xmc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c0e42d5b",
   "metadata": {},
   "source": [
    "# Conversions of mole fractions, molality and molarity\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "939a47ff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Needed libraries\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math\n",
    "from scipy.optimize import curve_fit\n",
    "from IPython.display import Audio\n",
    "\n",
    "# soundfile = 'Pika Pika Happy.mp3' # Ignore these I was playing around with audio\n",
    "\n",
    "# Audio(soundfile,autoplay = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8b63435",
   "metadata": {},
   "source": [
    "# Definitions\n",
    "\n",
    "m = molality  \n",
    "c = molarity  \n",
    "x_salt = mole fraction of solute  \n",
    "x_solv = mole fraction of solvent  \n",
    "\n",
    "v = neu, moles of ion  \n",
    "M_solv = molecular weight of solvent  \n",
    "M_salt = molecular weight of salt  \n",
    "d_solv = density of solv  \n",
    "d_salt = density of salt  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2243eaf6",
   "metadata": {},
   "source": [
    "# Calculating m (molality) and c (molarity) from mole fractions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ab2e4b16",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Mole fractions of salt and solvent ranging from 0 to 1\n",
    "x_salt = np.linspace(0.0001,1,num=100) # Created a random range of numbers for fractions (always 0<x<1)\n",
    "x_solv = 1-x_salt\n",
    "\n",
    "# Molecular weight of salt(LiPF6) and solvent(EC) in g/mol\n",
    "M_salt = 151.905 # LiPF6\n",
    "M_solv = 88.062 # EC\n",
    "\n",
    "# Densities of chosen salt and solvent in g/mol\n",
    "#d_salt = 0 # LiPF6 # 0 because solids alone has no molar density (they do have volumetric density but that's irrelevant here)\n",
    "d_solv = 1.321 # EC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bd8a7f7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate molality(mol/kg) and molarity(mol/L)\n",
    "\n",
    "totalmass = M_salt+M_solv # total molecular mass of salt and solvent in g/mol\n",
    "\n",
    "solutionvolume = totalmass/d_solv # total volume of salt in solvent in mL\n",
    "\n",
    "c = x_salt/(solutionvolume/1000) # Convert mL to L\n",
    "\n",
    "m = x_salt/(totalmass/1000) # Convert g to kg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3a39df96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'c')"
      ]
     },
     "execution_count": 4,
     "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": [
    "# Calculate molarity from molality multiplied by d_solv\n",
    "c2 = m*d_solv\n",
    "\n",
    "# Compare c from mole fraction and c computed\n",
    "plt.plot(c) # molarity converted from mole fraction\n",
    "plt.plot(c2) # molarity calculated from molality multiplied by d_solv\n",
    "plt.xlabel('x_salt')\n",
    "plt.ylabel('c')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4dd7ece",
   "metadata": {},
   "source": [
    "Proves that c = m*d_solv (molarity = molality * density of solvent)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "219b037d",
   "metadata": {},
   "source": [
    "# Getting the factor value between c (molarity) and m (molality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c8b251c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TD vs c^1/2, Digitized from Figure 7 of a literature paper\n",
    "fig7 = pd.read_csv('TD vs c_1_2.csv') # read data from raw data from a paper\n",
    "pd.set_option(\"display.max_rows\", None) # Display all rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "114bf822",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>c^1/2</th>\n",
       "      <th>TD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.004246</td>\n",
       "      <td>1.002717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.016985</td>\n",
       "      <td>1.002717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.027601</td>\n",
       "      <td>1.002717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.038217</td>\n",
       "      <td>0.994565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.050955</td>\n",
       "      <td>0.994565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.061571</td>\n",
       "      <td>0.994565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.072187</td>\n",
       "      <td>1.002717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.082803</td>\n",
       "      <td>1.002717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.095541</td>\n",
       "      <td>1.002717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.106157</td>\n",
       "      <td>1.010870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.118896</td>\n",
       "      <td>1.010870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.129512</td>\n",
       "      <td>1.019022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.140127</td>\n",
       "      <td>1.027174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.150743</td>\n",
       "      <td>1.027174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.163482</td>\n",
       "      <td>1.043478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.174098</td>\n",
       "      <td>1.043478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.184713</td>\n",
       "      <td>1.059783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.197452</td>\n",
       "      <td>1.067935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.208068</td>\n",
       "      <td>1.076087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.218684</td>\n",
       "      <td>1.084239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.231423</td>\n",
       "      <td>1.100543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.242038</td>\n",
       "      <td>1.116848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.252654</td>\n",
       "      <td>1.116848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.263270</td>\n",
       "      <td>1.141304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.276008</td>\n",
       "      <td>1.157609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.286624</td>\n",
       "      <td>1.165761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.297240</td>\n",
       "      <td>1.173913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.307856</td>\n",
       "      <td>1.198370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.320594</td>\n",
       "      <td>1.214674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.331210</td>\n",
       "      <td>1.230978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.341826</td>\n",
       "      <td>1.247283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.354565</td>\n",
       "      <td>1.271739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0.365180</td>\n",
       "      <td>1.296196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.375796</td>\n",
       "      <td>1.312500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0.388535</td>\n",
       "      <td>1.336957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0.399151</td>\n",
       "      <td>1.353261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.409766</td>\n",
       "      <td>1.377717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0.420382</td>\n",
       "      <td>1.402174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.433121</td>\n",
       "      <td>1.426630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.443737</td>\n",
       "      <td>1.451087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.454352</td>\n",
       "      <td>1.475543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0.467091</td>\n",
       "      <td>1.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>0.477707</td>\n",
       "      <td>1.524457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>0.488323</td>\n",
       "      <td>1.548913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0.498938</td>\n",
       "      <td>1.581522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0.511677</td>\n",
       "      <td>1.614130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>0.522293</td>\n",
       "      <td>1.638587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0.532909</td>\n",
       "      <td>1.671196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0.545648</td>\n",
       "      <td>1.703804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.556263</td>\n",
       "      <td>1.728261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>0.566879</td>\n",
       "      <td>1.760870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>0.577495</td>\n",
       "      <td>1.793478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>0.590234</td>\n",
       "      <td>1.826087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>0.600849</td>\n",
       "      <td>1.866848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>0.611465</td>\n",
       "      <td>1.899457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>0.624204</td>\n",
       "      <td>1.932065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>0.634820</td>\n",
       "      <td>1.972826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>0.645435</td>\n",
       "      <td>2.013587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>0.656051</td>\n",
       "      <td>2.046196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>0.668790</td>\n",
       "      <td>2.078804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>0.679406</td>\n",
       "      <td>2.119565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>0.690021</td>\n",
       "      <td>2.160326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>0.700637</td>\n",
       "      <td>2.201087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>0.713376</td>\n",
       "      <td>2.233696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>0.723992</td>\n",
       "      <td>2.282609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>0.734607</td>\n",
       "      <td>2.323370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>0.747346</td>\n",
       "      <td>2.364130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>0.757962</td>\n",
       "      <td>2.404891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>0.770701</td>\n",
       "      <td>2.445652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>0.779193</td>\n",
       "      <td>2.494565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>0.789809</td>\n",
       "      <td>2.535326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>0.800425</td>\n",
       "      <td>2.576087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>0.811040</td>\n",
       "      <td>2.616848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>0.821656</td>\n",
       "      <td>2.657609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>0.832272</td>\n",
       "      <td>2.706522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>0.842887</td>\n",
       "      <td>2.747283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>0.851380</td>\n",
       "      <td>2.788043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>0.861996</td>\n",
       "      <td>2.828804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>0.872611</td>\n",
       "      <td>2.869565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>0.881104</td>\n",
       "      <td>2.918478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.891720</td>\n",
       "      <td>2.967391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>0.900212</td>\n",
       "      <td>3.008152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>0.910828</td>\n",
       "      <td>3.057065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>0.919321</td>\n",
       "      <td>3.097826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>0.927813</td>\n",
       "      <td>3.138587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>0.938429</td>\n",
       "      <td>3.179348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>0.946921</td>\n",
       "      <td>3.228261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>0.955414</td>\n",
       "      <td>3.260870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.963907</td>\n",
       "      <td>3.309783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>0.972399</td>\n",
       "      <td>3.350543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.980892</td>\n",
       "      <td>3.399457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>0.991507</td>\n",
       "      <td>3.440217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>0.997877</td>\n",
       "      <td>3.480978</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       c^1/2        TD\n",
