Phase-Equilibrium-of-pure-substances.ipynb

{
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   "metadata": {
    "id": "JoMUEsh83hls"
   },
   "source": [
    "# **Exercises about phase equilibrium of pure substances**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "t43skNl0Vcyw"
   },
   "outputs": [],
   "source": [
    "# Loading of the necessary packages to solve the exercises\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bwrS2o8qWK4k"
   },
   "source": [
    "# Exercise 1) \n",
    "Use the temperature-vapor pressure data, given below, to calculate  $\\Delta_{sub} Hº$, $\\Delta_{vap} Hº$ e $\\Delta_{fus} Hº$ of water at 0ºC:\n",
    "\n",
    "Ice:\n",
    "\n",
    "|   |   |   |   |   |   |   |\n",
    "|---|---|---|---|---|---|---|\n",
    "|p/torr | 3.880 | 4.045 | 4.217 | 4.395 | 4.579\n",
    "|T/ºC | -2.0 | -1.5 | -1.0 | -0.5 | 0.0\n",
    "\n",
    "Water:\n",
    "\n",
    "|   |   |   |   |   |   |   |\n",
    "|---|---|---|---|---|---|---|\n",
    "|p/torr | 4.579 | 4.750 | 4.926 | 5.107 | 5.294\n",
    "|T/ºC | 0.0 | 0.5 | 1.0 | 1.5 | 2.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "a7IXD1xzYDyM"
   },
   "source": [
    "### Solution:\n",
    "According to the  Clausius-Clayperon equation, ($ \\ln(\\frac{p_2}{p_1}) = - \\frac{\\Delta_{vap} Hº}{R} \\times (\\frac{1}{T_2}-\\frac{1}{T_2})$, a plot of  ln(P) versus 1/T should be linear and have slope equal - $\\frac{\\Delta Hº}{R}$.\n",
    "\n",
    "Solving initially for the ice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 788,
     "status": "ok",
     "timestamp": 1607792508714,
     "user": {
      "displayName": "Leonardo Baptista",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjRLOphTSKAaa1hk9s-yG76WfgeyIS9u1K4s3iv8A=s64",
      "userId": "16746628627498894795"
     },
     "user_tz": 180
    },
    "id": "OPna3sQ4Yqsj",
    "outputId": "7eb54ed8-c1e5-4809-a93e-c52dcfbffc5b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope = -6129.91617\n",
      "linear coefficient=  23.97549\n",
      "enthalpy of sublimation (J/mol)=  50964.12304\n"
     ]
    }
   ],
   "source": [
    "# Arrays that will be plotted\n",
    "\n",
    "p = np.array([  3.880 , 4.045 , 4.217 , 4.395 , 4.579]) # torr\n",
    "t_celsius = np.array([ -2.0 , -1.5 , -1.0 , -0.5 , 0.0]) # ºC\n",
    "T = 273 + t_celsius\n",
    "\n",
    "lnP = np.log(p)\n",
    "iT = 1/T\n",
    "\n",
    "# linear fit\n",
    "deg = 1\n",
    "z = np.polyfit(iT, lnP, deg)\n",
    "y = np.poly1d(z)\n",
    "\n",
    "DH_sub = -8.314*z[0] # calcualtion of the sublimation deltaH\n",
    "\n",
    "print('slope = ' + format(z[0] , ' 6.5f'))  \n",
    "print('linear coefficient= ' + format(z[1] , ' 6.5f'))  \n",
    "print('enthalpy of sublimation (J/mol)= ' + format(DH_sub , ' 6.5f'))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "executionInfo": {
     "elapsed": 736,
     "status": "ok",
     "timestamp": 1607792524341,
     "user": {
      "displayName": "Leonardo Baptista",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjRLOphTSKAaa1hk9s-yG76WfgeyIS9u1K4s3iv8A=s64",
      "userId": "16746628627498894795"
     },
     "user_tz": 180
    },
    "id": "gVu_UB-vb4P3",
    "outputId": "c05c48b2-b58b-46f2-aafe-f389390ee57d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(*args, **kw)>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ln(p) versus 1/T plot:\n",
    "\n",
    "plt.plot(iT,lnP,'*')\n",
    "plt.plot(iT,y(iT), color='blue', linewidth=1)\n",
    "plt.xlabel('1/Temperature (1/K)')\n",
    "plt.ylabel('ln(P)(torr)')\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 658,
     "status": "ok",
     "timestamp": 1607792692316,
     "user": {
      "displayName": "Leonardo Baptista",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjRLOphTSKAaa1hk9s-yG76WfgeyIS9u1K4s3iv8A=s64",
      "userId": "16746628627498894795"
     },
     "user_tz": 180
    },
    "id": "NGN5e9U1aaiP",
    "outputId": "a4eed81e-a0ff-49a1-9471-9527e906509e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope = -5445.28900\n",
