alkalinity_from_scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4a5a597b",
   "metadata": {},
   "source": [
    "# Carbonate system solved from scratch \n",
    "The following code will calculate the pH of a solution in an open carbonate system. The alkalinity of the solution is purely described by $H^+$, $OH^-$, $HCO_3^-$, and $CO_3^{-2}$. There are no other acid-base systems added in the example , like present in very organic rich soil water or in the seawater. This is a simplification made to show the concept behind it and avoid making the calculations too long and too complicated. However including further variables just can be done easily by adding the acid constants and append the conjugate base to the total alkalinity expression."
   ]
  },
  {
   "attachments": {
    "co2_closed_open_lab_EN.png": {
     "image/png": 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Uq6lzIN4+vpXh9Chej0WS/B25nJ7zZt8QxhOOb9hn9yL8Xqfi6z9uoSFBJCr1gHYah8F41RQ/yUWkmcSHgkhU6gHtNO4URIriFdZ2CiJRqQe007hTECmKV1jbKYhEpR7QTuNOQaT3k9/KYW2X/BWRqNQD2v9K8y5BpJeTkOG/FhXIl4zzIpV6eJEmX9KlK/SxforGZLEf/mgyK/gDjfoBMX/PtR5AwGpo1gO/Z0Sh7c+UBfE0g03laRp3yksMFolEIsJw2jNDQ37da8FYd5sUf9Vt6s/AjfSn1gZDt60ra9JK8VpvD2WVdSsLVn3V6jbd5cGGuc4EBjFc18AChqGrTM/SplsbuCUpOZZtGFLcsLottyJ9XDbbWqBMxK9r6apItfHrypXRwHqBSVq/LQFRlplY1x9yk0odjhpvzqY+GYQlQ7uVhQxjqBOhZXnV6dcfsXPLKNvrVSg3GxuKtdSCLiXYUEtXbX51PnUppUy8IPUrbg2/W6c2EmG4bWuIKuuj2cQng8iLF5JVILLXtzdUrpUtrG59upr8ayZ+cEW3r3VxXhq5kUza0JliWVyxxVVGZb39dCHLW6p85DalrLXbKzLw2cSngxhpYAHDGGLPUjachrFfXEzLMgzZ7EdS1lobSkPxgWAIXWOpnkY/w4hEIpFIP/xn8O9Dvftzui46f6agIOi76FBNGPRddKgmDPouOlQTBn0XHaoJg76LDtWEQd9Fh2oq+FB/AFPg794m0HfRoRrysXPu7Fv9yOYLW09+7PT6J1gS+i46VAMemlb9tdc7yLS8fqrT8Wkx8fRddKgGQLH93q+VvpJXdybbgBZy0LcEvrThSqcgUnWounaDaoD9wHFZ+/1a7YzERQ8g0jy16485i9pbNgv3798RybLzf4xJyEHfDEbiogcQaZ7azz7SnfsbPdbJjv/VHUn6Q+euf1O7vzMSFz2ASHPVXkA3+G8/va7CHc91hL4ZjMRFDyBSZ9o11R9+rIf5j7D3Z9A3g5G46AFE6kz7FOibwUhc9AAiRe0+6tqNNr/qfVG0/wflhPAufTMYiYseQKQZtc8HRuKiBxCpQ+2vc1kPI3HRA4jUnfZL48Bfsr9A2q+Nx79msQ5G4qIHEKkz7c9cG+tv3DaCkbjoAUTqTLsqf/NPXKmBkbjoAUTqSvsrr+pvOjdMPCNx0QOI1JF2/KTz4NmQ33S+KNr1R3016c9irQZG4qIHEKkr7ULDDV5gJC56AJGidh917bVE7U1gJC56AJGidh917bVE7U1gJC56AJGidh917bVE7U1gJC56AJGidh917VPhe5mnmulnJC56AJE60j4YP6Pax82eU8JIXPQAInWlXZSPB8+9zZUaGImLHkCkzrS/+krjRy9eOO2D8fj1hh9ZXTztzzR+3ujF0z4Y/5aFWhiJix5ApA61X+KyHkbiogcQqUPtzWEkLPiNZacgUq12WncKIkXtUXvHIFLU7oPttO4URIrao/aOQaSo3Qfbad0piBS19/qMvyrYTusuSR58iAUrOwWR4jbvg+207hRECtH+D/4K7DT+QVsPiDQX7f9u8oyif9PYAyIFaJ/Xkx2rYDutp8JYNdDYAyIFaGePlfDXkWldBpH60M6fy6axB0San/YD/bFugdZlEKkP7fYQkvlrz/08fuFxJ/q4GzwXitZlEGl+2iUsnzKjj3s8sgco4JEFRzVZmFk7n0x1T/7pYx1TaF0GkbrQbj+LfkNGMeXH+AsgUrh2wbTbqz1qacqPwOdBpDlqV7TARy1pzjvWTtV4tSdzPS7tSd7teaq9aZedC48+sEcQuBu6nkDrMog0b+0HR7v2IF3b82QW9o/Tx9HR2AMitc27BLBNbp8b3mPTrg9V1QcCHp3oSGTHP0qfs0RjD4gUqp0cFZ/1J3ORPoKC1mUQaX7aSTbrJK2gsQdECtCev66bCHh4KrsB6Pu6blK6PYID0NgDIgVob/DkiWnS56n9R0abyo809oBIIdpnBJHmon1WEClqj9o7BpGidh9sp3WnIFLUbgH7elh1FWxX056e4I2FVgQ8BrkViNRIO2NNZ8qlRB2IlNPOLmsw31Yg0vy0zzyUqL0QUK6H7d2avkHr4hHlVbBdTRmLT7K8qSPp4rntWGgFe6R2k2yfiNgnQvoEbMN8czQ5LGHPRKRw7Z4nYAPrNSPgWI1IPu0KnovYydPZq2B7rlOMhIrlHz+eS1DLHOGPrMdCK9iY5F2123O356DdvBApPO+VD/9WyxysrcFMEalau27zfDB9/vHX5puD1R72J7wQKVx79nGcbgHpBwUh2o8O0vyZKSJVasdzz/VFPwNqoF0/OJKJEu6xZk7ai18E5I68apmDtXhk+27xMH3YULuPeu3H7kRe9QHx/ODene6nAVtq9zHRaQ7WSmh9hmh2mD7C41SJmSJSTnv1YbLJNk/FukXSOPvQcH7aj0+zrXfyuo7VjF84TGfDr9A+bbZT/mmWOVif+8g6HylBLRGpkfbv6DaNRz+pZQ7WM77nMG2YKSLltbeCXeJbCvv4WmYhd2wBaolIjbS3gqFkELrBeQ7Thpki0ty0566+ZMffz47GhloiUg/aj+xYpyMpHqYNM0Wk+WkvcGhfW2WoJSL1oL1I79qPzov2frb5adhVNCJ1p73RBx612mlWzXc0DAKRwrT/iwGroWEYiNROe6uIiBSmneGmQMMwEClqn6Jdz9v7O/KP64CGQSDSDNr1owsZTfHgRcMwEKlWu75v3FX9XAc0DAKRZtEuFw1Rew4ahoFIDbQr50M7RtKnduS9SMnMS/FUiEiz572ImYWeChGpU+3FiIjUiXaWp2BmKYhUq12P87cLNw8qJTM/ZpaASLNox3G+SNnMi5mlIFKtdj+TZnvuJgY25c5GRJpBu5dJs7t2Y+mOHJ7sQ5sEM0tBpHbasSNzRXB7pwfy1lV067caGWaWgEhh2us/xDAzloWb7uRY38DKeyn7HCXBzFIQyau9IeyWNzZqxLlrbwjDCZpsGU5/2u1YyI8LHrd2+SeHZxtJL9ot2c4+j3/seZfDjoyhv7yrbv187Bxo33EnD9ztPrWf3HS7J6b93mPWfrrvdg5lCm7LaFod5xvCbqdAQ4BIXWuvgIYEkTrVXvz2AJE60V7/7TMNCSLNor3uA7KJbw8QqRPttWmY+JANkWbRHggidaM9EESK2qP2jkGkqN0H22ndKYgUtUftHYNIUbsPttO6UxCJEfv7rY+3qLTMWzCgdZcUf+vjr6ztEkR6mUrLvAwDWnfJXxAp2dL+zuru+ACBfkmlZX4Bgw9o3x1/Q6D3By+y8CUbuoLSq3f3dIfvWvyXjPNiGrEnXqJOHy/Rpick4h9Y7AeorIA2/fBHjfgeV/rgV6axil/Rqg/eQ0iu9cDvEbCS39OuBxhx8AbXu2Z61pW+Mv8G4wlPs6pTph3mMno54D3NYOT5195hQxe89fIvGKeeX77MK7xOeOe15xknEolEIpEnDselD7fKwgUlavdTqX2aU4/MMIxNN4T/2ra7ogu3tTQYLG26DbSuUbvWr6jdcMSyc9tare2rVy+7zcHy9paZzgAH4TSwLDkMXb2szRJd4qxL3MFoaGUOY+i2l+V1feiuDlaluhFufbC5qtqvuOWl7e3BshRHUr082JAuJfII2lHvZFrccmIj1VfU6LKF2xbvkdbNAAcxcBpExCfDcMur6Hlte7A0tMiOZVvZFLViO5Txuu3NwVajHAylZ0H8VZYsVddgcBWzbXnOtItik4yyBdV/l51olxwl6zPAQVg3V1wyDFtF4tcswPZQh4YyGuXfldFgKFMgo8FQalExgtiaubzIRrwkE63IPGpdss1b0gcbMp6kLP+ULdOOdTVtj7nLiy6lT+udq7prCrJxD1T4lmwVVkajsqG7YzaUWnJ559J6Hl3VAvuBdquXFTNBWZZY60S7bOwcBnqG9sFgXduZWSvLEmuB2geyV2F/H+mutjkYXtZsL0n1iuw0EnAT2lGvx6K07JYuq9dgbX1u2jkI3cFXJG46DGmC9tHq4Kqka0OPqizrMLa3lwbDlVDtS1t2TJHSupPj3mBpJEdKO8COVqx19appZ73OVVLWI4tu/vK6mm58ajMDGIR0I4FlyWFor9taP1jm+UemPCnbMIZOzw9DGdZKMpT5002vk9RF4dG2XzZmPoM3ok7aliU/EolEIpFIJBKJRObHz/8f7+7qmHd/zoCRc0FPaZfEM2DkXMCs9AADRs4FTEoPMGDkXMCk9AADRs4FTEoPMGDkXMCktOK+u86S8aH7lCUvDBg5FzApfu5/7Nz1j79C8bpzH915aPXgG+e+YNGYXJ+AASPnAibFxyeS6Idn396XnVqKH0vxU9kMvmXr2dktd4slcst9yJIPBoycC5gUD58599lkUXbpNNdS1uO6bAuGGNx3zo4NfhiwKf87D+sWHsoBrAuBnoB17WBSPNzKspgVc3n/CpX2ess2AamZcoZnwGooBxT/OI4WCw/lANaFQE/AunYwKR5kR072dynet4Jk9s7Z2R3ZvdO86woP/zPmnXJAzLsPegLWtYNJ8SF7uZ7U78tJ+yPJ98Ozh3rGt6aHstvjOC+5Ts/4Mx7nKQfEvPugJ2BdO5gUL99+KvnG9bwV3a3PmONbTi7sP9KN4Fut1x1eKma8rqMcEPPug56Ade1gUoK4rwd7u7C7r7nGhf4XZ1/M+D6OckDMuw96Ata1g0kJQY7/ghwFJNGyEejqR3olMOvnNpQDYt590BOwrh1MSg8wYDWUA2LefdATsK4dTEoPMGA1lANi3n3QE7CuHX9mVjrn/zBgNZQDYt590BOwriU/7yPz7/7fBrdZUQ6IefdBT8C6fnnmGRbmB+WAmHcf9ASs65XnxuPnWJwblANi3n3QE7CuT/40Fl7lyrygHBDz7oOegHU98vpYEv/C+G2uzgnKATHvPugJWNcbl96UY/x4PHhmfI0184FyQMy7D3oC1vXFU9fGvx1o3gdPjcdPsXIeUA6IefdBT8C6npC9XJOteR9cGo/neFlPOSDm3Qc9Aev64anx25d0aXkfDN7WfX9OUA6IefdBT8C6fmHe5wnlgJh3H/QErOuXmPc2UA5gXQj0BKzrl5j3NlAOYF0I9ASs65eY9zZQDmBdCPQErOuXmPc2UA5gXQj0BKzrl5j3NlAOYF0I9ASs65eY9zZQDmBdCPQErOuXmPc2UA5gXQj0BKzrl5j3NlAOYF0I9ASs65eY9zZQDmBdCPQErOuXmPc2UA5gXQj0BKzrh0tv4j4b5v25V+f3jRzlgJh3H/QErOuJV8av6wJ5f2WeN91QDoh590FPwLq+eNZut9C8X3p9/ALq5gLlgJh3H/QErOuN3+o38JL3S9fGz7JqLlAOiHn3QU/Auv64NB7/Wv6/du3XrJgPlANi3n3QE7CuRy69rffTXrMbMOYH5YCYdx/0BKzrlTfH49fnnPaY93roCVjXL6/M++75mPcG0BOwbuGhHFBc45/ZLTyUAyg7BHoC9rnwUA6IefdBT8A+Fx7KATHvPugJ2OfCQzkg5t0HPQH7XHgoB8S8+6AnYJ8LD+WAmHcf9ATsc+GhHBDz7oOegH0uPJQDYt590BOwz4WHckDMuw96Ava58FAOiHn3QU/APhceygFFiZ/TZMH5nHIAcxkCPcEFmZT/ohxQlPgDbRacHygHMJch0BNczEnhEtBk4aEcwFyGQE/APhceygEx7z7oCdjnwkM5oBuJP57Oj/9hnyFQDmAuQ6AnYJ8zc74mhUtAi5nh6OYD+wyBcgBzGQI9AfucGcqZD+wzBMoB51HijSN3dINlgX2GQDmAuQyBnoB9zgzltESm5HCXZYF9hkA5oGuJd5071uUNt2fr4Pj2DeduHpxY8aZzO7uHaDAOnHO5dfYZAuUA5jIEegL2OTOUI+w526yPnbtr6+Bof8c5TMTRvszPjb0jqwf7Mim5dfYZAuWAriVKDm20osjWlWPRJ4If7B1ocUeUHknuD9gqHGNbIewzBMoBzGUI9ATsc2YoR9h1ThdHedH3ZOuXmbp380iL8np6KNOUy/SR+SSwzxAoBzyOvEuuWcqKewWNBdhnCJQDmMsQ6AnY58xQjuDJ+wOXHhCzoiQehTLsMwTKAT3knaR5F7lJOSsm24cH9hkC5QDmMgR6AvY5M5QjSN5JmnfRn5SzIrcPH+wzBMoBve7vkmY9ccsRzdoEOYuhIBKPTw/RPgH7DIFyAHMZAj0B+5wZyhEK+7vuGcdaTvZ3Ke6jZLOj7eVdgn2GQDmg17wLu9CoJ/UH+wd2VrsnZzW5jJEF2ydgnyFQDmAuQ6AnYJ8zQznC5HGe6dWT+r3do9PbUnxwenJXToKYjBvl3Z59hkA5oGuJdzn2m9icD6H0aE9OXbiet+KNfds49JpVl0XYZwiUA5jLEOgJ2OfMUI6w527qQi5q7Xp+H7vGoR7+cT1vxZu3beakmHtTm8A+Q6Ac0LXEItXnq4SD9DSXwj5DoBzAXIZAT8A+Z4ZyJjnKrnyq2C+f/dhnCJQDupH4PxxdET19p+cuHxPvUcG/2GcIlAOYyxDoCdjnzPgnRTX7rmpSdNcvnftmnxQuAS0WHsoBzGUI9ATsc+GhHBDz7oOegH0uPJQDYt590BOwz4WHckDMuw96Ava58FAOiHn3QU/APhceygEx7z7oCdjnwkM5IObdBz0B+1x4KAf4Jf6LbxPnwHfsslcoBzCXIdATsM8LNilcAlpUft7WBnbZK5QDmMsQ6AnY5wWbFC4BLWLe87DPJzDvO/hw9dC5B7bcc27HbgI6uWvfJdgXLFWwy16hHMBchkBPwD4nJuUBP1zdx5fKJ3dv6tdL+oHqYkwKl4AWk3nnl6j4TlW/JTw+PTkUuXp31MnpsWwGU75aYJe9QjmAuQyBnoB9TkxK8iWq5FheZSb2ZSYOZB4WZFK4BLSYlve72c2AIs32f60rfYuWwi6r6ORqiXIAcxkCPQH7nJb3dCYWZ1K4BLQo5z3hSHUmX5nJOgrpDQQ+2GUVtJoL7LKvvCfkZmJxJoVLQIty3rP9XV6S/V02AXxBKHVyrhPFviMbu6yCVoHU3KFBOYC5DIGegH2W857t7/KS7O/FSTmWcfq+eGaXVdAqEAk97Q4NygHBedfe9/T8fgP3Q5+cPpCa22bHu2mKsMsqaFUgu3CUot6ZY9dLRY49Gxm77D/vJzJIPakf7JUn5cD35Tq7rIJWeRpdOB55NjJ22SbvO5BwD1v1yYGMAGk51vv7d/ZMmB74fLcPsMsqaJUjd+EoRd3GZIPbmRTpuRGv17zL9bzdEXgb1/M2E0hLflL0VpPktJiHXVZBqxzNLhw9N+LNkvemHLe4E4xWGbkLx7Qok1zUeDj96Ek5gLkMgZ6AfbadFO99VOyyClplNLpw9NyjJrDLRnn/jj4h6P7uSUbdR5I0y5BjWLKHZMWJvOtxzrMjscuO8t5mUnR/9yQjeFKkG5ay4uSFoxxlhNJRkF02ynuPcHQZuQtHXC8KIlE2KT2S2moV7LKjvPcI9WTIhu6/cKy6ms5gl+c+7yqMF452Vjs+PdYzvjX5rltysMsLmPdpF47eq+kMdnn+856/cLSi2xWdevXgPWbmYJcXMO+VF45VV9MZ7HIB8j4F37v2DHZ5IfNejfdqOoNdnre8P+Lw6tH9feqp7BG7XPy8N5+UiqvpjKpJ4RLQwsdP3zcfjJ/v2dME37N5Vh599xN77C/vCzwpXAJa+Phv9jQD2abXNZQDmMsQ6AnYp48FnhQuAS18cJgzwa66h3IAcxkCPQH79EFdM8GuuodyQMy7D3oC9umDumaCXXUP5YDZJSYfG8n7SV1Mu8pgV91DOYC5DIGegH36oK4y+ApL33/olejxtPef7Kp7KAfMN+8iV7F6D+yqeygHMJch0BOwTx/UVSafd/zFa+V7LXbVPZQD5pL3BF2N+7vCHUB4Ivb3GtiVMPMboEcVb4AA5QDmMgR6Avbpg4MpUzzOT4VdCb1OCpeAFj7YdZlWee/4DRDlAOYyBHoC9umDQynTKu+9TgqXgBY+2HGZVnlnxUywKx+UA5jLEOgJ2KcPjqRMq7yzYibYlQ/KAbNLDIBdCayYCXblg3IAcxkCPQH79MGRzAS7ElgxE+zKB+WAxhJn/UBSyB2EWFPgRI4Yhv6yWbKnJDuOB3blg3IAcxkCPQH79NH9pDzA3RTyfkC/iZvjpHAJaOGlze0meR79M/uo2CfxOPmSXd733C1IrPgCll35oBzAXIZAT8A+vXQ9KYfJl+yS/geFSdG3UZ4vYNmVD8oBzSXOFY4yj6SbG7Gps43cOMf7+3yhrjySbhRwFcUZEfrb3+cKR5lnbzLvczukhUNPwD67h7ry7EzmfW6TwiWgRfdwlHnuUZRuAHbfWMy73UhuZ7gT2fHlBH8R8376QDZu46beVRXzbuC3HgX7GPRC5j0UduWDcgBzGQI9AfvsHuqaCXblg3JAzLsPegL22T3UNRPsygflgMckcQ73EU37LJpyAHMZAj0B++yeXieFS0CLhYdyAHMZAj0B+1x4KAfEvPugJ2CfCw/lgJh3H/QE7HPhoRwQ8+6DnoB9LjyUA2LefdATsM+Fh3JAzLsPegL2ufBQDoh590FPwD4XHsoBMe8+6AnY58JDOSDm3Qc9AftceCgHDN5hwfiBJgvOD5RjvMNchvAETMprLBmf02bB+ZxyjNeYyxCegEl5niXwJY0Wmi8pBjzPXIbwJEzKGyyCD/5Gu4Xl7x9QCniDqQzjCZiU37Cc8pfPv17QU9oPX//XXygi5TdIZCBPwqQ8zZULydOWxnCehEn5WfGodoF442dQ2IInYlJ+x6oLxu8orx1PxKT87j1WXxjemy3ryhMxKT/7I9suBH9of4TP84RMym9evABntTdebHcNX0WclEgkEolEIpFIJBKJLBrr7ipLgWy7FZYiC8jQjVgKxLlVliILSH95jweIPI97NvrLezxA5Hkcs7G0iV/a2JQy8750FVVu24ZzRRpH2zj1r2w5N5IVt6Zrgw3YySI38Mx+y22gastdydWvwMttS8vSSGulV7NcdSN2ubYmQQTxe4xMzMTQXWEFdBVnQ1o5l5gcIFUj0bg+WE7qpXA5V5+fjYoOt1dk7hTxmxMSdV2XS5tyqEHeZVxDrdI2mfZV52xNWXPbS1bYMq8tHh8Kec/ZJ1I3dKvK95Nu4WKBwoZtV2JjM7qmWmW5xNE9JiZmQuYHepYgfGI2pNUGezk/G7lDqIha1qXtBIVDa+JQ7pDT5za1Xjqe2/ngaj4+BpNVSWB5lW1ta91GLOPZGhkmXLKEYRYPVDl7SJXxql2uPnXYcNvoUDZsWU23jaR9xIl/PEzORJos0SWKirORtSZbi6H79RqmacNtyesVO7Tm61O1FR2WZmUOjJLBKgiUVUGtsMpNbruQBuZTmBxQYm9SZadNjk9pfeJQ2OzOXd4nZyKfd3ktzkbWWsi7sCbHczuM6Xkvm7SsPlFb0WEXeZdh4NC1IV0ikITBwTU5BxhWXi8eaXjS1wNRaUD03XQbVwsnadQzajHEucv75EwkB96lbcvXxGxU5t064mlLLltyJ2nWJ7NR0WFpVubBCq6fbDdkoORSz+k5X8UatmUm1tRBwyuj3IAK9ioVx7ViPVakkMayiT1neZ+YCRn1Jiu41RZmw5t32aUNOMhexp2gUJ/Ohr/DTvLeNTgVXgzSzLbGrnCfBGRbnd+bj8fNzHmXHfvC7ATT2S6cvxecIa9n2rLCzwEikUgkEolEIpFIJBKJRCKRyBPDYPD/AUjqElsTBvGfAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "id": "4aef9807",
   "metadata": {},
   "source": [
    "![co2_closed_open_lab_EN.png](attachment:co2_closed_open_lab_EN.png)\n",
    "\n",
    "source: https://www.aqion.de/site/161"
   ]
  },
  {
   "attachments": {
    "Henrys-law-2.png": {
     "image/png": 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L1evbOZSNNOlHRy18gWZnCMKub3xspjBDGMVRM5gO3cYeT2r+WfHnVXJnWTiTYa72/SYO/VttbyRcTZI2DsZMqRaVljmEtLsomTVLjoZHDpbGDfJwbOQBcEu4btU/Ocrot0sGITKq6pEU/GobBEy+NQxS+I5zYxjHXrnOegA9wA9OXDfC+GuV0cOjJZXK2yqTzzIFNghlsI+LzMpFPnGMm6dMZz0AGO3uYc2rPwq07rB3qunU7YfILkjyK1DxT490/YNmcVSgq7R3FKPm8fY9hTEak5nGdDqMJCv5GQMySM4Vw3IiQyeVfMIBdXx3LyDLqWs45RTOlbDujJpQ1nmePcPdIHVD9qeUdmgVa5FbAn7PaGqmIPLcrrz3y5DOsKGTyVPJS4ArQougiZIiyySRl1PJQKooQhllfCY/lJYNnGVFPATOfDjrnpjOQASXQXwfKCyS2ElVEFMpKEUwmuibwKonyTOfAqkfHQxc+0ufZkAeU1klfM8pVNTylDIq+Wcp/LVJjGTJKeHOfAoXBsdS59uOoA8KLoJHRTVWSTUcHymgRRQhDrqFIZQxESmzgyh8ELk2cF656YzkAe0AW7aS2ruG/wBk5Axm2tAOtG13V+3ZWlamtD/ZVPvKO8taMIWKfs9uoxta8LzXrSUfO3COImU6vECodTm8XjKQC4IjpsodNNNwgodZD3pEhFUzHVbdSF94TKU2cnQ6qFx48dS9TY9vtwAPeAMZ3Frmbs/d/PbujcWbLWqU1ovCSX4lx+qpOvtZhpb7QTfOkpfZNrJeH0pOv4R0swnWBEI4zJowIk2NnC2FT/LwBdXxX2juTcukKpsPfvH55xe2nNPbU3sGlX+x6jtl1Vm0NbJuFgHat6o2C1uV+k1fj2sphNHGDNMPPIU6qJmzkCvnvzL2Z98a9DOssS594S+U9Lk2DM8fL9rrGS56p/w/Zn2AD2e8N/ePdPPR968n3j3bzSe8eRk+U8L+T4vM8nKmPD4unh6+zr1AH4y6RMZ0igok4dNCFMs0TWS89MyhMqIEVLk3VDK+MfJyfpjOPb9wAUB4sbR3LuTS9fv+/OPrzi/s6Tl7gxmdNP8AZFQ2y6r0fB22aha5JqXejYLXZD6VV5g1k8IpYwdph35CnU6eTZAtZ7gfM7YnFS79vWt63haNYY/lhz81bxR2QvamszIOK/SbrVL/ADszJ1NSEnodGPuTN5VECIneketSEMpg7Y2clMQDJaALeONe0dy7ZqFwnN38fXnHCywO2djUqu1F7smn7QVtmv6tOGj6btAsxS//AE+FSvcZj3nES46u2Phzg5jlOQ5gLgkl0F/NwisktlFUyC3lKEU8pcmC5Oir4M58tUmDYzkuemcdcAD2gDGh3EeZ+xeJc/2+4vWcLRbG15WdxfRXD/Y6ttazMgpX6Hs2B2HKWGVqh4Oehk2F3j16ihhqo9K8aEKdTCjY+clyQC6VLae5z8q3WmFOPL5LQCWjUNituUmdlU40e72mpdDV9bSpdSF/+e03KFax8YzO5/8ATs46Nunm5xkAXA4eszZzgrtsbOHOWWcYXSznDwpfHlpnGD+xzgntyn/D6e3oAPYddFNRFJRZJNVwY5UEzqEKouZMmVDlRIbODKGImXJs4LjPQuOv3AB7QB8pHzJVFVym8aqN0MqlXcEcJHRRMjjqthVUp8kTylj+F1zjw/ugC1niPzL07zW1vZdo6YUsBa7WNo7U1K5QtzCOh5l1YdQ2x9S7NJtIxjLy6ma67mY85mS6pklVkMlOdJIxvBgC3/tH80dg88+AOj+VO5oih1HYWz5/csNJQdCQl4upp517vLZOs4NOGZ2WesMxl09gaa3WcFO8W8bo6piYInkpCgZKlXDdEyJFl0UjuFPKbkVVImZdXw5N5aJTmxlVTw4znoXrnpgAfpZZJukouuqmgikXJ1VljlTSTIXHUx1FD5KQhS4+7nOemAB+Cumx1SoFcIGXOhh0VEqqeVTNsmwTDgqeDZPlDJ89PH08PX2dQB+jroJqpIHWSIs48zKCJ1CFVW8ouDK+UnnODqeUXOMm6Yz4cZ9oA8EcIKI4cprInbmJ5pXBFCGRyljHiyphUpskyTpjr169OgA/SKyLhJNduqmuiqXB0lkTlVSUJn7hk1CZMQ5c/v4z0AHow/YmImph60yms4y0RPhyjkirvBjly1TNg/hO4wZM2PBjqbqXPs9gA+sAelJw3XysVBdFYzdXKK5UlSKZQWLjBspLYIbOU1cFNjOSm6Z6ZAH5O8aJHVTUdN01G6HvS5DrpEOi1+Vj3lUpjYymh8g3y89C+zPt9gAtT2nzR0vp/lFxn4iW5xP42vyrhtzT+uFY9jHLVSMitGVaMttxcXOZdS7NxCGeMJhulGkSbOjOlzZxnyylycAdslNp7jacoKfqCM4/u5fQk9p2xXywcnSbJp7WPrGxoyysYqF1N9Vi/wD86TK85BLqSXxhA3uKJcYSzgxsKZIBcEs4bt/K89dFHz1iN0fOVIn5y6nXy0UvGYvmLH6Z6Fx1znp7MADysui2SOu4WSQQSL4lFllCJJJlx90x1D5KQhcfv5yAGF0TK5QwsllcqRFjI4UJlXCKhjEIrlPGfHhI5yGxg3TpnOM4/cAHlVZFAmVV1U0Ui5xgyipypkxk2cFLjJz5wXGTGzjGP385AFmncV5GXPiJwW5WcnddxVanLzovSV42TVYe4tpN7VpGarMUq+ZNJ5pDSkJKuIxVUmMKkbvGypi/wVC59oArtoS+S209F6W2dPto9lO7G1Nrm+TTOJTcJRTSWt9Ph7BItoxJ24duk49B5IHKiVVVVTCeMYMc2eucgUlkeaGlozmlEcD3TmeJu6Y44THKNN0ZjHJUZpriG2TFarUYu7CvLpO8XF5ZpUp0Y9Nmpj3NI6p1SfeynAutXcN2qRl3S6LZAnh8ay6pEUieI2CF8SihikL4jmxjHXPtznoAPcALdt97S3PrWX0Qy1Jx7e71jNj7tq+vdszDTZNP16TR2sJhjKrzm5HTS19XF9QrblmgnmDjOkg88/70bBsYKYDq+weZ2mdacrtF8N7ItPl25yAom1Ni05w1ZRhqhFVzUTeFcWTNqmnUw0dxcg/+PoFj0Umrn3jOD5OZIuC5MBdWq4bokIosuikRQ6aSZ1VSJkUUWNgqKZDGNjBjqmzjBcY9ps59gA9wA+Yz1mTLnB3bYmWSZVXmDLpFy0SOUxyKOcZPjyEzkJnOMn6YzjGc/uAD6CmKcpTkMUxDFwYpi5wYpimx1KYpsdcZLnGfZkAfgqqR1FEiqpmVRwTKqZTlyolhTGcp5UJjOTEwpgucl64x16ewAes7xomdZNR03TUboe9LkOukU6Db5WPeFimNjKaHyDfLN0L7M+32AC1TZvNDTGpuU3HPiBa15/G2eTtc3Ba6AsxYxqlTi4bSUBE2G2rXCZdS7NzDrPWs0gnHJpNnOXSuTYN5ZS+LIHa7dtPckJyO01qutcfnVv0jfqbsae2NyLS2VT4ZjqWyVZCMWplUV1o/62+6nvyjtVMruPyVFh5eDqYMTCmSAXCGWSIomkdVMqq3j8pMxylUV8sviP5ZM5wY/gL7c9MZ6YAGNnuZ8ydlcMKjxEsGs4ClWB3v7uBcVeKNuSu7KbfN4zX+87PLQtqmq8WDnYFRvbo5swIZgs4M5ZpnznKrdbHQoAyVAD5MP2OSkPh60yRRz7mmfDlHJTvPEYnupDePoZz4y5x4MfK64zjoAPcuug2SMs5WSbokyXBlV1CJJFyc2CEwZRTJS4yY5sYx7fbnPQAeSKpHOqmRRM6iJikWIQ5THSOchVSlVLjOcpmMmfBsYz0zkucZ+5kAeEl0V8HMgsksVNRRE+UlCKYIskbJFUj5JnOCqJnx0MXPtxn2ZAA66CaqSB1kiLL4UygidQhVVsI4wZXKSec4OphIpsZN0xnw4z7QAVXQQwTK6ySOFVU0E8qqETwosrnwpIkyfOPGqob2FLj25z9wAeFXDdE6Kay6KSjg+Um5FVSJnXUwXJspolMbBlT4LjOeheuegAGcNyLptjLolcqkOok3MqTC6iafTzDppZNhQ5Cdcdc4xnGOvtAH498adVS+9NvEisk3WL56XVJwvkmEEFceLqmstlUvgLnoY3ix0x7cAD2HXQSOikoskmo4MYiCZ1CEOuchDKHIiQ2cGUMVMuTZwXrnBcZz9wAe0AetRVJLweaqml5ihEk/MOUnjVUz0IkTxZx4lD5+4XHtyALB+6Tyqv3CHt/coOVuroWpWK/6T1+ja6xC3tpLv6jIP1LLAwxkZxnAzNel3DTDWUUNgqD1ufxlL8rp1xkC82i2NS0U+oTj0zNKWnqjXLE/ZNDZKRurMxTZ4r5KCqqzhNphwqcqeTmNnoXpk2c4zkAdqWWRbpHXcKpIIJFydRZZQiSSZcfdMdQ+SkIXH7+c9AAMuiREzg6yRG5EsrGXMoQqJUSl8eVTK5zgmEsE9uTZz06e0AeMuW+G/veV0cNMI+8e9ZVJhv7v4PM8/wA7xeX5Pl/K8XXw9Pb16ADwd02Tb+9qOUCNPLKt70dZMrfyjYxkqvnGNhPyzYNjODdemeoA94AtS5X8yNPcNYjS0xt81kOjvrkZqLi/Q29XjWEm6+sfdMy5haq8nCyEtEIxVRYLM1VZF/41Mtki/ISVUMRMwFvnPjmjsLi7srtz1HW0PRLFCcv+b1J41bAf2ZtMSLiHo9jpt1sL+XpbiEn4hq1s6L6tIkSVeEfNcJmPgyGTZwYoGSxJZFbB8oqpK4TVOiplJQqmE1ks+FRI/hznwKpm9hi59uM/dAHhRdBEyRVVkkjLqeSgVRQhDLK+Ex/KSwbOMqKeAmc+HHXPTGc/uAD2gDGpjmVsv/N//wAv34BSfqg/y6leXf0o9zm/rF+sVPkc11BiC+IfHPo59Dc1tfK/k/DffffcYN7z5f3sAXQ6B2nufZkjvRrt/j090Iz11u+2a91S+ebKp+w/rs1ZCs4lau7pbtqn0Woba2OHrghIOS6yDPDbqqbOT9MAXAqPWaXvHmu2yfuiZFXfmLpE91SUwbKajjxHx5KamCZ6ZN0xnpnp9wAfozpsRRBE7hAizrx5apGVTKo58ouDqeQTJsGW8smcZN4cZ6Yz1yAPPvDf3jDTz0feso5cYbeaT3jKGD+XlbCPi8zKOFM+HxdOnX2deoAt90PtLcuyJzfMdtrj490XF633TYqBqaYebIqGwMbx1hFx0Q5hdxtmFW6OqC2sbx44SLCyfV+2w3xlQ3U2SlAtY7uPM/YvAngltnk7p6Fo1q2Dr64aIr7OCv7WZk6xlptPemttYy6ssyrc9XJgrhCBuThdmYrtIpXJEjHKqngyZwMl4AAAAAAADHlzq7fcNzFk9NbWpW59icXOVnGqUtMtx85K6sawcxO0wl6jmcReKlbaTaG7isbK1vc46PQJJQr7yirZRL4FkymWKqBj51x3GOZNc4894jUu76/ri9c2+1VquVscZszTcDJsNYb1aXnjvZN06Pt/0Fll5ler3VJrC4zZYBJw5bJL9CNvvamC4AsXv/Aji/WOyGt3L4S7W5Ln9D8L4fm9H9wlPattU3tP8h3eu2G2yxi9zUsKzN5RbRdXX0ZTqKiKkMRk4I3K096LhUAXVc5r/b9sPfTYbT2FD4rt+2VzM0Ff7vX8NztMQdvuPFq3WKyw+GqpSKNsRszIrI+WbGDE8HhzjGcACuHBkxm/fP76zZycyKr6m9sOTjm65zEO7jkeOtxjnD9kifOPNZpyKJ0DqExkuFi5LnPi9gAtj4BPW0hxq9Sk7ZvEX7NXuRdzf3Z02ckdtlCJ6BoCR8ILpnUSMRNZMxM4LnoUxc4+7jOABZbrPt88W0PTpa/5zYlrVEcxNQcAiciNS8vEdm21DauqtgaroTu1a+11Q5xlYEoys68hH8A1qhay1bpsXCHjyuipJKKOcgXzc3NjXnblN9NHtfZTA8LsbaHOHiDsDYEThDLD3C5XPjLcbHZ2JmRSpYaFbzcgsXyMlL5XTwZxjp0AFw8X/wDqZ7R/+SHDf44sgCz3gJqnW+7e1p3lKFt2lwOxKW47hfdFnnFZtTPEnELTFLtJLbVJE7ZU2Me9QFlhGj5qbGcZSctyHx7S4AHeO1/2xOKW6uwnT9Y17UdE1vbueXCOhxe6dkV2DTaWG231nATUjrvYlndEydSYm6Hc5j4uzMfGfCv4umOhugAoRo3eN07oTvs78LdqJqmv3F2ybJ5E9yqsLOsLSETsnt1Wlbjnras3RJI50FUdwci3iFlMyWzgrlhH5UwQxSZwUCTPyr2PbtOcXuSG3KBDfSO96t0Nt/YtKr/u53eJy20nX1hstciMtU8GUclkZiMRRymXGTHwfw4xnOcYAEYKG4EcX7R2Qc9y2w3e3uefkrwqf84XXcHNtW3t96QnIoutVtuFioy4IWJsziKLCXRuWrYqLZBGHwwR92w0w7++gD6e5nQaFzV40+nP3/yo0dS5/cPIHmd2+KXuFvZIAmXK9J3vqG3XjbmrHbXPu+EKfabUybuXUeYhfCdskXPhyTOMgSuNZ60oOm9f0/VWrKnC0TXOv4COq1KptcaFYQVZrsSgVtGw8SyJnJGrFk3JgiZMewpcdABHN4b8WtFd1De/c23xztqspuDY2k+fe6+HmkaJY7rcYiP4waY0bFVNlRpbUsNWbBBmoF+2KrNL2B3Z2WEZRw4OQ7ZyTGFMqAUl7au7NA8cOyDzL2VyrsGxNraVj+YfNmn3eRi7FOS23N2K3vkE513BRkZaa1O1iblL/tafn2jfEg3kmHjdvjODuEEvGqUDqelKhsTib3f+2QypHA+l9t7WXMek8xKBsnV1D5L/AFsvt0NNZaUY7YrEnubWVZq0drOp7D1rYI5qZtNR8zYXzwkq6aru/LSTyoBVruKaXguPvOTcfPjuEcZH3M/gHNQfHaP1ztysXeQPdu2cvSTkrtulE9MFnq7Jy9Dv9+l0bDLWqqrrzbNPJ27lqq3LgpwJRrN41kGbV+xXSdMnzZB4zdImwdFy1cpFWbrpHx7DpLJHwYucfdxkARetC/faR6qBNXJlE/rv5KJ+AxzZxghuFMP4iF9vUuM9c/c6ADHrtjijq7QHYF4kd1nXbq/Ne4JqXU/AfcNX5LyOx7w9uqiVyvekqI91HINcz5K8po2P13a8wTWqpMkoorFkgZRJRwZwsuBOTRPlVFJXOOmVEkz5xj7mMnLg2cY/7OoAwQ9uv9ct6gP/AIt7bH+FSxgDC1onaWxaX6eDg/rek3y1ashOWHdEkeJG5dt0yYcV62a40ZufnpvSP2TOwlqQwZarvJSIiiw2X+DEMglJn8JynMXIAvQ578AOJPCblJ2VnXFajn0c3ufc11RAXTXdUulsVp2y/gNA2BJROxLjU56fl29i2NUXKirbFlMXMouhOuEnzhx5jfywL2E8ma+pjd5cmM3SleyQwSi8LHMmnIuI3m9IqyKbEp84I5XYIOkjLYJjJkyKFybpjOAB8/b4eN3new7+5mrtF2k3V7ZTNTLdyRyk3eNuNV6I7aG8s500XTdX5KqfsOQ/sNjGQBhn05tPY9E9PVxwo9Evlo1VFcnO6bYOKm39wU+ZUr9q1do7dPPfbMHsqzw1oxjJqy6eQrTEPl/4iGbpyZskORTwGwBdx3C+3dw94U8juyfOcW9ffUq4sHdT0PVrVSq1dLa4rGx0mtQ2BItthXOrT9gl29m2RV3Dc7YtmUJmWOhOuUnbhfCyOCASyABGa7Wmudqbl7eHd81RpTZSuotwbH7i3dJo+s9o4O9weh3Ox2MsRXbIRzH+KUYYipF0mphy0xl006echjKpCYyBUvs3RPH/AI8bYvXDmx8IluD/AHBKvx717e9woMr6rtSkcptWw1hcUfHI6j7Ma2B+lczS+xFFyyyk2wZWZm5epNnSjjCWcpgV777+19j614Q1yta8vdk1K05C8qOMHGPaG46hKZgLNqbTW69oxdY2TcIWx4x0rb5aCyaKLIeJM7X4nk6ZyK4IbAGM3uO9ufh3wl3T2VbBxb15nTL6c7u3FOm2yqV66W13AbObJRGwZZDYF9rs/YJZG37KrDyPyinZ1yHlvJnHaTlwqVwnggF+D7Jv2maul8RvD/kiWLPg8RvB4v6cMJjxeDr4fF09nXp16AC2jtd8StV7u5990zkDts1qvE7xk7q24VOOtPkLfZWGvNSXiw65oD+8bRh6dDSsbBzt+uUbJMo1Z5Lov/dI+LTSaFQ85xlUCwak0bfXcTX53bkv/bKuPMTar/lhyj0bqLkUbnFqXTFm4dRembZK661hQND0ienmlg0nZdZEj282/kmiST2xyz9V46UctV0ksAX5clZDlfea52Ie3pzht9n1wry5kL/Wu4HY9e7FNBy21LXxx0OnbK/ph9tOgv2KrON5E3JMq00SGetFpHCSjRst4DKFyBmj0323eC/Humbf11pjjNrTX1C37WEaduamQbB/9Gdi1xGOnog8fZYV7Iu492Z9G2d8i8XwmVw+IvnDhRXwk8IGHH03fEPjFr7jptXkJSNGa7qu7M8oObGlsbOhoJJtbs6mr/ICTbQlB+LeM6+azFIVWOTRb/wSFZJfulznIFnnDvjLb+Svpd9Nr6iIqlyN44bF3xy54wybRHK0kx3nx05mbyv9aj41IvhMq7uUQwkK/gniKXPxXrnOOnUAX78YN11Xu19ybjlykqPlyHH7gtwao22YViVwZy2jOY3PyrIyD6uyGCGMxeTum9BV1Rq7TN43EbIzuOuEzGxkwGQnvMZ6dpnuPZx90vDDkMbGfuZwYutLCYucZx7cZxnHXGf3MgDAvyr4YaG0R2Ude90HW1gt1d7gupeOfGHkvU+aDjYdmkdr3TZFha6vcL0GzSRprELZtTXhOxnrrWm+7fAG7Bdug1alymXxAXed1qhOOSvOXsLapvcrdddRG+pLmlAbijKHZJam2V9THvGKm3nYOrPpNDuGdig4e6p1s8DKrMXDWQ+GOnBEV0VD+PAHN8otEauuXcF7cPaPlYuWoPbyqvEvdO7Geha/cLVXqjv256bnKhS6Bpi4yqE0labnTNW1uVXsriDVkFUJA/lqP010ki4AHYeOGt6jwS72LrhfxPSf1PivvbgDNcltg8cY2fl5fXOj9t0bdETryubG17XpN/IIa0i9nwMkvHvYtjhsyfvWeHJSeJLGCAWc9qntucROc3HrmnYeV1emdxSED3D+emutcKzd9skehxrhWe5Jqyne6UawkvHMdaXh3YrS5nXM8kn8YXUXQIouZkg3QKB0GO5jcorp6f7g8vYty32HmuRHNzWPArZ/LOKm3ERsRnxalOU1600+3aheFPNXibFY9c01lEq2EyvnqLSB3hV8OFSKAC6rmhxG0B2q9r9s/eHb8pjnRezdnc+9CcSdo68ptwtzuK5QaU3U3sUXsNvtWuTk9Ml2DcKUyh051pZXybiTYOEDrLuDdUzJgOTHFfWfNL1CM9oHfKlon9BLdovXuy9iahhbZY6fWtwTFM5cX+vUaG2O7qUpCT0xUas9vruWJGEdpNXcm3aHclWTb4TyBw/cn4Q8Rt1d9HtKwe2OPWstgRW8dN86mu32lnr6cklsVtpbTmvj6nRtRVlM4ky6/O6VzGZN8pvlU2eufZ0Aul2VDxlb9QZwQrcCyQiYCC7YPJmHh4hkXyWMdFxO1taMY1i1blz4E27JmiRNMv8AqkLjH7gAt54a8TeP/dh2T3Id5dwOlr732JrHntv/AIj6r1zcrZa2ULxd0zo74BEUBpq+sQU5DI0K+W5CVUn3toZpoyz1y5Iqi5LgpsnAtujtpbJ2D6bnus0+/wB8tG24fjZZ+ePGDTG5rlLq2K07X0bpS8rQusbhL2o/ttDplGrGiCyHiUM4JFFyc51MHNkD7eU3FLV/C/Rvan7gukHuwYzmdaeWHAymbn5BTWyLtO3XkJTOR+Y+G3DTtyJyU44g7LVLGhKG9zj02iDSDIQiMam1QxlPIGRTuLOeOnI/lrTeIzfgFG9w7k/SNGOtqzlb2VtvGpOPuiNQXW1nr8RZL1NzRrNDurzb7VX8pxiMRVJqwotGx1vNatumVAMWOqLps6Z9OL3k9WbQwsyd8XNndxXjJT6ursed3Clr2ha1ftHUBrKM2vZ2cdYdi13XStjcQ8VLPG7ZZ3Fs25soolxhIgEp/hz/AFROK/8Adw0f+bKsACPvuPgZw12/6lSJiNncbNU3qNu3assnIq3M7FW0X6E5vGv8tKdRITakkkZQpHFwjac2JGIujYzkrXHg6dcYzgCr0TpPV3cx7tHci1Pzlrmdt6l4MVnipSONnGe5TMulqtvH7y1dI7I2BvyZoDGQj4m8XCfsiBYmPlnqTosU0Y+Slkq2CGTAq32dn03rLkD3VeD9ZtVtu/GHhryX1fCcZ5O4WqYvTygwu39NROxNg6AibfPu5OYf1zS1vUy1ZNXjt07j032UVD+wuMAfjvjmMWxdmfwmOXr3u+EeDeE5i+IuWe0OpTeHOPEXP7uM+zIAtb598HeIW+e/pwEjtycddW7IZbv4r8t5/byFqriMmnsKZ1VC6zg9bydoIofBJF5Sok5m8ec2PEgmbpj7hegHfu7hxdn2vIehcvtz8V1uf3bp0lxXsdGv3Fut3clcufG20wtrVuNg5Xa51rLzdbrO4JlPXLFGIO2RkGlhiW8dhePN1yYAZ5ePF41ZszQmldhaNfFk9MXXVNAs+p3+MyOcuddTVVi39NOpiYUVmCrYr6zfByuzGdFPjOFc5UwYAR6WfFHR/L7v0dyrXfIyOe7G1XAcWeEFvW0JLWSVZaxv9oUg77ARty2BToqQjyX1SgRbx02jW0h7zFs1pxRwdDLorRZECoPbu2HS+Fu0O93xvmLnYke392+bVrHZusH8/YrLbi6UpWz+Ob3ce9tM1OeevpKyKVfV0lGZUjIxJyq5j8v8pFz5ymMmAxhXFvnTewe0zzX4l9upnwL1ZvTn3xV1TG7tl+UEhO8h+RGhOTfxqI+im9tIQzG3Rs9C7Dpj4s6R1ZbpL2CDeskDeSRZVfKYF+/IXixrHml6ha/aE34a02PQRO05p3aF60/D26yVCq7asdP5U7Pr9DZbHcVKThJ2cq1QcXd9JpRZXaTR1JptVXJFitiJgD4u4zwg4i7v77na5h9uceNYbDjt46F5tqbfbWivJSaWxDad1nrlvqw9pKqp4ZI9CScKFjTGx4m/mZ6Zz7OgFyvLWLj4DvrdkaAhWiMZCw/H3uORUZGNMZSZso6M1LrNnHs0ES58JUGbVIpEy/6pS4AGNTuOtdNcs9cdzTkbxF7e7S+WbjKlvRhb+5TsDlJO6RuOveQHGqiKPLbL8WImPa7D2LLIacdVxoUrRtim1ifkGyzRNRVNZdyYC6HuKbHs+4u3J2GNu3Z58Rue0+4D2b9j26Q8sqXv1nvES2s0888omCkT96lZRU/hxjGMeLpgASfwBEj7WXbj4lc7tV9wia5ZViX3Y4rnc95/az1uwnbzZmEdx6hktsOLU4ldOR0BLxjbXmwpWxW1eWcWJInxpTPuqeF8NW6KWAKK7Q31uLZ/pJt5bD2JfJvYlz1pIu9f0bc084zI2DZNR0Pz0rFI1bsWUknHn4nZReCqbNNd6plXMis0MuqZQyp8mAvB7j+ni9vPgvpLT/E6A2vZ7b3Aue/GnVnLLYKW95Wo7u5AvdpxEirsp/K79vdhWa6pue+MUJnWDyzLLCPi28sdJqi2LlPwAdx4PcWeVOku4BqHYWm+2u27dHEuxar21ROXVMjOWmqNt0bZU+lGxtj0JseI1dR5d4ZntOuXCOkIyUnypZfSUZO5w5VPhubJgKb8htP1LiP3E9k8xO4/xmW5KcfNu8ktDvuMvPKDvsjIy3AxyvikUbXGmLzp9SfgpWh6y+tdqmupZKyWQZS68t/60godfySAVQ7vXHCab8nIjm5yR4tvu4N28dXcXZeq7A0NXr0aEvfFO0wFvlbzeuV1F1fKT1Zr23JF9QyoMnKjJ+1tEQhF+ayNhMufEB2Ln5eNbXvcXp0toailUn2krvzDrczrOw4VfJx8hTLzxbt77WxMuJZTL7Lmbhl0MN0nRsulVOpTdVPEAKk8jHrY3qFe23HJvEDPEOC/NR46jyOSZcotXk9QEWLtw0KfzU27tZi4IioYuCqGQUwXOckN0Atj4kcU9X8mu9J3fLhu81pu0HxX5Q8LNsaO1ma3WSC1zVt4S3GWgSGd0SlbrsnEtrheIRrriLaRPxbLxjHIZd5Tb5UdKHAFidOpO9u4lO8+9u7G7ZNw5nbGzy65