       "0   0.004246  1.002717\n",
       "1   0.016985  1.002717\n",
       "2   0.027601  1.002717\n",
       "3   0.038217  0.994565\n",
       "4   0.050955  0.994565\n",
       "5   0.061571  0.994565\n",
       "6   0.072187  1.002717\n",
       "7   0.082803  1.002717\n",
       "8   0.095541  1.002717\n",
       "9   0.106157  1.010870\n",
       "10  0.118896  1.010870\n",
       "11  0.129512  1.019022\n",
       "12  0.140127  1.027174\n",
       "13  0.150743  1.027174\n",
       "14  0.163482  1.043478\n",
       "15  0.174098  1.043478\n",
       "16  0.184713  1.059783\n",
       "17  0.197452  1.067935\n",
       "18  0.208068  1.076087\n",
       "19  0.218684  1.084239\n",
       "20  0.231423  1.100543\n",
       "21  0.242038  1.116848\n",
       "22  0.252654  1.116848\n",
       "23  0.263270  1.141304\n",
       "24  0.276008  1.157609\n",
       "25  0.286624  1.165761\n",
       "26  0.297240  1.173913\n",
       "27  0.307856  1.198370\n",
       "28  0.320594  1.214674\n",
       "29  0.331210  1.230978\n",
       "30  0.341826  1.247283\n",
       "31  0.354565  1.271739\n",
       "32  0.365180  1.296196\n",
       "33  0.375796  1.312500\n",
       "34  0.388535  1.336957\n",
       "35  0.399151  1.353261\n",
       "36  0.409766  1.377717\n",
       "37  0.420382  1.402174\n",
       "38  0.433121  1.426630\n",
       "39  0.443737  1.451087\n",
       "40  0.454352  1.475543\n",
       "41  0.467091  1.500000\n",
       "42  0.477707  1.524457\n",
       "43  0.488323  1.548913\n",
       "44  0.498938  1.581522\n",
       "45  0.511677  1.614130\n",
       "46  0.522293  1.638587\n",
       "47  0.532909  1.671196\n",
       "48  0.545648  1.703804\n",
       "49  0.556263  1.728261\n",
       "50  0.566879  1.760870\n",
       "51  0.577495  1.793478\n",
       "52  0.590234  1.826087\n",
       "53  0.600849  1.866848\n",
       "54  0.611465  1.899457\n",
       "55  0.624204  1.932065\n",
       "56  0.634820  1.972826\n",
       "57  0.645435  2.013587\n",
       "58  0.656051  2.046196\n",
       "59  0.668790  2.078804\n",
       "60  0.679406  2.119565\n",
       "61  0.690021  2.160326\n",
       "62  0.700637  2.201087\n",
       "63  0.713376  2.233696\n",
       "64  0.723992  2.282609\n",
       "65  0.734607  2.323370\n",
       "66  0.747346  2.364130\n",
       "67  0.757962  2.404891\n",
       "68  0.770701  2.445652\n",
       "69  0.779193  2.494565\n",
       "70  0.789809  2.535326\n",
       "71  0.800425  2.576087\n",
       "72  0.811040  2.616848\n",
       "73  0.821656  2.657609\n",
       "74  0.832272  2.706522\n",
       "75  0.842887  2.747283\n",
       "76  0.851380  2.788043\n",
       "77  0.861996  2.828804\n",
       "78  0.872611  2.869565\n",
       "79  0.881104  2.918478\n",
       "80  0.891720  2.967391\n",
       "81  0.900212  3.008152\n",
       "82  0.910828  3.057065\n",
       "83  0.919321  3.097826\n",
       "84  0.927813  3.138587\n",
       "85  0.938429  3.179348\n",
       "86  0.946921  3.228261\n",
       "87  0.955414  3.260870\n",
       "88  0.963907  3.309783\n",
       "89  0.972399  3.350543\n",
       "90  0.980892  3.399457\n",
       "91  0.991507  3.440217\n",
       "92  0.997877  3.480978"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a30a3da3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24331fb9c10>"
      ]
     },
     "execution_count": 17,
     "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": [
    "# Define c and m\n",
    "c_fig7 = fig7['c^1/2']**2\n",
    "m_fig7_1 = c_fig7/d_solv\n",
    "\n",
    "# Plot c vs m\n",
    "plt.plot(m_fig7_1,c_fig7,label='density as a factor')\n",
    "plt.xlabel('molality(m)')\n",
    "plt.ylabel('molarity(c)')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98fc2f6c",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Equation 17"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee23b24f",
   "metadata": {},
   "source": [
    "Equation 17 from the Stewart textbook and another equation 17 from the Newman textbook provide equations that convert molarity to molality (and vice versa). The following cells examines how accurate those equations are compared to the previous density formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ff0fc49a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Eqn 17 from the Stewart textbook for Ethyl Carbonate and LiPF6\n",
    "density = (0.1428*c_fig7/1000) + d_solv\n",
    "\n",
    "# Eqn 17 from the Newman textbook\n",
    "c_solute1 = c_fig7 # mol/L\n",
    "M_solute1 = M_salt # g/mol\n",
    "cM_solute1 = c_solute1*M_solute1 # g/L\n",
    "\n",
    "m_fig7_2 = c_solute1*1000/(density*1000-cM_solute1) # mol/kg\n",
    "\n",
    "# removed sum() to get correct results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c5ee5da9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24332094760>"
      ]
     },
     "execution_count": 19,
     "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": [
    "# Plot m vs c (eqn17)\n",
    "plt.plot(m_fig7_2,c_fig7, label='using Eqn 17s')\n",
    "plt.xlabel('molality(m)')\n",
    "plt.ylabel('molarity(c)')\n",
    "\n",
    "# Plot m vs c (density as factor)\n",
    "plt.plot(m_fig7_1,c_fig7)\n",
    "\n",
    "# Plot m vs c (if slope = 1)\n",
    "m_fig7_3 = c_fig7\n",
    "plt.plot(m_fig7_3,c_fig7)\n",
    "plt.legend(['using Eqn 17s','density as a factor','slope=1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9d795e4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# % error\n",
    "\n",
    "slope_17 = c_fig7/m_fig7_2\n",
    "slope_density = c_fig7/m_fig7_1\n",
    "\n",
    "percent_error_molality = (m_fig7_1[92]-m_fig7_2[92])*100/m_fig7_1[92] #picked the 92nd value at random\n",
    "percent_error_slope = (slope_density[92]-slope_17[92])*100/slope_density[92]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9f034fd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.439701642820074"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "percent_error_slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a24004a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-12.917415427714175"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "percent_error_molality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7f5e88cb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}