol\\n\"%(V2_bar)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.2 Page: 338"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.2 - Page: 338\n",
      "\n",
      "\n",
      "Volume of alcohol required is 1.223 cubic m while volume of water required is 0.842 cubic m\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.2 - Page: 338\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "Vol = 2## [Volume of the mixture, cubic m/mol]\n",
    "y1 = 0.4## [mole fraction of alcohol, cubic m/mol]\n",
    "V1_bar = 38.3*10**(-6)## [partial molar volume of alcohol, cubic m/mol]\n",
    "V2_bar = 17.2*10**(-6)## [partial molar volume of water, cubic m/mol]\n",
    "V1 = 39.21*10**(-6)## [molar volume of alcohol, cubic m/mol]\n",
    "V2 = 18*10**(-6)## [molar volume of water, cubic m/mol]\n",
    "#*************#\n",
    "\n",
    "# From Eqn. 9.9:\n",
    "V = y1*V1_bar + (1 - y1)*V2_bar## [molar volume of the solution]\n",
    "n = Vol/V## [number of moles of solution]\n",
    "n1 = y1*n## [number of moles of alcohol required]\n",
    "n2 = (1 - y1)*n## [number of moles of water required]\n",
    "V_alcohol = V1*n1## [Volume of alcohol required, cubic m]\n",
    "V_water = V2*n2## [Volume of water required, cubic m]\n",
    "print \"Volume of alcohol required is %.3f cubic m while volume of water required is %.3f cubic m\\n\"%(V_alcohol,V_water)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.3 Page: 339"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.3 - Page: 339\n",
      "\n",
      "\n",
      "Mass of water added is 1138 g\n",
      "\n",
      "The volume of vodka obtained after conversion is 3047 cubic cm\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.3 - Page: 339\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "Vol = 2000## [cubic cm]\n",
    "y1_1 = 0.96## [mass fraction of ethanol in laboratory alcohol]\n",
    "y2_1 = 0.04## [mass fraction of water in laboratory alcohol]\n",
    "y1_2 = 0.56## [mass fracion of ethanol in vodka]\n",
    "y2_2 = 0.44## [mass fraction of water in vodka]\n",
    "Vbar_water1 = 0.816## [cubic cm/g]\n",
    "Vbar_ethanol1 = 1.273## [cubic cm/g]\n",
    "Vbar_water2 = 0.953## [cubic cm/g]\n",
    "Vbar_ethanol2 = 1.243## [cubic cm/g]\n",
    "Density_water = 0.997## [cubic cm/g]\n",
    "#***************#\n",
    "\n",
    "# Solution (i)\n",
    "# From Eqn 9.9\n",
    "Va = y1_1*Vbar_ethanol1 + y2_1*Vbar_water1## [Volume of laboratory alcohol, cubic cm/g]\n",
    "mass = Vol/Va## [g]\n",
    "# Let Mw be the mass of water added in laboratory alcohol.\n",
    "# Material balance on ethanol:\n",
    "Mw = mass*y1_1/y1_2 - mass## [g]\n",
    "Vw = Mw/Density_water## [Volume of water added, cubic cm]\n",
    "print \"Mass of water added is %d g\\n\"%(Mw)#\n",
    "\n",
    "# Solution (ii)\n",
    "Mv = mass + Mw## [Mass of vodka, g]\n",
    "Vv = y1_2*Vbar_ethanol2 + y2_2*Vbar_water2## [Volume of ethanol, cubic cm/g]\n",
    "V_vodka = Vv*Mv## [Volume of vodka obtained after conversion, cubic cm]\n",
    "print \"The volume of vodka obtained after conversion is %.d cubic cm\\n\"%(V_vodka)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.4 Page: 339"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.4 - Page: 339\n",
      "\n",
      "\n",
      " Mathematics is involved in proving but just that no numerical computations are involved.\n",
      "\n",
      "\n",
      " For prove refer to this example 9.4 on page 339 of the book.\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.4 - Page: 339\\n\\n\"\n",
    "\n",
    "# Mathematics is involved in proving but just that no numerical computations are involved.\n",
    "# For prove refer to this example 9.4 on page number 339 of the book.\n",
    "\n",