      "linear coefficient=  21.46772\n",
      "enthalpy of vaporization (J/mol)=  45272.13274\n"
     ]
    }
   ],
   "source": [
    "# Solving for the water\n",
    "# Arrays that will be plotted\n",
    "\n",
    "p = np.array([  4.579 , 4.750 , 4.926 , 5.107 , 5.294]) # torr\n",
    "t_celsius = np.array([ 0.0 , 0.5 , 1.0 , 1.5 , 2.0])  # ºC\n",
    "T = 273 + t_celsius\n",
    "\n",
    "lnP = np.log(p)\n",
    "iT = 1/T\n",
    "\n",
    "# linear fit\n",
    "deg = 1\n",
    "z2 = np.polyfit(iT, lnP, deg)\n",
    "y1 = np.poly1d(z2)\n",
    "DH_vap = -8.314*z2[0] # calculation of the deltaH of vaporization\n",
    "\n",
    "print('slope = ' + format(z2[0] , ' 6.5f'))  \n",
    "print('linear coefficient= ' + format(z2[1] , ' 6.5f'))  \n",
    "print('enthalpy of vaporization (J/mol)= ' + format(DH_vap , ' 6.5f'))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "executionInfo": {
     "elapsed": 723,
     "status": "ok",
     "timestamp": 1607792756862,
     "user": {
      "displayName": "Leonardo Baptista",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjRLOphTSKAaa1hk9s-yG76WfgeyIS9u1K4s3iv8A=s64",
      "userId": "16746628627498894795"
     },
     "user_tz": 180
    },
    "id": "h9ucZ5Qgbqep",
    "outputId": "b0e584e7-ef57-465b-837a-d5de67b159d7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(*args, **kw)>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ln(p) versus 1/T plot:\n",
    "\n",
    "plt.plot(iT,lnP,'*')\n",
    "plt.plot(iT,y1(iT), color='green', linewidth=1)\n",
    "plt.xlabel('1/Temperature (1/K)')\n",
    "plt.ylabel('ln(P)(torr)')\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JIWAoHfyjKqy"
   },
   "source": [
    "We know that: $ \\Delta_{sub} Hº = \\Delta_{vap} Hº + \\Delta_{fus} Hº$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 646,
     "status": "ok",
     "timestamp": 1607792745824,
     "user": {
      "displayName": "Leonardo Baptista",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjRLOphTSKAaa1hk9s-yG76WfgeyIS9u1K4s3iv8A=s64",
      "userId": "16746628627498894795"
     },
     "user_tz": 180
    },
    "id": "q5G4kcDsjeyg",
    "outputId": "91a4ea43-5e75-4692-82ac-8331c6c7f20a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "enthalpy of fusion (J/mol)=  5691.99029\n"
     ]
    }
   ],
   "source": [
    "DH_fus = DH_sub - DH_vap\n",
    "print('enthalpy of fusion (J/mol)= ' + format(DH_fus , ' 6.5f'))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6AU9_WGr67tB"
   },
   "source": [
    "Since the chemical potential depends on the vapor pressure of a pure substance, it is illustrative to plot the equations obtained for solid and liquid water in the same graph. The phase stability is related to the lower values of the vapor pressure. The most stable phase should present a lower vapor pressure. The point where the curves intersect each other is the temperature where both phases are in equilibrium."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "executionInfo": {
     "elapsed": 677,
     "status": "ok",
     "timestamp": 1607793182056,
     "user": {
      "displayName": "Leonardo Baptista",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjRLOphTSKAaa1hk9s-yG76WfgeyIS9u1K4s3iv8A=s64",
      "userId": "16746628627498894795"
     },
     "user_tz": 180
    },
    "id": "PSJB23fZmWj7",
    "outputId": "f27ec2ef-c66d-4120-b81e-f5eb5d2d6ff5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(*args, **kw)>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = np.arange(270,276,0.5) #defining a range of temperatures\n",
    "iT = 1/T\n",
    "plt.plot(T,y(iT), color='red', linewidth=1,label='solid')\n",
    "plt.plot(T,y1(iT), color='green', linewidth=1,label='liquid')\n",
    "plt.xlabel('Temperature (1/K)')\n",
    "plt.ylabel('ln(P)(torr)')\n",
    "plt.legend(handlelength=4,loc='best')\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "uPOTO4h10Nay"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "name": "Exercícios-Fis-Qui2-Eq-Fases_paper.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}