pHcalc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# pHcalc\n",
    "\n",
    "This notebook is testing the useful package [`pHcalc`](https://github.com/rnelsonchem/pHcalc) developed by Ryan Nelson. pHcalc is a Python library for systematically calculating solution pH, distribution diagrams, and titration curves.\n",
    "\n",
    "The package was installed in the Anaconda Python distribution provided by ~~[continuum.io]~~(https://www.continuum.io/) [anaconda.com](https://www.anaconda.com/). The software versions used are listed at the end of this notebook. Most of the code in this notebook is lifted directly from the documentation page on PyPI / Github.\n",
    "\n",
    "The package can be installed from PyPi (https://pypi.python.org/pypi/pHcalc) and the source code can be found here: https://github.com/rnelsonchem/pHcalc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pHcalc.pHcalc import Acid, Neutral, System\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### pH of 0.01 M HCl\n",
    "HCl is a strong acid, so we should expect complete dissociation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.99999771118\n"
     ]
    }
   ],
   "source": [
    "cl = Neutral(charge=-1, conc=0.01)\n",
    "system = System(cl)\n",
    "system.pHsolve()\n",
    "print(system.pH) # Should print 1.9999"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### pH of 0.01 M NaOH\n",
    "NaOH is a strong base, so similar to the previous case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.0000022888\n"
     ]
    }
   ],
   "source": [
    "na = Neutral(charge=1, conc=0.01)\n",
    "system = System(na)\n",
    "system.pHsolve()\n",
    "print(system.pH) # Should print 12.00000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### pH of 1 M H$_2$SO$_4$\n",
    "H$_2$SO$_4$ is a polyprotic acid with the pK$_a$ values (pK$_{a,1}$) -3 and (pK$_{a,2}$) 1.99. The pK$_{a,2}$ value is from \"Physical Constants of Organic Compounds,\" in CRC Handbook of Chemistry and Physics, 98th Edition (Internet Version 2018), John R. Rumble, ed., CRC Press/Taylor & Francis, Boca Raton, FL, and both pKa values can be found in http://evans.rc.fas.harvard.edu/pdf/evans_pKa_table.pdf."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.00390396118164\n"
     ]
    }
   ],
   "source": [
    "# we'll treat it as a neutral compound with two possible dissociations here\n",
    "so4 = Acid(pKa=[-3, 1.99], charge=0, conc=1.0)\n",
    "system = System(so4)\n",
    "system.pHsolve()\n",
    "print(system.pH)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.00433654785157\n"
     ]
    }
   ],
   "source": [
    "# we can also treat it as a negatively charged compound (complete dissociation of first proton)\n",
    "so4 = Acid(pKa=1.99, charge=-1, conc=1.0)\n",
    "system = System(so4)\n",
    "system.pHsolve()\n",
    "print(system.pH)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribution Diagrams\n",
    "For a Numpy array og pH values, a 2D array of fractional distribution values is returned, where each row is a series of distributions for each given pH. The 2D returned array can be used to plot a distribution diagram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Phosphoric Acid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  8.60553811e-06,   6.12037500e-01,   3.87952033e-01,\n",
       "         1.86113567e-06])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phos = Acid(pKa=[2.148, 7.198, 12.319], charge=0, conc=0.01)\n",
    "phos.alpha(7.0) # Input pH value -> Returns array with mole fractions of  H_3PO_4, H2PO_4^-, HPO_4^2-, and PO_4^3-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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S5cwMn2l0OKa2LmMd4f7h/LH4j0aHclrbH/+E8Pcn/LbbjA5l3FSS0ElCmIP35yXw/N5q\n+p0mKKa1VcLRt2DRJ8DmG+9oDJFxtXZc677fGx0JAG+deIu2gTbuyla9iLE4bA4+nPlhNtVsorG3\n0ehwcHV20vnyy4R98IPYInxnLZJKEjq6c2kq3YPDvF5Ub3QosPd3ICxaklBGZ7Fq/42Ob4GWo0ZH\nw/qj60kJSZny24B7ys2ZN+OWbl469pLRodD56qvIwUEi7rzD6FAmRCUJHS2dEUl6VCDP7TN4b5lh\nJxz6G8x9P4QmGhuLL1hwF1hssM/YAnZ1VzV7G/ZyU8ZNpt3CwWxSQ1NZGr+U9UfXG764rvNf6/HP\nziIgy7cWPqokoSMhBB9ZnMKe420cbzFwy4eKt6C/DRb8l3Ex+JLgWJh7IxT8XVtXYpB/V/wbi7Cw\nbpZvzIoxi5szb6a2p5Y9DXsMi2GgtJSBkhLCP+x7+2upJKGzWxYlYxHwTyN7EwX/gMBomHWVcTH4\nmrzbtMR6zJh59y63i5eOvcRliZcRFxRnSAy+6uq0qwnzD+PfR/9tWAwd6/+NsNsJu/H9hsUwWSpJ\n6CwuNIDVs2N46VCdMfO3+9vhyAaYdwtY7fq376syrtE2Pix83pDm9zXuo6mvaVqcOOdp/lZ/rk27\nlner36V/uF/39uXwMF2vvkrwNVdjDQ/Xvf1LpZKEAT6Ql0htRz8Hqzv0b7z4RXA5tXfGyvjZ/CD7\nJih/HQZ7dG9+Q9UGHDYHq5NX6972VHBD+g30D/ezpWaL7m337t6Nq72dsBtv1L1tT1BJwgDX5sTh\nZ7XwWqEBs5yKXoDo2ZC4QP+2fV3erdp+TmX6rpkYcg/x9om3WZOyBofN3JvBmdWiuEVEO6LZcHyD\n7m13b9iAJSiIoFWrdG/bE1SSMEBogJ3Vs2N4vaget1vHIaeeZji5Q3tHrGbHTFzKcghLgcP/0rXZ\nPfV76Bjs4Pp0tXXKZFktVq5Pv56ttVvpcerXE5RDQ3S/+RbBV1+Fxd9ft3Y9SSUJg9yYl0B95wAH\nTrbr12j56yDd2jbYysRZLNosp8pNMNitW7NvVL1BsD2YVUm++U7ULNamr2XQNci71e/q1mbvrt24\nOjsJXbtWtzY9TdckIYRYK4QoF0JUCCHuv8D3w4QQrwghCoQQxUKIT+oZn56uyY7Dz2bhNT0X1pW+\nAuFpED9PvzanmrnvB9cgVLyjS3PD7mHeOfkOa1LW4G/1zXeiZpEfk0+sI1bXJNG14T9YgoMJuuwy\n3dr0NN2ShBDCCjwB3ABkA3cIIbLPuewLQImUMh9YAzwmhJiSe0YE+9u4bFYU75Q26TPLaaATjm/W\nehFqqGnyUleAI1K3usTBpoN0Obu4KlVNV75UQgiuSLmC7bXbcbq8v2GjdLvpeXcTwVdc4bNDTaBv\nT2IpUCGlrJRSOoF/AOfO55NAiNCWkwYDbcCwjjHq6uqsOE629XGsWYcx0qNvabOa1GZ+l8Zqgzk3\nwJE3dFlYt6VmCzaLjZWJK73e1nSwJmUNfcN97G3Y6/W2BoqKcLW1EXzllV5vy5v0TBJJwJkryGpO\nPXamx4EsoA4oAv5bShMfVHuJrs6KBeDt0ibvN1b+HwiKgeQl3m9rqpv7fhjshKptXm9qU/UmlsQt\nIcge5PW2poNlCctw2By6DDl1b9oEVivBq3x3qAnMV7i+HjgEJALzgceFEKHnXiSEuFsIsU8Isa+5\nuVnvGD0mIcxBdkIoG72dJNwubaXwrKu14qtyaWZeCbYAbVGiF53oOkFVVxVXpFzh1XamE3+rPysS\nVrC5ZrPXh3l7Nm0mcMECn1xAdyY9XzFqgZQzvk4+9diZPgmsl5oK4Dgw99wbSSmfkVIullIujonx\n7ZO5rsmKZd+JNtp7vThGWndI21Ii81rvtTGd+AVC2mVeL15vrt4MwBXJKkl40pqUNTT0NlDeXu61\nNoYaGhgsLSX4yjVea0MveiaJvUCmEGLGqWL07cDL51xzErgaQAgRB8wBKnWMUXdXZcXhlrD5iBd7\nRBVvA0J7B6x4RsbV0HpUOx/cS7bUbiEjPIPkkGSvtTEdXZ58OQDba7d7rY2eTVqCD16zxmtt6EW3\nJCGlHAbuA94ASoHnpZTFQoh7hBD3nLrsQWClEKIIeAf4ppSyRa8YjZCXFEZEoJ2tR734z6x4SzuK\nMyjKe21MNxnXaJ+91JvoH+7nQOMBVbD2gmhHNJkRmeys2+m1Nnq3b8OemIjfTN8/PdCmZ2NSyteB\n18957Okz/n8dcJ2eMRnNYhGszIhme0ULUkrPnxPQ1wa1+2H1Nzx73+kuejaEJmu9tMWeX85zsOkg\nQ+4hdbiQl6xMWMnfyv5G/3C/x7c6kS4Xvbv3EHLdtVPi3A9VxTSBVRnRNHQNeGcqbOW72irrkXe+\nimcIoQ05Hd/ilamwu+p3YbPYWBS3yOP3VmBF4gqG3EPsb9zv8XsPlJTg7uoiaPkKj9/bCCpJmMCq\njGgAtnljyKliIwSEa8NNimdlXAODXVCzz+O33lW3i/kx8wm0B3r83gosjFuIn8XPK0NOvTu0ewYt\nX+bxextBJQkTSIkMJC0qkG0VXkgSVVtgxuXaWc2KZ824HBBQtdWjt20faKesrUwNNXmRw+ZgQdwC\ndtTt8Pi9e3ftxH/2bGzR0R6/txFUkjCJyzKi2VXZxpDLg2sH209os2/SL/fcPZX3OCIgPtfjSWJP\nwx4kkuWJKkl404qEFVR0VNDc57mZhe6BAfr3HyBoxdQYagKVJExjVUY0PYPDFNZ48CCiE6em+KWr\n3UO9Jv1yqN4Dw4Meu+Wu+l0E24PJicrx2D2V8y2NXwrA/ibP1SX6Dx5EOp0Erpg6CV4lCZNYNiMS\ngD3HPbh1eNU2bTO6mCzP3VM5W/oqGB7QZpB5yO763SyOX4zNouvkw2knKyoLh83BvgbP1ZR6d+wE\nm43AxVNn+xuVJEwiKtifjNhg9hxv9dxNq7ZC+mVqKw5vSl2BVpfwzD5OTX1NVHdXsyRu6rzImJXN\nYmNB7AKPznDq27sXR24u1uCps9eWevUwkaUzItlX1Y7LE6fVqXqEPgIjPVqXONB4AEBNfdXJ4rjF\nVHRU0DFw6cO87oEB+ouLCVw8tX52KkmYyNL0SLoHhylr6Lr0m6l6hH48WJfY37gfh83BnMg5HghM\nGctIMvZEXaK/oBCGhnAsUklC8ZKlp+sSbZd+M1WP0I8H6xIHmg6QH5Ov6hE6yY3Oxd/q75Ehp/4D\n2j0CF06tNUkqSZhIYriD5AiHZ5LEie2QtlLVI/SQemq644lL2zCuy9nF0fajLIybWi8yZuZn9SMv\nJs8jxeu+ffvxz8zEGhbmgcjMQ72CmMzS9Ej2VrVd2l73PU3QXgUpU2PFp+kFRkLMXKi+tNPODjUd\nQiJZFDu1hivMblHcIsrby+l2dk/6HnJ4mP6DB3FMsXoEqCRhOktnRNLS46SypXfyN6neo31OWeqZ\noJSxpSyFmj3gnvxiyAONB7BZbMyLmefBwJSxLIpbhFu6KWgumPQ9BsrLcff1EbhQJQnFy5acqkvs\nvZQhp5o9YLFDwnwPRaWMKWUZ9LdDa8Wkb3Gg6QDZUdke35VUubh50fOwCAuFzYWTvkf/fm1W2lSb\n2QQqSZjOzOggwhx2DlVfwpS86j2QkA/2AM8FplzcyNBe9e5JPd3pcnK45bAaajJAkD2IjPCMS0oS\nffv3Y0tMwJ6Q4MHIzEElCZMRQrAgNZyDJyeZJIadUHdQ1SP0FpWh7eU0ySRR2lbKkHuI/Jh8Dwem\njEdeTB6FzYW45eSGC/sPHiRwwdSccKCShAktSIngSFM33QOTOKegoUibjqnqEfoSApKXvlcPmqCi\n5iIAVY8wSH5MPt1D3VR1Vk34uUONjQw3NeHIz/N8YCagkoQJLUgNR0oorOmc+JNrVNHaMClLoaVc\nOw1wggpbCokLjCM2MNYLgSljyYvRXuAnU7zuL9Ce48hTSULRSX5KOAAHT05is7/q3RCWAqGJHo5K\nGdPIEN8kFtUVNRedfqFS9Jcemk6oX+ikksRAYSHY7fhnTc2FqypJmFCYw05GbPDk6hLVeyBZbQ5n\niKSFIKwTrku0DbRR01PDvGg11GQUi7AwL2YehS0TL173FxQSMHcuFn9/L0RmPJUkTGp+SjgHqzsm\ntqiusxa6alXR2ih+QRCbPeGexOGWwwAqSRgsPzqfivYKeofGv0ZJulz0FxfjmDd1f3YqSZjUgtRw\n2nqdVLf1j/9JddpcbZIXeycoZWxJC7TZZRNI7oXNhViFleyobC8GpowlPyYfiaSopWjczxmsOIbs\n65uyRWtQScK0FqREAHCwegJ1ifoCbbgjTp1oZpjEhdqiuvbj435KUUsRGeEZBNoDvRiYMpbcmFyA\nCa2X6C/UahgBU7RoDSpJmNbsuGAC/awTq0vUF2h7CNnVil3DJJ2aK197YFyXu6WbopYiNfXVBEL9\nQpkZNnNCSWKgsBBLaCh+6eneC8xgKkmYlM1qIS85bGIznOoLtJXWinFis8EWoA05jcOJrhN0O7vJ\ni56670R9SW50LiWtJeO+vr+gEMe8eQghvBiVsVSSMLG85HBKG7pxDo9jFWhXPfQ0qiRhNKsd4ueN\nu3g9Mv6titbmkB2VTXN/M019TWNe6+7tZbCiYkrXI0AlCVOblxSGc9jNkcZxbGFcf2p+t0oSxktc\nqP08XMNjXlrYXEiQPYgZYTN0CEwZS06UVs8rbike89r+4mJwu6d0PQJUkjC1eUna4SWHa8ex8rq+\nABDau1jFWEkLYahPW309huKWYnKicrBarDoEpoxlTuQcLMJCcevYSWKgUKtdTNWV1iNUkjCxtKhA\nQgJsFI03SURngn+w9wNTLi5xfMXrIfcQR9qPqKmvJuKwOZgVPmtcSaK/uBh7YiK2yEgdIjOOShIm\nJoRgXlLY+JOEGmoyh6gM8A99b93KKCo7KnG6ncyNnKtTYMp45ETlUNJaMuZC1oGSEgJypv50c5Uk\nTG5eUhhl9WMUr3tboKtGJQmzsFi0n8UYPYmytjIAsqKm5p4/vionKoe2gTYa+xpHvcbV08PQiZME\nZE/9n52uSUIIsVYIUS6EqBBC3D/KNWuEEIeEEMVCiM16xmdGuUlhOF1jFK9V0dp8khZCYzEMD456\nSWlbKQ6bg7SQNB0DU8YynuL1YGkpAAHZU3+oULckIYSwAk8ANwDZwB1CiOxzrgkHngQ+KKXMAT6i\nV3xmlZesFa8vOuQ0kiTip3YBzackLgT3EDQcHvWS0tZS5kTMUUVrk5kdORubsF20LjFQoq2lmKo7\nv55Jz57EUqBCSlkppXQC/wDWnXPNncB6KeVJACnl2JOVp7jUyEBCxype1x+CiHRwhOsWlzKGxAXa\n5/pDF/y2W7opaytTQ00m5G/1JyMiY4wkUYo1Jhp77NQ//0PPJJEEVJ/xdc2px840G4gQQmwSQuwX\nQnxMt+hMSgjBvOSwi0+DVUVr8wlPhYDw93p55zjZdZK+4T6yIlWSMKOcqByKW4tHLV4PlJRMi6Em\nMF/h2gYsAt4PXA98Vwgx+9yLhBB3CyH2CSH2NTc36x2j7nIvVrzub4f2KpUkzEYISMiDhgvvA6SK\n1uaWHZVN52AntT21533PPTDAYGUlAdNgqAn0TRK1QMoZXyefeuxMNcAbUspeKWULsAU479VPSvmM\nlHKxlHJxTEyM1wI2i3kXK143nNrWOGG+vkEpY0vI14rXrvPPKi9pK8FusTMrbJYBgSljyYk+Vby+\nwJDT4JEj4HKpnoQX7AUyhRAzhBB+wO3Ay+dc8xKwSghhE0IEAsuAUh1jNKW8JK3WcMEzr9XMJvOK\nzweXE5rPX3ld2lpKRngGdqvdgMCUsWSGZ2Kz2ChtPf/lZ6RorZKEh0kph4H7gDfQXvifl1IWCyHu\nEULcc+qaUmADUAjsAX4rpRx9esg0kRLpIMxhv3Dxur4AQpMhKFr/wJSLG0nc59QlpJSUtZWpldYm\n5mf1Y1bYrNPDgmcaKCnFEhqKPenckurUZNOzMSnl68Dr5zz29DlfPwo8qmdcZieEIDcp9MLFa1W0\nNq+oWWAPPFWX+Ojphxt6G+gY7FBFa5ObGzmXrbVbkVKetRX4SNF6Km8PfiazFa6VUeQmhVF+7rbh\ngz3QclSnxpqrAAAgAElEQVQlCbOyWLUNF+vPLl6XtGnDFXOj1HYcZpYVlUXbQBvN/e9NjpFDQwwe\nOTJtitagkoTPGCleH206o3jdUARIlSTMLP7UDCf3e8m9rK0Mi7AwO+K8iXuKiYzsqXXmkNNgZSXS\n6Zw29QhQScJn5CZeYNtwVbQ2v4R8cPacdeZ1aWspM0Jn4LCpY2bNbE7EHICzitcDxSNFa9WTUEwm\nNTKQEH8bh2u73nuwvgCC4yA0wbjAlItLOLVVyhkrr0vbStX6CB8Q7BdMakjqWT2JgdJShMMxpc+0\nPpdKEj7CYhFkJ4ZyuO6cnoTqRZhbTBZY7KfrEi39LTT1NamitY+YGzmX0rYzehIlJQTMnYuwTp/9\ntlSS8CG5SWGU1ncx7HLDUD80l6kkYXY2P4jNOj00qFZa+5asqCxqe2rpHOxEut0MlpZOq6I1qCTh\nU3KTQhkYclPZ0guNJSBdKkn4gpHtOU6tjwDtmEzF/EaK1+Vt5ThPnMDd10dAzvQpWoNKEj7lrOL1\nyBi3ShLmlzAf+lqhq5aS1hJSQlII9Qs1OiplHEaSRGlb6XtnSKiehGJWM2OCcditWvG6vgAcERCW\nMvYTFWONnPNRX0hpa6k6rtSHRDuiiXXEUtZWpm3HYbfjn5FhdFi6UknCh1jPLF7XH9J6EdNk1adP\ni88FBF21e6npqVHbcfiYuVFzTyeJgMxMhJ+f0SHpSiUJH5ObGMqRujZkY4na+dVX+AVBdCblDfsA\nVE/Cx8yNnMvxjkr6S0rxn0brI0aoJOFjcpLCSHJWIdxDqh7hSxLyKe2sBFSS8DVZkVmEd7pwd3RM\nq5XWIya8wZ8Q4oennncIOCSlPOLxqJRR5SaGkWM5tXpXJQnfEZ9HacNGYh1pRDvUjr2+ZG7kXGY0\naifUTbeiNUyiJyGl/B7wK6AT+JAQ4v88HpUyqsy4YPItJxiwBkHEDKPDUcYrIZ9SPztZAXFGR