    "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n",
    "print \" For prove refer to this example 9.4 on page 339 of the book.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.5 Page: 340"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.5 - Page: 340\n",
      "\n",
      "\n",
      " Mathematics is involved in proving but just that no numerical computations are involved.\n",
      "\n",
      "\n",
      " For prove refer to this example 9.5 on page 340 of the book.\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.5 - Page: 340\\n\\n\"\n",
    "\n",
    "# Mathematics is involved in proving but just that no numerical computations are involved.\n",
    "# For prove refer to this example 9.5 on page number 340 of the book.\n",
    "\n",
    "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n",
    "print \" For prove refer to this example 9.5 on page 340 of the book.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.6 Page: 341"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example - 9.6 and Page number - 341\n",
      "\n",
      "\n",
      "The expression for the partial molar volume of methanol(2) is\n",
      "V2_bar = V2 + a*x_1**(2) [cubic cm/mol]\n",
      "\n",
      "\n",
      "The partial molar volume of methanol at infinite dilution is 37.5 cubic cm/mol\n"
     ]
    }
   ],
   "source": [
    "print \"Example - 9.6 and Page number - 341\\n\\n\"\n",
    "\n",
    "#Given\n",
    "T = 25+273.15## [K]\n",
    "P = 1## [atm]\n",
    "# Component 1 = water\n",
    "# Component 2 = methanol\n",
    "a = -3.2## [cubic cm/mol]  A constant\n",
    "V2 = 40.7## [cubic cm/mol]  Molar volume of pure component 2 (methanol)\n",
    "# V1_bar = 18.1 + a*x_2**(2)\n",
    "\n",
    "# From Gibbs-Duhem equation at constant temperature and pressure we have\n",
    "# x_1*dV1_bar + x_2*dV2_bar = 0\n",
    "# dV2_bar = -(x_1/x_2)*dV1_bar = -(x_1/x_2)*a*2*x_2*dx_2 = -2*a*x_1*dx_2 = 2*a*x_1*dx_1\n",
    "\n",
    "# At x_1 = 0: x_2 = 1 and thus V2_bar = V2\n",
    "# Integrating the above equation from x_1 = 0 to x_1 in the RHS, and from V2_bar = V2 to V2 in the LHS, we get\n",
    "# V2_bar = V2 + a*x_1**(2) -  Molar volume of component 2(methanol) in the mixture \n",
    "\n",
    "print \"The expression for the partial molar volume of methanol(2) is\\nV2_bar = V2 + a*x_1**(2) [cubic cm/mol]\\n\\n\"\n",
    "\n",
    "# At infinite dilution, x_2 approach 0 and thus x_1 approach 1, therefore\n",
    "x_1 = 1## Mole fraction of component 1(water) at infinite dilution\n",
    "V2_bar_infinite = V2 + a*(x_1**(2))##[cubic cm/mol]\n",
    "\n",
    "print \"The partial molar volume of methanol at infinite dilution is %.1f cubic cm/mol\"%(V2_bar_infinite)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.7 Page: 342"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.7 - Page: 342\n",
      "\n",
      "\n"
     ]
    },
    {
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5aLSKDUFE/DG9+oKkPQAkLS5pucIjM7OO8eCDsNZasNJK0NUFy7gq2VCzPX1U0rHAWsCK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9070c5aed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For X1 = 0.5\n",
      "\n",
      "Partial molar volume of component 1 is 3.38e-05 cubic m/mol\n",
      "\n",
      "Partial molar volume of component 2 is 1.70e-05 cubic m/mol\n",
      "\n",
      "\n",
      "\n",
      "For X2 = 0.75\n",
      "\n",
      "Partial molar volume of component 1 is 3.83e-05 cubic m/mol\n",
      "\n",
      "Partial molar volume of component 2 is 1.72e-05 cubic m/mol\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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RGtjjnZrLre403AAFvD/fD1h/o4hEi0g9oAGw1Nv2cOA04IEs3yvwX3YPYF0Q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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9070ba6bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print \"Example: 9.7 - Page: 342\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "# Data = [X1 V*10**6(cubic m/mol)]#\n",
