pHCalc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9b805613",
   "metadata": {},
   "source": [
    "## Read Docs: https://github.com/rnelsonchem/pHcalc\n",
    "<span style=\"background-color: #FFFF00\">pka Acid Dissociation Constants: </span>http://ccc.chem.pitt.edu/wipf/MechOMs/evans_pKa_table.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9d2ed098",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pHcalc.pHcalc import Acid, Neutral, System #only x3 classes in .py\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3591c65",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">pH of 0.01 M HCl<br/> x2 ways of achieving same thing; via Neutral class & via Acid class</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "40ccb067",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9999977111816385\n"
     ]
    }
   ],
   "source": [
    "cl = Neutral(charge=-1, conc=0.01)\n",
    "system = System(cl)\n",
    "system.pHsolve()\n",
    "print(system.pH) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "06563f59",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9999977111816385\n"
     ]
    }
   ],
   "source": [
    "HCl = Acid(pKa=-8.0, charge=0, conc=0.01)\n",
    "system = System(HCl)\n",
    "system.pHsolve()\n",
    "print(system.pH) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdbf1385",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">pH of 0.01 M NaOH<br/>For alkalis only Neutral class method</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9258f9c8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.000002288818362\n"
     ]
    }
   ],
   "source": [
    "na = Neutral(charge=1, conc=0.01)\n",
    "system = System(na)\n",
    "system.pHsolve()\n",
    "print(system.pH)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5d5a125",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">pH of 0.01 M HF</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1211a2f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.76e-04\n"
     ]
    }
   ],
   "source": [
    "HF_pka=3.17\n",
    "HF_ka=10**(-1*HF_pka)\n",
    "print('%.2e' %HF_ka)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "73434602",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.6413261413574203\n"
     ]
    }
   ],
   "source": [
    "hf = Acid(Ka=6.76e-4, charge=0, conc=0.01)\n",
    "# hf = Acid(pKa=3.17, charge=0, conc=0.01) will also work\n",
    "system = System(hf)\n",
    "system.pHsolve()\n",
    "print(system.pH) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ad3c41e",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">Distribution diagram H3PO4 from WIKI</span><br/> <img src=\"https://upload.wikimedia.org/wikipedia/commons/1/16/H3PO4_speciation.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f078144d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "phos = Acid(pKa=[2.148, 7.198, 12.375], charge=0, conc=1.e-3)\n",
    "phs = np.linspace(0, 14, 1000)\n",
    "fracs = phos.alpha(phs) # alpha() calculates the fractional distribution of species \n",
    "plt.plot(phs, fracs)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5de29c9",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">These are individual plots of H3PO4, H2PO4-, HPO4_2-, and HPO4_3- <br/> Salts of H2PO−4 may be crystallised from solution by adjustment of pH to about 5.5 and salts of HPO2−4 may be crystallised from solution by adjustment of pH to about 10. The species distribution diagram shows that the concentrations of the two ions are maximum at pH 5.5 and 10</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f783eb72",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(4,1)\n",
    "ax[0].plot(phs, fracs[:,0])\n",
    "ax[0].get_xaxis().set_visible(False)\n",
    "ax[1].plot(phs, fracs[:,1])\n",
    "ax[1].get_xaxis().set_visible(False)\n",
    "ax[2].plot(phs, fracs[:,2])\n",
    "ax[2].get_xaxis().set_visible(False)\n",