6JM\nUFJwEnOb/ZBCEDBn+k1dHjNJCCH+eOqQoNOklI1SyjeklA9LKT/rvfCUc9mtFhb5n6TSOgssarTQ\nV/THzOa43U4W6pAhXyOEILvVQUusP5bAQKPD0d14XmWqgZ1CiPQzHxRC5Akhfu+NoJSLcA0z03Wc\n/c6UUQ9pV8znyEATbiGY23uBI2gV00uqG+RIzBDD7mGjQ9HdmElCSvkd4PvA20KI9wshbhJCbAKe\nBTZ5NzzlPK1H8ZOD7HemUdPeb3Q0yjiN7CSa3XLC4EiUiRpubcXR3kdFnKSqs8rocHQ33sL1FrRj\nRV8BmoBbpZRbvBaVMro6baV1kZzB4dpOUiKnX/fXF5W1lRFu8Se+9SgMdEGAWnHtKwZKtARfFaet\nvM6IUIvpziKEeBIoAnqALGAj8CUhhHp1MkJ9AdIeSLVIPHtHWMXUSlpLmBuSioBTh0UpvmKgRDtD\noi4x4IJnXk9146lJFABzpZT3SynLpZR3AjuBXUIIdbSW3uoLEPHzmBUXdvbZEoppDbmGqOioICtu\nofbAyGFRik8YKC3FnpJCUvxslSQuREr5Gyll/zmPPQZ8GXjdW4EpF+B2a7uJJuSTmxjK4dpOVbz2\nAcc6jzHkHiI7fjEEx2s/Q8VnDJSUEJCVxdwo7WyJ6fY3N+k5lFLKjcCVHoxFGUtbpXYUZkI+uUlh\ntPY6aewaNDoqZQwjReu5kXO1BZCqJ+EzXN3dDJ08SUB2NlmRWXQ7u6nrrTM6LF1d0kR7KWW1pwJR\nxuGM7cFzk7TC51lnXiumVNpWSqAtkNTQVO1sieZy7dAoxfQGRrYHz846vZ1KWev0GnJSq7F8SX0B\nWP0gZi5ZCaEIgSpe+4CR7cEtwqL1JKRLOzRKMb2RonVAdjaZEZlYhOWs40ynA5UkfEl9AcTlgNVO\noJ+NWTHBqidhci63i/L28ve2Bx/Zb2ukV6iY2kBxCba4OGzR0ThsDmaGzVRJQjEpKbUkccb24Frx\nWs1wMrOqrir6h/vfO9M6LAUCwlVdwkcMlJSctfNrVmTW6RrTdKGShK/oOAEDHWft/JqbFEZD1wDN\n3ap4bVYlrdpwRVbkqSQhhPYzVDOcTM/d14ezsvKsJJEdlU1zfzPNfc0GRqYvlSR8xcg7z3OSBECx\nqkuYVmlbKQHWAGaEnbFjb0I+NBaDa8i4wJQxDZSVg5QE5JydJOC95D8dqCThK+oLwGKD2DN+YRO1\nGU7FdWrIyaxKWkuYHTkbm+WMHXAS8sHlhObpNUvG15wuWufknH5sbuRcBIKSNpUkFLOpOwQxWWAP\nOP1QaICd9KhAVbw2Kbd0U9ZW9t5Q04jTxWtVlzCzgeJirFFR2GJjTz8WaA8kPSxd9SQUk5FSmw2T\neP5JdDlJYWoarEmd7DpJ71AvOVE5Z38jchb4BUO9qkuY2UjRWghx1uPTrXita5IQQqwVQpQLISqE\nEPdf5LolQohhIcQtesZnWp010NcKiQvO+1ZuYhjVbf109DkNCEy5mJGpkqdnNo2wWCB+nupJmJh7\ncJDBiooLnmmdHZVNY18jrf2tBkSmP92ShBDCCjwB3ABkA3cIIc77CZy67mHgTb1iM726g9rnhAsk\niSRVlzCr0tZS7BY7s8Jmnf/N+DxtN1i3S//AlDENHjkCLteoSQKYNusl9OxJLAUqpJSVUkon8A9g\n3QWu+yLwL7RzKxTQhposNm0h3TlyE7UZTqouYT4lrSXMjpiN3XqBI0sT8mGoV9uPSzGdgeKRovX5\nSWJke47pUpfQM0kkoR2FOqLm1GOnCSGSgA8BT13sRkKIu4UQ+4QQ+5qbp8F85bqDEHt20XpERJAf\nSeEODquehKlIKSlpKzl/qGmEKl6b2kBxMZawMOxJSed9L8QvhLTQNJUkDPJL4JtSSvfFLpJSPiOl\nXCylXBwTE6NTaAaRUpvZdMZK63PlJoVSrHoSplLbU0u3s/v8mU0jYuaA1V9tz2FSWtE667yi9Yjp\nVLzWM0nUAilnfJ186rEzLQb+IYSoAm4BnhRC3KRPeCbVWQ39bZB4kSSRGEZlSy/dA2pxllmMvMs8\nb2bTCKsd4rJVT8KEpNPJ4JEjF6xHjMiOyqaut46OgQ4dIzOGnkliL5AphJghhPADbgdePvMCKeUM\nKWW6lDIdeAH4vJTyRR1jNJ+RovUFZjaNGFl5XVrfrUdEyjiUtpViE7aLn4eckK9Ng51mh9iY3eCx\nY8ihoTGTBDAtFtXpliSklMPAfcAbQCnwvJSyWAhxjxDiHr3i8Dl1p4rWsaO8IwVyTs1wKlJDTqZR\n2lrKrPBZ+Fv9R78oIV/bj6vjpH6BKWM6c3vw0Uyn4rVt7Es8R0r5OucceSqlfHqUaz+hR0ymd5Gi\n9YjYkABiQ/xVXcIkpJSUtJawJmXNxS+MP6N4HZHm9biU8RkoLsYSGIhf2ug/kzD/MJKDk6dFkjBb\n4Vo50+mV1qMPNY3IVSuvTaOht4H2wfbT7zZHFZej9RJHhhQVU+gvOkxAbi7CcvGXx6yo6VG8VknC\nzDpOQn/7RWc2jchNDKWiqYd+p1qcZbSiliIA5kXPu/iF9gAtUdTu1yEqZTzcTicDZWU48sb42aHV\nJWp6augcnNpvzlSSMLPTRetxJImkMNwSShvUegmjHW45jN1iZ07knLEvTlqs/ZzdF531rehksKwM\nhoYImJc35rXTZdtwlSTMrP4QWOwQlzvmpafPllB1CcMVtRQxN3Iufla/sS9OWgSDXdB61PuBKWPq\nL9R6gePpSeRGa3+Xh1sOezUmo6kkYWa1B7Site0iM2ROSQgLIDLITx1najCX20Vxa/HpF5AxJS/W\nPtfs815QyrgNFBVijYnGFh8/5rWhfqGkh6ZT2Dy1d/NVScKs3C4tSSQvGdflQghyEkNV8dpgxzqP\n0T/cP3Y9YkRUJviHqrqESfQXFuGYlzfqSutz5cXkUdhSiJzCa11UkjCrliPg7B53kgBtyOlIYzeD\nw6p4bZSRoYdxJwmLRZu9Vqt6EkZzdXXhPH58XENNI/Ki82gbaKO259zNI6YOlSTMqmav9nkiSSIx\njCGXpLxBrbw2SlFLESF+IaSGpo7/SUmLtDOvh/q9F5gypoHDWoIPmDf+JDEvRrt2ZEbbVKSShFnV\n7IWAcIi6wFkEo8hL1orXBdVTfz8ZsypqLmJe9DwsYgJ/WkmLwD2sTqoz2Omide4460lAZkQmAdaA\nKV2XUEnCrGr2a0XNcY6NAiRHOIgJ8efASZUkjNA31EdFR8X4i9YjRorXqi5hqP6iIvzS07GGhY37\nOXaLneyobApbVJJQ9DTYDU0lExpqAq14vSg1gv0n2r0UmHIxZW1luKRr/PWIESHxEJqk6hIGklLS\nX1hAwATqESPyYvIoay3D6ZqaRwirJGFGtQcA+d47zAlYmBbOybY+mrsHPR+XclEj49IT7kmANuSk\nehKGGa6vx9XcgmMci+jONS96Hk63k/K2ci9EZjyVJMxopGidtGjCT12UFgHAgZOqN6G3guYCkoKT\niHZET/zJSYugvQp6WzwelzK2vgPa7gaOhWPvk3auvBgtsUzVISeVJMyoZh9EzwZHxISfmpMYht0q\nOKCGnHQlpeRg00Hmx469hcoFpSzVPo+8QVB01X/gACIwkIA549hK5RxxgXHEOmKnbPFaJQmzkVJ7\noZhgPWJEgN1KblKY6knorKa7hpb+FhbGLpzcDRIXgtUPTuzwbGDKuPQdPIgjPw9hm/jpCUII5sXM\nm7LTYFWSMJv249DXMqmhphELUyMoqOnEOaw2jdPLwWZtuGLSPQl7gLao7uQuD0aljIerp5fB8nIC\nF0wywQP5MflUd1fT0j/1hgtVkjCbEzu1z6krJn2LRWkROIfdlNSrfZz0crDpICH2EDLCL3Jc6VhS\nl2s7wqpFdbrqLzgEbjeOhZNPEgvjtOceaDzgqbBMQyUJszm5Q6tFxIxxYM1FjBSv1VRY/RxsPEh+\nbP7EFtGdK3UluIfULCed9R88BELgmJ8/6XtkR2YTYA3gQJNKEoq3ndihvViMcSrWxcSFBpAU7lDF\na510DnZyrPMYC2InPjPmLCPF65M7Lz0oZdz6DxzAf/ZsrMHBk76H3WonLyZP9SQUL+tugLZKSJv8\nUNOIJekR7D7eNqV3pzSLQ02HAC49SQRGQmz2e0OOitdJl4v+goJJTX0916K4RZS1ldHtnFp7p6kk\nYSYjM1vSVl7yrZbPjKKlZ5Bjzb2XfC/l4g42HcQmbJNbRHeu1OVQvUfbKl7xusHycty9vQReQj1i\nxMK4hUjk6TcNU4VKEmZyYgfYgyB+8mOjI5bPjAJgV2XrJd9Lubj9jfvJjsrGYXNc+s1SV2pbxDcW\nX/q9lDH17t4DQODSpZd8r7zoPGzCNuXqEipJmMmJHdq4tHXic7XPlRYVSHxogEoSXtY71MvhlsMs\nTbj0FxlA60mAqkvopG/XLvzS07HHxV3yvQLtgWRHZU+5uoRKEmbR16Zt6pd2mUduJ4Rg+cxIdlWq\nuoQ3HWg8wLAcZmm8h5JEeAqEpUDVNs/cTxmVHB6mb98+Apct89g9F8YtpKiliIHhAY/d02gqSZjF\nyZ2A9Eg9YoSqS3jfnoY92C32yS+iu5AZV0DVVlWX8LKB4mLcvb0ELfdcklgSv4Qh9xAFzQUeu6fR\nVJIwi8pNYA+c1M6vo1F1Ce/bXb+b/Jh8z9QjRsxcA/3t0DA19wIyC0/WI0YsiluETdjYWTd1hgtV\nkjCLyk1aL8Lm77FbqrqEd3UOdlLWVua5esSImVdonys3efa+yln6du3CPzMTW1SUx+4ZZA8iLyaP\nnfUqSSie1FkLLUdg5pUeva0QghWzoth5rBW3W9UlPG1fwz4kkmXxnhuuACA4FmJzVJLwIul00nfg\ngEfrESOWJy6ntLWUjoGpcUKkShJmMPJiMHONx2+9enY0rb1OiuvUPk6etrthNw6bY+In0Y3HzDXa\nojq1j5NX9BcWIgcGCFzm4V4gsCJhBRLJ7obdHr+3EVSSMIPKTRAUA3E5Hr/15ZkxAGw+0uTxe093\nu+p3sTB2IXar3fM3n7kGXINQPTVeaMymZ9s2sFoJ8mA9YkRudC4h9pApU5dQScJoUmpJYuYaEMLj\nt48O9mdeUhibjzR7/N7TWXV3Ncc7j3NZkmemLJ8nbSVYbGrIyUt6tmzBMX8+1rAwj9/bZrGxJH4J\nu+p3TYnp57omCSHEWiFEuRCiQghx/wW+/1EhRKEQokgIsUMIcelLj82uoQh6mzxejzjTFbNjOHCy\ng87+Ia+1Md1sq9XWMaxOXu2dBvyDIXkpVLztnftPY8PNzQyWlBK82ks/O7S6RG1PLdXd1V5rQy+6\nJQkhhBV4ArgByAbuEEJkn3PZceAKKeU84EHgGb3iM8yRDYCAzGu91sQVc2JwuSXbK6begShG2Vqz\nldSQVNJC07zXyOzrtDcRXXXea2Ma6tmqJfjg1Zd7rY1ViasA2Fq71Wtt6EXPnsRSoEJKWSmldAL/\nANadeYGUcoeUcmR/611Aso7xGePIBu0UuuBYrzWxICWckAAbm8vVkJMnDAwPsKdhD5cne+9FBoDZ\na7XPRzZ4t51ppmfrFmwxMfjPnfyZLWNJCU1hZthMNlVv8lobetEzSSQBZ/a9ak49NppPA/+50DeE\nEHcLIfYJIfY1N/vwC193o3bAzJy1Xm3GZrVweWY0m440TYkxUqPtbdjLoGuQy5O8nCRi5kJ4GpSr\nJOEpcniY3u07CFp9OcILNcAzXZFyBfsa9vn81uGmLFwLIa5ESxLfvND3pZTPSCkXSykXx8TE6Buc\nJx19U/s827tJAuDKObE0dg1SVNvp9bamui01WwiwBrA43nOr4y9ICJhzAxzfDM4+77Y1TfTtP4C7\nq4vg1Vd4va0rU65kWA6zvW6719vyJj2TRC2QcsbXyaceO4sQIg/4LbBOSjm1lwof2QChyRDngXMI\nxnBNVhxWi2DD4QavtzWVuaWbjSc3sjJxJf5Wz62OH9Xs62F4QEsUyiXrfusthL8/wZev8npbedF5\nRPhH+PyQk55JYi+QKYSYIYTwA24HXj7zAiFEKrAeuEtKeUTH2PTn7INjG7UXAS93ewEigvxYPjOS\nDYcb1JDTJShsLqSpv4lr07030eAsaavALwTKXtOnvSlMut10v/UWQZevwhIY6PX2rBYrlydfztaa\nrQy7h73enrfoliSklMPAfcAbQCnwvJSyWAhxjxDinlOXfQ+IAp4UQhwSQuzTKz7dHX0Thvog5ybd\nmlybE09lSy8VTT26tTnVvHXiLWwWG1cke3+4AgCbnzbkVPYquNQU5ksxUFTEcGMjodddp1ubV6Ve\nRZeziz0Ne3Rr09N0rUlIKV+XUs6WUs6SUv741GNPSymfPvX/PyOljJBSzj/14eVBXwMVr4egWI+d\nHzEe1+XEA6ghp0mSUvL2ibdZkbCCEL8Q/RrO+ZC2K6xaWHdJut58E+x2gtes0a3NVUmrCLIHseG4\n704+MGXhesob7IEjb0L2OrBYdWs2LjSAhanhvK6SxKSUtJZQ11vHtWk6DTWNyLga/MOg+N/6tjuF\nSCnpfvMtgpYvxxoaqlu7/lZ/rkq5irdPvs2Qj/YEVZIwwtE3YLhfe4eosw/kJ1Ja30V5g29PyzPC\nhqoN2ISNK1O8tzr+gmz+MPf9UPoqDA/q2/YUMVBQwFB1NaFrr9e97bUz1tLt7GZH3Q7d2/YElSSM\ncHg9BMe/d56xjj6Qn4jVIlh/sEb3tn3ZsHuYVytfZVXyKsIDwvUPIPfDMNgJFe/o3/YU0PHSSwh/\nf0Ku1z9JrEhYQZh/GP+puuCyL9NTSUJvvS1w5A2Yd4uuQ00jooP9WTM7hpcO1uFSZ0yM2866nbT0\nt7Bu1rqxL/aGmWsgMBoK/mZM+z7M7XTS/fp/CLnmGqzBwbq3b7fauSb1Gjae3EjvkO8dJayShN4K\n/gHuIVhwl2EhfGhhEg1dA+w8NrWXoXjSy8deJsw/zHsb+o3Faof826H8P9Djw7sMGKBn82ZcnZ2E\nrfugYTHclHET/cP9PlnAVklCT1LCwT9D8hKI9d6+MWO5JiuOEH8b/zqghpzGo8vZxcaTG7kh/Qb8\nrH7GBbLgLnAPQ+FzxsXggzpffAlrdDRBK1caFkN+TD6zwmax/uh6w2KYLJUk9FS7H5rLYMF/GRpG\ngN3KhxYm8VphPa09qhA6llePvYrT7eSmDP3WtFxQ7FztDcbBP2tvOJQxDdXX0/Puu4TftA5hsxkW\nhxCCD2d+mMKWQo60+9Y6YZUk9LT/WbAHQs6HjY6Eu5an4XS5eW6f7+93701u6ebvZX8nNyqXnGjP\nnxw4YQvu0t5oqBPrxqX9uedASsJvv8PoUPjArA9gt9h9rjehkoReepqg8J+QfwcE6DdPezSZcSGs\nmBnFX3edVAXsi9hVt4uqriruzLrT6FA0826BgHDY9aTRkZie2+mk4/l/EnzllfglX2zDaX1EBERw\nTdo1vFjxok/tDKuShF72/k47s3j5vUZHctrHVqRR29HPO6WNRodiWn8t+yuRAZFcn67/1MkL8guC\nxZ+C0legvcroaEyte8MGXG1tRHzUJAke+Hj2x+kd6vWp3oRKEnoY6oe9v9W2BI/ONDqa067NjiMp\n3MHTm4+pTf8u4HjncbbWbOUjsz9ibMH6XEvvBmGF3b8xOhLTklLS+vtn8Zs5k6AVK4wO57Sc6ByW\nxC/hL6V/YcjtGyuwVZLQQ8Hfoa8FVnzB6EjOYrNauGfNLA6c7GBnpZoOe67/K/w/AmwB3DHX+PHs\ns4QmQO7NcOBP0NdmdDSm1PPuuwyWlRF192cRFnO9zH0i5xM09DbwRtUbRocyLub6rzcVDQ3Alp9p\ns1LSvXyS2SR8ZFEysSH+PL6xwuhQTOVE1wleO/4at86+lShHlNHhnO+y/wZnL+z4tdGRmI6UkpYn\nn8KekkLYjTcaHc55ViWtIiM8g98U/MYnthBXScLb9v8Bumrhqu/ocm7ERAXYrdy9eiY7jrWy57h6\nVzrimcJnsFvsfCL3E0aHcmFx2VoRe/dvtGNwldN6t25l4PBhrRdh4LTX0ViEhfvm30dVVxWvHHvF\n6HDGpJKENzl7YetjWg9ihk7nD0zCR5elER8awI9fL8WtZjpxpP0Ir1a+yq1zbiXaEW10OKNb8y1t\nw79tPzc6EtOQw8M0Pfoz7MnJhK8zaAuVcbgq9Spyo3J5quApnC6n0eFclEoS3rT159DbBFd915S9\niBEOPytfv34OBdUdvFxQZ3Q4hpJS8vCehwnxC+FzeZ8zOpyLi5oFCz6qzZxr9q0FWt7S8cILDB49\nSuw3vo7wM9Fkg3MIIfjSwi9R31vPX0v/anQ4F6WShLe0VGjjxXm3Qeoyo6MZ04cWJJGbFMrDG8ro\nc5p/nNRbNp7cyJ6GPdw3/z7C/MOMDmdsV31XW6D5+len/SpsV1cXzb/6NYFLlhByrc5nfkzC8oTl\nXJF8BU8VPEV9T73R4YxKJQlvkBL+83WwBcC1DxodzbhYLILvfyCH+s4BHtlQbnQ4huh2dvPQ3ofI\nCM/gltm3GB3O+ATHwtXfheNb4PC/jI7GUI0PP4yrs5O4b92PMHHPfYQQgm8t+xZSSh7a85DR4YxK\nJQlvOPBHOLZRe5cXEmd0NOO2JD2Sj69I4w87qtg9DafEPrr3UZr6mvjByh9gs5iv4DmqxZ+ChPnw\nn29A9/Q8dbBnyxY6/7WeqM98hoDsbKPDGbek4CQ+l/85NlZvNO0OsSpJeFpLBWz4lrb//5LPGB3N\nhH1j7VxSIh18/YVCugZ8Y7GPJ2yq3sS/K/7Np3M/TV5MntHhTIzFCh/6jTZR4sV7we02OiJdDbe3\nU//d7+GfmUH0feZaizQeH8/5OHnRefxw5w+p7ak1OpzzqCThSc4++NentOMmb3oaTLaIZzyC/G38\n/Nb51Hb089XnC6bFbKeTXSf59rZvMzdyLvfk32N0OJMTOxeu/7HWg51Gayeky0XdV7+Kq72dhIce\nwmLiYvVo7BY7D61+CDdu7t9yv+nOwva9VzGzcrvhxXugvlB7VxeaYHREk7YkPZJvvy+Lt0oaeeLd\nqb3Irm+oj/9+97+xCAu/WPMLc22/MVGLPw3Z6+DtB7TDiaaB5l/8gt4dO4n//vdw5Jhgl95JSglJ\n4YEVD3Co+RA/3PVDU22To5KEJ0gJ7/wASl6C6x6E2SbZDO4SfOqydNbNT+Sxt47w/N6puZ240+Xk\ny+9+mcrOSh5d/SjJIclGh3RphNB6sAn58MKnoe6g0RF5Vduf/kzrb39H+G23EX7zzUaHc8nWzljL\nPfn38GLFizxT+IzR4ZymksSlkhLe/Qls/6VWQFxxn9EReYQQgkduyePyzGjuX1/Iq4VTa/3EkHuI\nr23+Gjvrd/KDlT9gRaJ5NoG7JH6BcMc/IDAK/nQT1B0yOiKv6PjXehp/8hOCr7ma+O9+x+hwPObz\n+Z/nxpk38vihx/n94d8bHQ6gksSlcbvgze/Alke0w2De95ipF81NlL/Nym/uWsTC1Ai++PeD/GXX\nCaND8ogeZw9fePsLvFv9Lt9e9m3jT5zztNAE+MSr4B8Kf/ogVG03OiKPkVLS+rvfU/+//0vQypUk\n/fznptx6Y7KEEDx42YPckH4Dv9j/C5449IThQ08qSUzWQBc891+w83Ft6+YP/NonC9VjCfSz8edP\nL+OqObF858XDPPhqCUMu3509U91VzSc2fIK9DXv54cofmm+HV0+JSNMSRXAc/GmdtmOsj3MPDtLw\nwA9oevRRQm5YS/LTT/lkoXosNouNn17+U27KuImnC57ma5u/Rv9wv2HxCKOz1KVavHix3Ldvn76N\nVm3XitSdNbD2YVh2t77tG2DY5eZHr5Xyhx1VLEgN5+e3zmdGdJDRYY2blJLXjr/Gj3b9CKuw8ujq\nR1mZtNLosLyvvwNe+KQ26ynnw/D+xyAw0uioJmzw2DFqv/51BktKifrMp4n5yldMtwW4p0kpebb4\nWaBzSDkAAAyaSURBVH65/5ekhabx41U/9uj0bCHEfinl4jGvU0liAnqaYdNPYd/vISJdm8XkA1tu\neNJrhfXcv76QwWE3X1iTweeumEmA3Wp0WBdV1VnFT3b/hJ31O5kfM59HVj9CQrDvzj6bMNewVjPb\n9FMIjIZrvg95t/tEz9fd30/L07+h9fe/xxoYSMJDPyXkyiuNDktXu+p38d3t36Wpr4mPZn2Uz+V9\nziNbxqgk4Uk9zdrJcrue1BYsLfkMXP098A/2brsm1dQ1wA9fLeHVwnriQv35/JoMbluSYrpkUd1V\nzW8P/5aXK14mwBbAFxd8kdvm3IbVYq44dVN3CF79sjbrKT4PVn8N5t6oLcYzGXdfH+3PPU/r736H\nq6WFsJtuIvYbX8cW6Xu9IE/odnbz2L7HWH90PcF+wXwq91PcOudWQv1CJ31PlSQuldsFJ7ZD4XNQ\n+E/tfOo574drHoCY2Z5vzwftONbCL986yp6qNsIcdm5emMytS5KZExdi2N45Q64hNtdsZv3R9Wyv\n245N2Lhl9i18Nu+z5t72Wy9ut7bH08YHoeMEhKdps/Jyb4bwFENDk1IyWFpKxwsv0PnKq7i7uwla\nuYLo+75I4MIFhsZmFkfaj/CL/b9gW+02guxB/HjVj7k69epJ3cuUSUIIsRb4FWAFfiulfOic74tT\n338f0Ad8Qkp54GL39GiS6GmGqq3aR9lr0NOo7bCZdxss/7xKDhcgpWRXZRt/3X2CN4obGHJJ0qIC\nuTYrjtWzY1iQGk5IgN2r7df11rGvYR+bazazo24HvUO9xAbGsm7WOu6YewcxgTFea99nuV3a7/iu\np+DkDu2x5KWQcY22pUzSQrB67+c2wtXZSX9hIT1bttKzcSNDtbUIPz9C1l5PxO13qOQwitLWUv5Y\n8kfum3/fpNf3mC5JCCGswBHgWqAG2AvcIaUsOeOa9wFfREsSy4BfSSkvOug/6STRVa91uxuLofGw\n9tF6anWxXwjMWqO9u8q8Xpt7royppWeQDYcbeKukkZ3HWnG63AgBc+JCyEsOIzM2hIzYYDJig4kP\nC8BundiYeN9QH8e7jlPVWcXxzuMcbT9KQXMBrQPaZoQxjhhWJ6/m6tSrWZm4cvoOK01U23EoXg8l\nL0N9ASDB5oC4HG1hXvw8iMrQ6nChiZManpJDQzira3BWHcd5/DiDFcfoLyzEeewYAMLfn6AVKwi+\n8kpCr78Oa3i4Z/+NynnMmCRWAA9IKa8/9fW3AKSUPz3jmt8Am6SUfz/1dTmwRko56mbrk04Sb/yv\nNn0VtF/+uFzt3dOMK7QdNa1TZ+61EXoGhzlwoo29J5rZf7KV8oZ22vr6QbhBDCMsLiICrUSGQHiQ\nm8CAIew2J1abE2EdBEs/A+5Oeobb6BpqpdPZRt9wz+n7W4SF5OBkcqPnMT8mnwVxC5gTMccntog2\ntb42OL4FeXIX1BUi64qQ/d1It0BKkNKODIqHgCjctjDcIhg3gbhlAK4hgdspcTslw139DHf2MtzW\nhau9g+G2jrM2HrRGRuKYNw/Hgvk45s/HkZ+PxeEw8B8+/Yw3Sej5SpgEnLm/Qw1ab2Gsa5IAj5/I\n8cauWvzfST1j8dvhUx9/hIvkTQEX+f4o3xjrfv+/vbuPkaOu4zj+/uzu3dGWohgCYq+11TSYhmAh\nxDRCCBE1VQn1TxQVtQkxEUVDYkCTJv5jSDQ+JBqaBmtJaFBTMTYECg3WGPEhaBVoKUgjhrZQWzWi\nwZre3nz9Y37X7t3t7N7e0+x0P69kszO/m4fP7cN8d2Z25zd1klS4O27uZrTMyROp0+eBGSxv+ixR\nuMyJv72L/DaT5cHkjEENQpDuRZ2IGkQtb+PvwD5gH/+I4Ndp4ZqyFlH8eBZnKX5AOuef3Xwd19fr\n661Ljk5qEdSycYayiY6nzk+3VmPA8XRru3IaIxmNJeMMLck474JxGhdnDC9vMrK8yfAFTerDrwAH\nGD/+I5p7GpzaUyd/pkSGQPl9pEctozZp+GwbkOYJiW6P8lTR8/S963UdvfwPr133Va64fmEvSVLJ\nj8uSbgNuA1i1atWsljEy+jZeX9nyC2K1blTOvhjU+oSlwWDK01j46XX6vNOnUL4dnDZJ28a5L7Pt\nPO2X2e5/77zis5vnmmrUVEOt9+hM+0Rbo9agUWswVGvQqA1Ro04WdZoZjDUzxiMYz/JbFkEzg/EI\nsiwYj/ycRERelCJERkDAxMVrs8hLZT7NZIXjZ5/86W1nRjWluWVImto07TFqp+MGqGC+jhugjtua\nguUJslqD8XqDrF6fPFxvkNXq+XitTnNomNMjSxgbHkGNQENQGwqGamOMxP8YyU4xEqcYijFq0aQR\nY9RjnDpN6tFyo0k9xtN/EygiFfbIy0Aan2hrnSaVlLw9evuRZ+/7nL2XCPU4T6/TL1228L0nLmaR\nOAa0fn1iNLX1Og0RsQ3YBvnhptmEuX7zFti8ZTazmpkNjMX8Nc1TwFpJayQNAzcDu6dMsxv4hHIb\ngNc6nY8wM7OFtWh7EhHRlHQ78Bj5V2C3R8RBSZ9Jf98KPEL+zabD5F+B/dRi5TMzs+kW9ZxERDxC\nXgha27a2DAdQvf4HzczOUf1/8RYzMyuNi4SZmRVykTAzs0IuEmZmVshFwszMClX+UuGSTgKz7Xz5\nIvJrO1RFlfJWKStUK2+VskK18lYpK8wt71sjouslkitfJOZC0u9ncoGrflGlvFXKCtXKW6WsUK28\nVcoKi5PXh5vMzKyQi4SZmRUa9CKxrewAPapS3iplhWrlrVJWqFbeKmWFRcg70OckzMyss0HfkzAz\nsw4GtkhI2ijpBUmHJd1Vdp4iklZK2ifpOUkHJd1RdqZuJNUl/VHSw2Vn6UbSGyXtkvS8pEOpm92+\nJemL6XVwQNKDks4rO9MESdslnZB0oKXtTZL2Snox3V9YZsZWBXm/nl4Lz0j6qaS+6Gy7XdaWv90p\nKSRdtBDrHsgiIakOfA/4ALAO+IikdeWmKtQE7oyIdcAG4LN9nHXCHcChskPM0HeAPRHxDuCd9HFu\nSSuAzwNXR8Tl5Jfcv7ncVJPsADZOabsLeCIi1gJPpPF+sYPpefcCl0fEFcCfgbsXO1SBHUzPiqSV\nwPuBlxdqxQNZJMi7XT4cEX+JiNPAD4FNJWdqKyJejYj9afg/5BuxFeWmKiZpFPgQcF/ZWbqR9Abg\nOuD7ABFxOiL+VW6qrhrAEkkNYCnwSsl5zoiIXwL/nNK8Cbg/Dd8PfHhRQ3XQLm9EPB4REx18/5a8\nd8zSFTy2AN8CvsTsut+ekUEtEiuAIy3jR+njDe8ESauBK4HflZuko2+Tv2h763C4HGuAk8AP0uGx\n+yQtKztUkYg4BnyD/FPjq+Q9Nz5ebqquLmnpXfI4cEmZYXr0aeDRskMUkbQJOBYRTy/kega1SFSO\npPOBnwBfiIh/l52nHUk3Aici4g9lZ5mhBnAVcG9EXAm8Tn8dDpkkHc/fRF7c3gIsk/SxclPNXOpU\nrBJfp5T0FfJDvTvLztKOpKXAl4EtC72uQS0Sx4CVLeOjqa0vSRoiLxA7I+KhsvN0cA1wk6S/kh/C\ne4+kB8qN1NFR4GhETOyZ7SIvGv3qvcBLEXEyIsaAh4B3l5ypm79JuhQg3Z8oOU9Xkj4J3AjcEv37\nG4G3k39YeDq930aB/ZLePN8rGtQi8RSwVtIaScPkJ/92l5ypLUkiP2Z+KCK+WXaeTiLi7ogYjYjV\n5I/pzyOibz/pRsRx4Iiky1LTDcBzJUbq5mVgg6Sl6XVxA318oj3ZDdyahm8FflZilq4kbSQ/XHpT\nRPy37DxFIuLZiLg4Ilan99tR4Kr0mp5XA1kk0omp24HHyN9kP46Ig+WmKnQN8HHyT+V/SrcPlh3q\nHPI5YKekZ4D1wNdKzlMo7fHsAvYDz5K/f/vmF8KSHgR+A1wm6aikzcA9wPskvUi+J3RPmRlbFeT9\nLrAc2Jvea1tLDZkUZF2cdffv3pSZmZVtIPckzMxsZlwkzMyskIuEmZkVcpEwM7NCLhJmZlbIRcJs\ngUj6haSrW8ZXt7uKp1k/c5EwM7NCLhJmc5T2EJ6XtDP1SbErXVvHrPL8YzqzOUpX530JuDYinpS0\nnfzyHjcClwKn0qTDQJb6gjCrBO9JmM2PIxHxZBp+ALg2Dd8SEesjYj3gy6lY5bhImM2Pqbvk3kW3\nc4KLhNn8WNXSP/ZHgV+VGcZsvrhImM2PF8j7Hz8EXAjcW3Ies3nhE9dmc5ROXD/sE9J2LvKehJmZ\nFfKehJmZFfKehJmZFXKRMDOzQi4SZmZWyEXCzMwKuUiYmVkhFwkzMyv0f8Uev9peRkCWAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fba03e70fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phos = Acid(pKa=[2.148, 7.198, 12.319], charge=0, conc=0.01)\n",