    "from numpy import mat\n",
    "Data = mat([[0, 20],[0.2, 21.5],[0.4, 24.0],[0.6, 27.4],[0.8, 32.0],[1, 40]])\n",
    "#************#\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import plot, title, xlabel, ylabel, show, grid\n",
    "plot(Data[:,0],Data[:,1])\n",
    "title(\"Example 9.7\")\n",
    "xlabel(\"Mole fraction\")\n",
    "ylabel(\"Molar Volume*10**(6)\")\n",
    "grid()#\n",
    "show()\n",
    "# Solution (i)\n",
    "print \"For X1 = 0.5\\n\"\n",
    "# A tangent is drawn to the curve at X1 = 0.5.\n",
    "# The intercept at X2 = 0 or X1 = 1, gives V1_bar.\n",
    "V1_bar1 = 33.8*10**(-6)## [cubic m/mol]\n",
    "# The intercept at X2 = 1 or X1 = 0, gives V2_bar.\n",
    "V2_bar1 = 17*10**(-6)## [cubic m/mol]\n",
    "print \"Partial molar volume of component 1 is %.2e cubic m/mol\\n\"%(V1_bar1)#\n",
    "print \"Partial molar volume of component 2 is %.2e cubic m/mol\\n\"%(V2_bar1)#\n",
    "print \"\\n\"\n",
    "\n",
    "# Solution (ii)\n",
    "print \"For X2 = 0.75\\n\"\n",
    "# A tangent is drawn to the curve at X1 = 0.75.\n",
    "# The intercept at X2 = 0 or X1 = 1, gives V1_bar.\n",
    "V1_bar2 = 36.6*10**(-6)## [cubic m/mol]\n",
    "# The intercept at X2 = 1 or X1 = 0, gives V2_bar.\n",
    "V2_bar2 = 12.4*10**(-6)## [cubic m/mol]\n",
    "point1 = mat([[0, V1_bar1],[ 1 ,V2_bar1]])\n",
    "point2 = mat([[0, V1_bar2],[1, V2_bar2]])\n",
    "plot(point1[:,0],point1[:,1],point2[:,0],point2[:,1])\n",
    "#legend(\"X1 = 0.5\"%(\"X1 = 0.75\"\n",
    "xlabel(\"Mole fraction\")\n",
    "ylabel(\"Molar Volume\")\n",
    "print \"Partial molar volume of component 1 is %.2e cubic m/mol\\n\"%(V1_bar)#\n",
    "print \"Partial molar volume of component 2 is %.2e cubic m/mol\\n\"%(V2_bar)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.8 Page: 352"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.8 - Page: 352\n",
      "\n",
      "\n",
      " Mathematics is involved in proving but just that no numerical computations are involved.\n",
      "\n",
      "\n",
      " For prove refer to this example 9.8 on page 352 of the book.\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.8 - Page: 352\\n\\n\"\n",
    "\n",
    "# Mathematics is involved in proving but just that no numerical computations are involved.\n",
    "# For prove refer to this example 9.8 on page number 352 of the book.\n",
    "\n",
    "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n",
    "print \" For prove refer to this example 9.8 on page 352 of the book.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.9 Page: 352"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.9 - Page: 352\n",
      "\n",
      "\n",
      " Mathematics is involved in proving but just that no numerical computations are involved.\n",
      "\n",
      "\n",
      " For prove refer to this example 9.9 on page 352 of the book.\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.9 - Page: 352\\n\\n\"\n",
    "\n",
    "# Mathematics is involved in proving but just that no numerical computations are involved.\n",
    "# For prove refer to this example 9.9 on page number 352 of the book.\n",
    "\n",
    "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n",
    "print \" For prove refer to this example 9.9 on page 352 of the book.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.10 Page: 354"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.10 - Page: 354\n",
      "\n",
      "\n",
      "Fugacity of the gaseous mixture is 40.095 bar\n"