    "ax[3].plot(phs, fracs[:,3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae2a933a",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">Titration Curves H3PO4 with NaOH</span><br/>Detailed description: https://chemistry.stackexchange.com/questions/36915/titration-of-h3po4-with-naoh <br/> <img src=\"https://www.chem.fsu.edu/chemlab/bluedoor_clip_image012.jpg\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8f908da5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "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",
    "    \n",
    "plt.plot(na_moles, phs)\n",
    "plt.plot([0,5.e-3], [7.198,7.198], marker = 'o', label='Buffer $pH\\ ≈\\ pK_a$')\n",
    "plt.ylim(bottom=0) # both axis meet at 0,0\n",
    "plt.xlim(left=0) # both axis meet at 0,0\n",
    "plt.legend()\n",
    "plt.yticks(range(1,15))\n",
    "plt.grid(alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "882475dc",
   "metadata": {},
   "source": [
    "## Examples from https://www.chemteam.info/AcidBase/Titration-calc-pH.html"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9bb1452",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">Calculate the pH of the solution that results when 20.0 mL of 0.600 M HCl is reacted with 25.0 mL of 0.600 M NaOH solution</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5ab6cf16",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.82390899658203\n"
     ]
    }
   ],
   "source": [
    "hcl_vol=20.e-3; naoh_vol=25.e-3;\n",
    "sol_volume = hcl_vol+naoh_vol\n",
    "\n",
    "hcl_mol=hcl_vol*0.6 # moles=vol*molarity\n",
    "naoh_mol=naoh_vol*0.6\n",
    "\n",
    "cl = Neutral(charge=-1, conc=hcl_mol/sol_volume) #Acid class with pka also works\n",
    "na = Neutral(charge=1, conc=naoh_mol/sol_volume)\n",
    "\n",
    "system = System(cl,na)\n",
    "system.pHsolve()\n",
    "print(system.pH)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a78ba1f",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">A 50.0 mL sample of 0.50 M HCl is titrated with 0.50 M NaOH. What is the pH of the solution after 28.0 mL of NaOH have been added to the acid?</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c24dc901",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8507003784179663\n"
     ]
    }
   ],
   "source": [
    "hcl_vol=50.e-3; naoh_vol=28.e-3;\n",
    "sol_volume = hcl_vol+naoh_vol\n",
    "\n",
    "hcl_mol=hcl_vol*0.5 # moles=vol*molarity\n",
    "naoh_mol=naoh_vol*0.5\n",
    "\n",
    "cl = Neutral(charge=-1, conc=hcl_mol/sol_volume) #Acid class with pka also works\n",
    "na = Neutral(charge=1, conc=naoh_mol/sol_volume)\n",
    "\n",
    "system = System(cl,na)\n",
    "system.pHsolve()\n",
    "print(system.pH)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bc9c477",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">Consider the titration of 80.0 mL of 0.100 M Ba(OH)2 by 0.400 M HCl. What is the pH of the solution (a) before adding any acid and (b) after adding 20.0 mL of HCl?</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3d8bcc96",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pure Ba(OH)_2 pH: 13.30103073120117\n",
      "Titration b/w Ba(OH)_2 & HCl pH: 12.99776611328125\n"
     ]
    }
   ],
   "source": [
    "hcl_vol=20.e-3; baoh_vol=80.e-3;\n",
    "sol_volume = hcl_vol+baoh_vol\n",
    "\n",
    "ba_pure = Neutral(charge=2, conc=0.1)\n",
    "system = System(ba_pure)\n",
    "system.pHsolve()\n",
    "print('Pure Ba(OH)_2 pH:', system.pH)\n",
    "\n",
    "hcl_mol=hcl_vol*0.4 #moles=vol*molarity\n",
    "baoh_mol=baoh_vol*0.1\n",
    "\n",
    "cl = Neutral(charge=-1, conc=hcl_mol/sol_volume) #Acid class with pka also works\n",
    "ba = Neutral(charge=2, conc=baoh_mol/sol_volume)\n",
    "\n",
    "system = System(cl,na)\n",
    "system.pHsolve()\n",