    "phs = np.linspace(0, 14, 1000)\n",
    "fracs = phos.alpha(phs)\n",
    "plt.plot(phs, fracs)\n",
    "plt.xlabel('pH')\n",
    "plt.ylabel('$X_i$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sulphuric Acid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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b4Inr4fC+sBOJSASoJHpg75G9fOWlr7D94HbuvfJeygaXhR0pOYZPgc894p0A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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9cc88f5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "so4 = Acid(pKa=[-3, 1.99], charge=0, conc=1.0)\n",
    "phs = np.linspace(0, 14, 1000)\n",
    "fracs = so4.alpha(phs)\n",
    "plt.plot(phs, fracs)\n",
    "plt.xlabel('pH')\n",
    "plt.ylabel('$X_i$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Titration Curves\n",
    "\n",
    "### Phosphoric Acid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9ca4b8780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "na_moles = np.linspace(1e-8, 5.e-3, 500)\n",
    "sol_volume = 1. # Liter\n",
    "phos = Acid(pKa=[2.148, 7.198, 12.375], charge=0, conc=1.e-3)\n",
    "phs = []\n",
    "for mol in na_moles:\n",
    "    na = Neutral(charge=1, conc=mol/sol_volume)\n",
    "    system = System(phos, na)\n",
    "    system.pHsolve(guess_est=True)\n",
    "    phs.append(system.pH)\n",
    "plt.plot(na_moles, phs)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The version_information extension is already loaded. To reload it, use:\n",
      "  %reload_ext version_information\n"
     ]
    }
   ],
   "source": [
    "%load_ext version_information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.6.1 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]"
        },
        {
         "module": "IPython",
         "version": "5.3.0"
        },
        {
         "module": "OS",
         "version": "Linux 4.10.0 35 generic x86_64 with debian stretch sid"
        },
        {
         "module": "numpy",
         "version": "1.13.1"
        },
        {
         "module": "matplotlib",
         "version": "2.0.2"
        },
        {
         "module": "phcalc",
         "version": "0.1.2"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.6.1 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]</td></tr><tr><td>IPython</td><td>5.3.0</td></tr><tr><td>OS</td><td>Linux 4.10.0 35 generic x86_64 with debian stretch sid</td></tr><tr><td>numpy</td><td>1.13.1</td></tr><tr><td>matplotlib</td><td>2.0.2</td></tr><tr><td>phcalc</td><td>0.1.2</td></tr><tr><td colspan='2'>Thu Oct 05 08:58:49 2017 CEST</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.6.1 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] \\\\ \\hline\n",
       "IPython & 5.3.0 \\\\ \\hline\n",
       "OS & Linux 4.10.0 35 generic x86\\_64 with debian stretch sid \\\\ \\hline\n",
       "numpy & 1.13.1 \\\\ \\hline\n",
       "matplotlib & 2.0.2 \\\\ \\hline\n",
       "phcalc & 0.1.2 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Thu Oct 05 08:58:49 2017 CEST} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.6.1 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\n",
       "IPython 5.3.0\n",
       "OS Linux 4.10.0 35 generic x86_64 with debian stretch sid\n",
       "numpy 1.13.1\n",
       "matplotlib 2.0.2\n",
       "phcalc 0.1.2\n",
       "Thu Oct 05 08:58:49 2017 CEST"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%version_information numpy, matplotlib, phcalc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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