     ]
    }
   ],
   "source": [
    "from math import exp, log\n",
    "print \"Example: 9.10 - Page: 354\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "x1 = 0.3## [mole fraction of component 1 in the mixture]\n",
    "x2 = 0.7## [mole fraction of component 2 in the mixture]\n",
    "phi1 = 0.7## [fugacity coeffecient of component 1 in the mixture]\n",
    "phi2 = 0.85## [fugacity coeffecient of component 2 in the mixture]\n",
    "P = 50## [bar]\n",
    "T = 273 + 100## [K]\n",
    "#*************#\n",
    "\n",
    "phi = exp(x1*log(phi1) + x2*log(phi2))## [fugacity coeffecient of the mixture]\n",
    "f = phi*P## [bar]\n",
    "print \"Fugacity of the gaseous mixture is %.3f bar\"%(f)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.11 Page: 354"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.11 - Page: 354\n",
      "\n",
      "\n",
      "Fugacity of the gaseous mixture is 45.479 bar\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.11 - Page: 354\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "x1 = 0.3## [mole fraction of hydrogen in the mixture]\n",
    "x2 = 0.25## [mole fraction of nitrogen in the mixture]\n",
    "x3 = 0.45## [mole fraction of oxygen in the mixture]\n",
    "phi1 = 0.7## [fugacity coeffecient of oxygen in the mixture]\n",
    "phi2 = 0.85## [fugacity coeffecient of nitrogen in the mixture]\n",
    "phi3 = 0.75## [fugacity coeffecient of oxygen in the mixture]\n",
    "P = 60## [bar]\n",
    "T = 273 + 150## [K]\n",
    "#***********#\n",
    "\n",
    "phi = exp(x1*log(phi1) + x2*log(phi2) + x3*log(phi3))## [fugacity coeffecient of the mixture]\n",
    "f = phi*P## [bar]\n",
    "print \"Fugacity of the gaseous mixture is %.3f bar\"%(f)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.12 Page: 356"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.12 - Page: 356\n",
      "\n",
      "\n",
      "Fugacity of liquid water is 1.0012 bar\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.12 - Page: 356\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "T = 372.12## [K]\n",
    "Psat = 100## [kPa]\n",
    "P = 300# #[kPa]\n",
    "Vspecific = 1.043*10**(-3)##[cubic m/kg]\n",
    "M = 18*10**(-3)## [molecular weight of water, kg/mol]\n",
    "R = 8.314## [J/mol K]\n",
    "#***************#\n",
    "\n",
    "Psat = Psat/100## [bar]\n",
    "P = P/100## [bar]\n",
    "Vl = Vspecific*M## [cubic m/mol]\n",
    "# Vapour is assumed to be like an ideal gas.\n",
    "phi = 1#\n",
    "fsat = Psat*phi## [bar]\n",
    "fl = fsat*exp(Vl*(P - Psat)*10**5/(R*T))## [bar]\n",
    "print \"Fugacity of liquid water is %.4f bar\"%(fl)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.13 Page: 357"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.13 - Page: 357\n",
      "\n",
      "\n",
      "The fugacity of the liquid water is 4.2051 bar\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.13 - Page: 357\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "Vl = 90.45*10**(-6)## [molar volume of liquid butadiene, cubic m/mol]\n",
    "fsat = 4.12## [bar]\n",
    "P = 10## [bar]\n",
    "Psat = 4.12## [bar]\n",
    "T = 313## [K]\n",
    "R = 8.314## [J/mol K]\n",
    "#************#\n",
    "\n",
    "fl = fsat*exp(Vl*(P - Psat)*10**5/(R*T))## [bar]\n",
    "print \"The fugacity of the liquid water is %.4f bar\"%(fl)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.14 Page: 357"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.14 - Page: 357\n",
      "\n",
      "\n",
      "The fugacity of the gas is 1411 atm \n",
      "\n",
      "The fugacity coeffecient of the gas is 1.411 atm\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.14 - Page: 357\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "b = 0.0391## [cubic dm/mol]\n",