    "print('Titration b/w Ba(OH)_2 & HCl pH:', system.pH)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bd1167b",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">Let us suppose we have a solution of a triprotic acid (call its formula H3A) that is strong in all three of its hydrogens. We mix 35.0 mL of 0.0875 M acid solution with 22.0 mL of 0.0585 M Ba(OH)2. What is the pH of the resulting solution?</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "609f8844",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Titration b/w Ba(OH)_2 & H3A pH: 0.9354446411132789\n"
     ]
    }
   ],
   "source": [
    "h3a_vol=35.e-3; baoh_vol=22.e-3;\n",
    "sol_volume = h3a_vol+baoh_vol\n",
    "\n",
    "h3a_mol=h3a_vol*0.0875 #moles=vol*molarity\n",
    "baoh_mol=baoh_vol*0.0585\n",
    "\n",
    "a3 = Neutral(charge=-3, conc=h3a_mol/sol_volume) #Acid class cannot be used pka unknown\n",
    "ba = Neutral(charge=2, conc=baoh_mol/sol_volume)\n",
    "\n",
    "system = System(a3,ba)\n",
    "system.pHsolve()\n",
    "print('Titration b/w Ba(OH)_2 & H3A pH:', system.pH)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "381eb159",
   "metadata": {},
   "source": [
    "# pH including solids & saturation\n",
    "<span style=\"background-color: #FFFF00\">For known Solubility Product Constant, Ksp; what is the maximum pH that can be established in solid / aqueous $Ca(OH)^{2}$ (Ksp = 5.5e-6)</span> <br/> ${aA(s) \\rightleftharpoons  cC(aq) + dD(aq)} \\nonumber$ <br/> $K_{sp} = [C]^c [D]^d \\nonumber$ <br/><br/> For $Ca(OH)^{2}$ $K_{sp} = [Ca^{2+}][OH^-]^2\\nonumber$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b9eb8a69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 5.5 \\cdot 10^{-6} = 4 s^{3}$"
      ],
      "text/plain": [
       "Eq(5.5e-6, 4*s**3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OH molarity s: 0.0111199004528466\n"
     ]
    }
   ],
   "source": [
    "import sympy as sm\n",
    "s=sm.symbols('s')\n",
    "ksp = 5.5e-6\n",
    "eq= sm.Eq(ksp, (s)*(2*s)**2) #RHS & LHS of equation\n",
    "display(eq)\n",
    "sol=sm.solve(eq, dict=True)[0]\n",
    "print('OH molarity s:',sol[s])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a2b96a6a",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.34712905883789\n"
     ]
    }
   ],
   "source": [
    "ca = Neutral(charge=2, conc=float(sol[s]))  #convert to float bcz sol is sympy obj\n",
    "system = System(ca)\n",
    "system.pHsolve()\n",
    "print(system.pH) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea24db4f",
   "metadata": {},
   "source": [
    "# Industrial HCl furnace\n",
    "<sup> http://www.graphitequip.com/hcl-synthesis-furnace.htm</sup><br/>\n",
    "<span style=\"background-color: #FFFF00\">HCl furnace produces 37% HCl by weight having $ρ=1.18g/mL$. Part of the acid (about 500L) is in excess & has to be neutralised in a pit. How much NaOH 20% by weight having $ρ=1.22g/mL$ is required to achieve resultant pH of 8 before pit is drained?</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8543fe2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HCl molarity (M):11.961643835616439\n",
      "NaOH molarity (M):6.1\n"
     ]
    }
   ],
   "source": [
    "hcl_vol=500.; hcl_wt=0.37; hcl_rho=1.18; \n",
    "pH_target=8.0; naoh_wt=0.20;\n",
    "hcl_mw=36.5; naoh_mw=40.; naoh_rho=1.22;\n",
    "\n",
    "# Calculate HCl molarity from w.t%; assume 1L of HCl\n",
    "hcl_mass=(1000*1)*hcl_rho\n",
    "hcl_molrty=(hcl_wt*hcl_mass) / (1*hcl_mw)\n",
    "print(\"HCl molarity (M):\",hcl_molrty, sep=\"\")\n",
    "\n",
    "# Calculate NaOH molarity from w.t%; assume 1L of NaOH\n",
    "naoh_mass=(1000*1)*naoh_rho\n",
    "naoh_molrty=(naoh_wt*naoh_mass) / (1*naoh_mw)\n",
    "print(\"NaOH molarity (M):\",naoh_molrty, sep=\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0c264c22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Multiplier of argument conc= represent volume units of respective molarity\n",
    "HCl = Acid(pKa=-8.0, charge=0, conc=hcl_vol*hcl_molrty)\n",
    "x=[]\n",
    "j=np.linspace(100,1000) #arbitrary range for NaOH volume units but must not start with 0\n",
    "\n",
    "for i in j: \n",
    "    na = Neutral(charge=1, conc=i*naoh_molrty) #iterate through NaOH volume units\n",
    "    system = System(HCl,na)\n",
    "    system.pHsolve()\n",
    "    x.append(system.pH)\n",
    "\n",
    "plt.plot(j, x)\n",
    "plt.plot([0,1000], [8,8], marker = 'o', label='pH Target 8.0 achieved by ~970L NaOH addition')\n",
    "plt.xlim(left=0) \n",
    "plt.xticks(range(0,1000+1,100))\n",
    "plt.legend()\n",
    "plt.grid(alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7b4f3b54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NaOH (L): 981 | pH: 14.515621948242186\n"
     ]
    }
   ],
   "source": [
    "#more accurate algorithm to identify exact NaOH volume\n",
    "HCl = Acid(pKa=-8.0, charge=0, conc=hcl_vol*hcl_molrty)\n",
    "\n",
    "i=100 #initial guess NaOH vol\n",
    "while True:\n",
    "    i+=1 #accuracy upto 1L of NaOH\n",
    "    na = Neutral(charge=1, conc=i*naoh_molrty) #iterate through NaOH volume units\n",
    "    system = System(HCl,na)\n",
    "    system.pHsolve()\n",
    "    x=system.pH\n",
    "    if x>pH_target:\n",
    "        break\n",
    "\n",
    "print(f'NaOH (L): {i} | pH: {x}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6112620",
   "metadata": {},
   "source": [
    "<span style=\"background-color: #FFFF00\">Lets check results analytically bcz HCl & NaOH react 1:1 stoichiometric ratio</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a741e7e2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NaOH (L): 980.4626094767573\n"
     ]
    }
   ],
   "source": [
    "naoh_molesT = hcl_molesT = hcl_vol*hcl_molrty #at ph=7 equal moles\n",
    "naoh_volT=naoh_molesT/naoh_molrty\n",
    "print(f'NaOH (L): {naoh_volT}') \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "14db69ff",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.9.13 64bit [Clang 12.0.9 (https://android.googlesource.com/toolchain/llvm-project c935d99d]"
        },
        {
         "module": "IPython",
         "version": "8.4.0"
        },
        {
         "module": "OS",
         "version": "Linux 4.19.113 24856341 aarch64 with libc"
        },
        {
         "module": "sympy",
         "version": "1.11.1"
        },
        {
         "module": "numpy",
         "version": "1.20.3"
        },
        {
         "module": "pHcalc",
         "version": "0.1.2"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.9.13 64bit [Clang 12.0.9 (https://android.googlesource.com/toolchain/llvm-project c935d99d]</td></tr><tr><td>IPython</td><td>8.4.0</td></tr><tr><td>OS</td><td>Linux 4.19.113 24856341 aarch64 with libc</td></tr><tr><td>sympy</td><td>1.11.1</td></tr><tr><td>numpy</td><td>1.20.3</td></tr><tr><td>pHcalc</td><td>0.1.2</td></tr><tr><td colspan='2'>Sun Oct 30 14:34:13 2022 PKT</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.9.13 64bit [Clang 12.0.9 (https://android.googlesource.com/toolchain/llvm-project c935d99d] \\\\ \\hline\n",
       "IPython & 8.4.0 \\\\ \\hline\n",
       "OS & Linux 4.19.113 24856341 aarch64 with libc \\\\ \\hline\n",
       "sympy & 1.11.1 \\\\ \\hline\n",
       "numpy & 1.20.3 \\\\ \\hline\n",
       "pHcalc & 0.1.2 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Sun Oct 30 14:34:13 2022 PKT} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.9.13 64bit [Clang 12.0.9 (https://android.googlesource.com/toolchain/llvm-project c935d99d]\n",
       "IPython 8.4.0\n",
       "OS Linux 4.19.113 24856341 aarch64 with libc\n",
       "sympy 1.11.1\n",
       "numpy 1.20.3\n",
       "pHcalc 0.1.2\n",
       "Sun Oct 30 14:34:13 2022 PKT"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%reload_ext version_information\n",
    "%version_information sympy, numpy, pHcalc "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e84e848a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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