    "P1 = 1000## [atm]\n",
    "T = 1000 + 273## [K]\n",
    "R = 0.0892## [L bar/K mol]\n",
    "#deff('[Vreal] = f1(P)','Vreal = R*T/P + b')#\n",
    "#deff('[Videal] = f2(P)','Videal = R*T/P')#\n",
    "def f1(P):\n",
    "    Vreal = R*T/P + b\n",
    "    return Vreal\n",
    "\n",
    "def f2(P):\n",
    "    Videal = R*T/P\n",
    "    return Videal\n",
    "\n",
    "def f(P):\n",
    "    f12 = f1(P)-f2(P)\n",
    "    return f12\n",
    "\n",
    "#**************#\n",
    "\n",
    "# We know that:\n",
    "# RTlog(f/P) = integral('Vreal - Videal',P,0,P)\n",
    "\n",
    "from sympy.mpmath import quad\n",
    "f = P1*exp((1/(R*T))*quad(f,[0,P1]))## [atm]\n",
    "phi = f/P1#\n",
    "print \"The fugacity of the gas is %d atm \\n\"%(f)#\n",
    "print \"The fugacity coeffecient of the gas is %.3f atm\"%(phi)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.15 Page: 359"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.15 - Page: 359\n",
      "\n",
      "\n",
      "Fugacity of liquid butadiene at 313 K & 10 bar is 8.109 bar\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.15 - Page: 359\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "Vl = 73*10**(-6)## [cubic m/mol]\n",
    "P = 275## [bar]\n",
    "Psat = 4.360## [bar]\n",
    "T = 110 + 273## [K]\n",
    "R = 8.314## [J/mol K]\n",
    "#**************#\n",
    "\n",
    "# Acetone vapour is assumed to behave like ideal gas.\n",
    "phi = 1#\n",
    "fsat = Psat## [bar]\n",
    "fl = fsat*exp(Vl*(P - Psat)*10**5/(R*T))## [bar]\n",
    "print \"Fugacity of liquid butadiene at 313 K & 10 bar is %.3f bar\"%(fl)# "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.16 Page: 362"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.16 - Page: 362\n",
      "\n",
      "\n",
      "The entropy change of mixiong is 0.749 cal/K mol\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.16 - Page: 362\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "V1 = 2.8## [Volume of Oxygen, L]\n",
    "V2 = 19.6## [Volume of hydrogen, L]\n",
    "R = 1.987## [cal/K mol]\n",
    "#**************#\n",
    "\n",
    "n1 = V1/22.4## [moles of Oxygen]\n",
    "n2 = V2/22.4## [moles of Hydrogen]\n",
    "n = n1 + n2## [total number of moles]\n",
    "x1 = n1/n## [mole fraction of Oxygen]\n",
    "x2 = n2/n## [mole fraction of Hydrogen]\n",
    "# From Eqn. 9.88:\n",
    "deltaS_mix = - (R*(x1*log(x1) + x2*log(x2)))## [cal/K mol]\n",
    "print \"The entropy change of mixiong is %.3f cal/K mol\"%(deltaS_mix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.17 Page: 363"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.17 - Page: 363\n",
      "\n",
      "\n",
      " Mathematics is involved in proving but just that no numerical computations are involved.\n",
      "\n",
      "\n",
      " For prove refer to this example 9.17 on page 363 of the book.\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.17 - Page: 363\\n\\n\"\n",
    "\n",
    "# Mathematics is involved in proving but just that no numerical computations are involved.\n",
    "# For prove refer to this example 9.17 on page number 363 of the book.\n",
    "\n",
    "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n",
    "print \" For prove refer to this example 9.17 on page 363 of the book.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.18 Page: 364"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.18 - Page: 364\n",
      "\n",
      "\n",
      "The free energy change of mixing is -1513.46 J\n",
      "\n",
      "The enthalpy change of mixing is 0 J\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.18 - Page: 364\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "n1 = 0.7## [moles of helium]\n",
    "n2 = 0.3## [moles of argon]\n",
    "R = 8.314## [J/mol K]\n",
    "T = 273 + 25## [K]\n",
    "#******************#\n",
    "\n",
    "n = n1 + n2## [total moles]\n",
    "x1 = n1/n## [mole fraction of helium]\n",
    "x2 = n2/n## [mole fraction of argon]\n",
    "deltaG_mix = n*R*T*(x1*log(x1) + x2*log(x2))## [J]\n",
    "print \"The free energy change of mixing is %.2f J\\n\"%(deltaG_mix)#\n",
    "\n",
    "# Since the gases are ideal:\n",
    "deltaH_mix = 0## [J]\n",
    "print \"The enthalpy change of mixing is %d J\\n\"%(deltaH_mix)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.19 Page: 364"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.19 - Page: 364\n",
      "\n",
      "\n",
      "Free Energy change of mixing is -15.37 J\n",
      "\n",
      "Enthalpy change in mixing is 0.00 J\n",
      "\n",
      "Entropy Change in mixing is 0.052 J/K\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.19 - Page: 364\\n\\n\"\n",
    "\n",
    "# Solution\n",
    "\n",
    "#*****Data******#\n",
    "V = 20## [Volume of vessel, L]\n",
    "V1 = 12## [Volume of Hydrogen, L]\n",
    "V2 = 10## [Volume of Nitrogen, L]\n",
    "P = 1## [atm]\n",
    "T = 298## [K]\n",
    "P1 = 1## [atm]\n",
    "P2 = 1## [atm]\n",
    "R = 0.082## [L atm/K mol]\n",
    "#************#\n",
    "\n",
    "n1 = P1*V1/(R*T)## [number of moles of Hydrogen]\n",
    "n2 = P2*V2/(R*T)## [number of moles of Nitrogen]\n",
    "n = n1 + n2## [total number of moles]\n",
    "Pfinal = n*R*T/V## [atm]\n",
    "p1 = Pfinal*n1## [partial pressure of Hydrogen, atm]\n",
    "p2 = Pfinal*n2## [partial pressure of Nitrogen, atm]\n",
    "deltaG_mix = R*T*(n1*log(p1/P1) + n2*log(p2/P2))## [J]\n",
    "print \"Free Energy change of mixing is %.2f J\\n\"%(deltaG_mix)#\n",
    "\n",
    "# Since mixing is ideal:\n",
    "deltaH_mix = 0## [J]\n",
    "print \"Enthalpy change in mixing is %.2f J\\n\"%(deltaH_mix)#\n",
    "\n",
    "deltaS_mix = - (deltaG_mix/T)## [J/K]\n",
    "print \"Entropy Change in mixing is %.3f J/K\\n\"%(deltaS_mix)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.20 Page: 367"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.20 - Page: 367\n",
      "\n",
      "\n",
      " Mathematics is involved in proving but just that no numerical computations are involved.\n",
      "\n",
      "\n",
      " For prove refer to this example 9.20 on page 367 of the book.\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.20 - Page: 367\\n\\n\"\n",
    "\n",
    "# Mathematics is involved in proving but just that no numerical computations are involved.\n",
    "# For prove refer to this example 9.20 on page number 367 of the book.\n",
    "\n",
    "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n",
    "print \" For prove refer to this example 9.20 on page 367 of the book.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: 9.21 Page: 373"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example: 9.21 - Page: 373\n",
      "\n",
      "\n",
      " Mathematics is involved in proving but just that no numerical computations are involved.\n",
      "\n",
      "\n",
      " For prove refer to this example 9.21 on page 373 of the book.\n"
     ]
    }
   ],
   "source": [
    "print \"Example: 9.21 - Page: 373\\n\\n\"\n",
    "\n",
    "# Mathematics is involved in proving but just that no numerical computations are involved.\n",
    "# For prove refer to this example 9.21 on page number 373 of the book.\n",
    "\n",
    "print \" Mathematics is involved in proving but just that no numerical computations are involved.\\n\\n\"\n",
    "print \" For prove refer to this example 9.21 on page 373 of the book.\""
   ]
  }
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