O8f9Q78Nzg1NpWf4eQOk7I917rWhaHo9hnGk9pe3UFNqhPyMwzSTfWKWkju3CjhqoiiUCVzwVY8lonh3xvhuYxG+OUMFqap1/d7lvOxVmxLXyBYEh5SwOZ6CUVhpOSshWRH7tRsYyPvTlTBc9MADEJzghuO3NjmPujj3rntvV3n9yG476w1rXt77G3FyFktBaY4/JbJjZ68app1VsRGuwrA121NQz9zLqv6jVEnrFudqZ1J4VTQRRAx+PNv7K3d6PHady25ZpW43uL0htfW0jZp2cdWealYvUXLOd1dVzStlelI8sT5nVqizbHfq4wq98nCx/lnMAKs9xPh3pDgvwA093G+LLi1RfPLUtw4f2KvcgS7Dttg2bysktpbK1pRrvrXaz5xOvmGzals6t3N+uWG92NHsEkCJxyLZmQyGQLttsawpXcH7z+3OKHL9m9uvG7ijwy07t/UnGGanpWP1jtm/7muVrhrzvC91SKfRyOzC68bwratx7eSw8io1w5UVIiVyr48geeAGtqxrDnh3YO1/UHM3cOC1U1Xx4vVY1RY7NNXKD0BM8mKPd47auiazJz0hKykPRrlDR6U2wgjL4QiUV1MNiETWznIGN6EsGx7b27qV2GpSxTSu+2/cWke2Hd5tN17pbz8H9XOscopbdLdEpsqJV6Y4aIRsK3U6FKsZ5hPHhNnPQC5PnOTYG7O6ohwuS4MLc3+MnF7gvq/YtD4iuOQWttDancWXYt+ttJd7nt9V2DItI3cbOi16mM6vBsXBHTGvOF3bjKOHDtusUDJX2etQcsdE655D645Cacl9CajS3/L2ziBqCy72q/ISf1NpO3VyDfyeqE71WJCUIan03YSMorAtnSx12UbIEa4MZJunnIFm3qMeOWiduV/tl2jZuqKZerE+7q3CvRLqVsUUV89d6f2zeZfGytcKreMihqtdyQzUsg2xnGF8IF9uOmABwneC4wajpCHZA4t6fhHOh9Ot+6Jr2owkDpZ+5oDypV2wa93FJ2JjTJiIOnI1V1MqSjzGXjJRJ42O7OsgomtgihQOzam0Fq/t9d8zT2ieJMI/1LonlrwW3RsDcumo2y2eX19M7W09seoI1XbLGGscxMfC7+5hp1ywfvUDk9+RVOosU66iipwMfcXV9v8AcK3r3JLzt3tg27nfIUHmbvTinqPYLrmrqvRTjijQtJpxtYpcBo6h2qbazWq9iOCSObY9t0emm9mXsukp5pkUCpYAk29uWF5WVng/xsq/ODCR+VNV1y0qu4XhLNF3NeYm6zJSUFEWGTtUKu5jJ2eslWj2D+RcJqKeN+5W8RjH8WQBjzx/+pox/wDkguP8ckeALLND7t2Nxx40eqC3zqZMy+zdR86eZ14oax2uJIkTZIDj3rR7FTyjBUqiTxtWnRcSCiJy5TUTbZKbHhzkAWu9wrtz8TdRenz2Dy8oj62OeUNt4uaW2RsDluptO4SOzuRUzvCX1obYEftWxyNhes9h0bYBrq5K1g3ia7GPyZsZgRFdBJQAZROZBjNu6p6ch6sczdhljz+izOVDmSaGkpHh/SjRsedTOSomePsNFcoJ5+Up5ZvDjPTIA7XJPWy/qa6qzQeIrLseyRa/fmiTkiijM7nm3XVW3vbYihjNlHCOMmT8ZS5OT2464AGOhHfm2eMfE/1Se9dIOXzPauvec+4HdLmmBPeH9SfS+qdLV1zdY9NVNwiV1RY2ZXmEsnIZIh2ODHxkmM4AFN+7n2w+FfGjszp700uxmybnWmeGslbN+Y2fcZe5crXF+3rpvFjkd2yUlZH7LbzawOpPNnZJO0liRT6PbLR/uzdAyZgJo4AAAAAAACyHlhwM1ly3sFJus/tblFpPYWvoibr1bv3GHkbsrRdgLX7E8jn8zDTLKqS2KrZWbx1FomxmRjXSyOS/ejkz9wDtvFXhNx44ba7tOudMVSUM02HZpe7bWuGxbXY9p7L3BdJ5smymLXtXYd9kp20XeXesUSN//OODoIty+Uikmn1KALKIjsYcDYiRYQpGW+ZDjzD3dLZMHwnmuRG05fhVDXhvOntDWYY8en08tVzRjOyH9+Rg1jLVxFyXBiR+PuAC+fkBxE1FyUunGa+bHJZiznE3dDHfGpi1yaJDR5L1H12YrDYtjae5OvjEHiLm18ZbFMhnJ/Dnx9MZLkCgvJftccaOT29IXkrNzm/NO7vZUtPWVp2Fxo31sbQU/tHVqLty+Q1zs95r6XjFbPWmzt4odE+Mt5FDqUqbohU0sEA7RobtucW+M2nOS2gtKVqepGquVFovVt2BV2E8Y6EHI7E1jWtTWNGiuVmh3UE0UrNVbKk887xf4gdZyooodUwAtVhOw3wMg6xrvVyZuRL/AI7a+QpbhbifJcjdmq8WdgWyit4fEdfdk6QbS7Wn2SyTMtCJSsy3Ik2hJqYUWevGCy66pzAX8cg+H+nuS9l4zWnYyVkQkeJm869yE1IjV5lOCj0b9WIOZr0UlPtCsXJZWupxs6uUzMmUPFnw/LwXGS5A/aHELUbfme954p/Sr69pDjS24ouPFPZzSvqqa7M+thLwVj3PoWz/AErz7X3n+1r968v/AFgB8XGnhjpPipRtx651qyn5Gqb23buHfuwo67y6VlK/u285AkjfmbXGWLJJtWHahPAgyMRTy0jGwY58mzkAUM0RxM1H2qdA7rdce4rljt/XMFEPbpTeM7bYVl3rI1NjXkpyUQ1bxgo1xl2pK6hOPphbwR2H2TO3HleYtnyyYwBRLtR8N7vq2zcvudfILU9c0vyh7iG3mm0rdqODdx0ytpLVFVivgWqNYWCwRmVY2a2K4aKu563vWRiNXc7KHJgnVtg2QMxiqSayaiKyZFUVSHSVSVIVRNRNQuSnTUIbGSnIcuc4zjOM4zjIAw8m7F/AzMgvCYY74Jx3dXfOyXXCRLkRtRPhQ4vOZ/FqNMrceST+KseMPZsYfmgvF9GzOcYNmP6Y6AC+Lkjw805ymV43KbNQsbYnFXkdrXlJqhtUJlOutW+zdUMLBG1JGcQTYuiSdUSaWRwVePJ5OFcYJjBy4L0yBdOAI2XOCjcPKrzD27enfFPvCxe5LrC1iO2UrwLqHIiA0PzuZx9RZqQ0BerLpiwt9eSr6DZSHwJ7Izz2pSCfkqIqu1WZfGYCuXbi7WtYje0q44Wc09LQENEcgbntzcGy+P8ADzypmGn8bS2zI7MoGv69bKu9aLx9l1DFoQhUn8Y5L7nMMDGbqnImRQwFzWue0nxn19u7j/yTf3jk3tnfPGx9dj632lvbkNfdwWdKt3ugWDXMpQZFS6OpJgnR2sNZnLlJowQYKrSflunSzlVMucAc/vntbcd+S+xbTcdzXvlDb6JfZur2PYfGlxyZ2y34tXyXppK2WANZNJN58lcPEJK1Jis5imuWsRIuEjLPGq6iihjAZH0000kyJJEImkmQqaaaZcETTTJjBSEIQuMFIQhcdMYx7MYAFk9W4A6DqEZzgiYj6b+6dwSy3K17/wDerOVZbMretco6unPoOqWOTNWG/wBF0C+QXPvOUnHy+ucYwXAHWdidtTjbtDt+17tp2f6wccbKzQdO63jMRduLH7BxXNG2GmWej+fbk4s5Tv8A4nRGHviuGpcOEvMJ4SYP7AL/AJMhUyETL18KZCkL19ufCXGC465/dz0wALYNRcQtR6T5E8reT9K+lX1ncyX+m5Hcfxie+I1z3jRdFea8o30Thfc0Po+n9Hnx/fceat7yv0P8np0AFFqJ2u+H1L4NyvbtkKLK7F4vzbm+PZSrbFsDmZnl32wdjzm2JGTb2qLSg5WKmYO8Tp3sQ+ZmbvY1VBBRJXCqWFMgYjuYXbGjNHb+7Qt21Jnl3ybs1E7j2ri2zZ+7dp7d5MWHTGhI+g7JcOolKVm15OG1lqxtP4jsvnpm7Uz1ygy9/eODot/CBmJ5e9ubj5zNuOqtpXuS3Bq/dmlCTLHWu9uOu27bpLb9erlmO2NaKb9MKg7QVk6jYsNS4cMnaS5SeJTKGUTKqmOB9XEnt0cZOEd/3Zsfj9B26CnuQcRqiO2jiyXedu+LFJ6ia3NCIuchLWpeUtMxfrU4vsi6sMxIyD17MOzkVVPjJMADg6H2w+INK4VWXt+SVDkNlcY7hJbDlrHT9lza89JyD7ZOwpfaUw7TsMcjCSUa/iLpMGeRLtoZB7GrIIKIrYWSKoAKGVTspcRK/ZNJ3ixXPlPt/YHHXbuv9taavm9eSWwtwWagY1q5knld1rV1ru6lY6v6vduJAhpRgwbNXkz7iy99eL+6IeADLwALG9XdvjQ2ntI8h9BUWT2zCUvk1uHcO8tiS8RtCx1e/wAbft3yzWbuT2hX6lq1mzUlBvIM0zx/uS5F2vTP30/iN1A/XGLt/aR4t7Cum5YSybt3HvO/1KG15Yt4ckdx3Ldu0Pq1rku+n4LXELO2x6o1rVKjpySWe5ZR7Zth08P57oy6xSnwBcJvvQmoeUGn77oPfVFhtk6k2bBqV66U2dIv7jKx5l0HjdRNyzWayEZJxki1RdsnrVZF2yeIJLoKJqpkOUDHBV+yZxBgZvTFssNz5U7bunHjb2tduaUuW8eSmwtvT2s86pmlJ6sa4phrw6loyt6zePvIxLMmTZB9MIsWibx4sRsjggF7avEPUa3M9pzwP9Kfr2ZcanfFJHpPdKV9VT3ZjfbC3jrPufyrN9K2xej73jHRr968v/WAHs48cR9S8YrVyTuGsvpP8Y5V73neRW1PpFNlmGudiWKDgq9I/RtErJpmHgfh9db+W1MZbJD+LPjzjOMYAtk2r2n+Omwtw3neVI2Nyr4w3nbci1md2p8TOS+y9DVbdU40ZEjE7FsWo1WS+j7u1LRyREV5hghHyrkpMZWcnP1NkCvXIbgpxt5U6GqHHbetRm7zSdeOKXL6+sTu8XJptijXLXrAkdT9kVbbzGbb7FitkxKRTGNNlkcvnZ1VfeTrYWVKcD6OK/ECv8U21tJFb05V70kLjiDRezXKHkHd95SMQwrppc0XG1ZKzLkiay2x8bWw5OzapOX/AIEsulVsop5KB0zjj289E8UN0bs3FpGe3NV2W+py1XC5aQcbatMvx2i9g3qdY2O7bGpeopJdeCqd1tMowxly6bGwQiSiiSKaSR8kAFMI7XMF2i+AsRqbhxx233ynR11NWCL1Npisy8RZNgWK4bl2VZLkq5t90nVK/E1rX0Zcbm4WlZpdM5IaIx5hklcJZ6gfP2ieBR+31xDjtc2iOprLd22b9d+Q3Io+v2mGtKb7h2tJFlZap0wuS4VzStbQaDCuROc5wVZpF4XwUmVjEwB3Xu11C2X/ALYPP+kUSsWG6XS2cRt8V+q1Gpw0jYrPZZ6V13PM4uEgIGIbPJSYl5F2qVJBs3SUWWUNgpC5znGABZRw67NvGFXRXCy1bVY8jJGPoGp9BbNS4fbI3htd5xeoG+Y2hVyYl7VnjZYZc1firNE3dZ09NEOyHiGEoZU6ceifxYAGUPcHEXUm79/8U+Sl2+lH1kcOJvbE/p34POFj6/h/uahY1xcvpXEGZOMzqP0cx/5TGFUMt1+p+psZyXIHC8t+EGguacJRmW4oq1xtu1RZVbnpvb+rbxZtWbo07bnLUrB7P632TTX8bYIBeTYFwg9bZOswfJFIVwgr5afhA4bibwH0Fw7kth3HX31jX7cO4FIQ+2+QO+Nk2jcu9Njo1pqZnXIuxbBuLx2+b1yAbnNhnExybGKbmOY5G+D5yYAYI+2z2jKVubTfLOS5AIcx+Ok9snn/AM0/rCqGuNybr41Q/I/TkpteTc0n6zafEv4RtdadKwckumwmGSTR29jFsoFfKtfCngCQtbOG3F+78XVeFlk0pSH3Fs9DitapaZTj1GNUY0+BKzzBMIsrBdtIxb6EdR6Dpo/brpyDd8iR0RfDguFQBbLoTtPcYNE7cpO8nlk5FcgtlalipiA0TOcqeQmyN/N9AQE8xTipeN07D3eVdQ9UcvohIrNSUMg5mzM8eRl7lLOS5AuRb8QtRtuZ8hzwT+lX17SXGppxSc+Ke60r6q2Wyz7XR8us+548Fm+lZ89X3vGerX715f8ArADoPMnt/aM5uudP2LZExt3XezdAWOesumt16A2lZNO7g164t8W2g7tGQN0rSuHBIK6wzNFrJtVUlSOEUi4x4M46gDu0jw71HK8qNU8xJBe5uty6d0fbeP8AU3S9lO4gHFEu0zDT06vPxjhoq5l7ItIwaJivTOS56ZN4imznGcAW3717S3F3eG4b1vVlZuR+gNh7gjYqF3494t8idl6DieQUNCRx4eMZ7ggKRLtImyPWsOfLTEogkzmctfvWXmSfJAFcbTwJ4xz/AApsXb6gaEXWfF+w6wk9RfQjWjvNedQ1PmMqKSWIeXdJSrn43IO11XLl+6w6dPHayq7g6qqhzmA8bx4KaM5B6X0TobYH0z+gnHbYuito68+B2QsbNfSjjus1X15mekjx7rEtH4OzJ78l5aeXXtzgyeemcAdP5D9uDQHIrd9f5IyFi3vpzeUTRS6qm9lcb95bA0XZdhaoTmVbE31rsV5RpVhizVdlOOFXLUxipP2iqmcoOU+hcFA6jTO1DxD13xK5P8JKPCXmt8f+WVr2fbtj11rdXjyWhn22oOvQFrZUiwS7aRkYiN9zrSB0MOjP18ODqqqqqmUMAL+NeUeE1jQKNras++fRvXtPrNHr/wARc++SHwSpwrKBiff3ngS97ee4ME/NU8JfMP1N0x16AC0Pkt28dE8nt26X5I2Kf3Rq7e2jGT2u1XaGg9t2nUlonNeS00wsM5qm9ua8t7vb9bzcvHEWcRzlLrgxlPKVT80/iA4jk921ePPKHatf39ITu8NFch69Uja8T33xc3RdNDbTm9bqSJpU+vbfNVB4nH3KpkkFDrIISjR0oxVUMdqogfPiAFduLfE7RHDTVqeoOPtL+iNUWsE3crE9kJmatdxvl9tC5HVq2FsS8Wh/LWq83mzOkyneyck7cOVMEIngxUk00yAcVya4haj5Zu+Or3a/0q8/i/yW1ryu1j9F57MET61dUpzaVV+khcM3fxqseGwOPemP3rz8+H74Xw+0CnvL7t9aL5n2PTV/v03uHWu2+P8AJ2V7qXdPH3a1n03tapR93Zx8fequ2tlZWKo6q10YRTZGQaLpKYORLHlmTyY+TAcHyc7cmoeV9kdzWxtt8tq5A2Ghs9Y7E1lqnlJtzWeqdq0NqWbTVr9/olYn2sS/xKtrE7QkHjLDCRkGymEHLhVEpSYAvWotHqOsqTUNcUCvRlSotBrMFTKZVoVvhpEVyrViLawsBBRbYuc4QYRUUySQRJ1z4UyYx1yAI773t+/0ke9X3DNkbAYcmdLxSPGfhrF6P5QaNumzNE2JCWLFXxjs6q0TatbMzr1raLt0o8k7DOCyjUiiLRVVBNdJuoUDL7ozt/8AFTj5x4v/ABfpGtSy+qtwmvbveCew56f2Jb95zm0I5SJ2NaNwXq2SMnar5ZblGK5bu3bx0Y5W5SIo+UkmmQgFosD2PeGcM00iwf2nlNd47jJtXVW1+NUVsvk1s3Y0JoJ7p6xxdjqdS1dX7hJy8DBU9bMK1j3hFGziSWiEsMiPU2/UmQL42XEHUTDmbOc7kPpT9etg45RPFuQyedKamfVdDbEc7PZ+TW8MsGJY/pO6N4nmXBsZb/e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    }
   },
   "cell_type": "markdown",
   "id": "92854cad",
   "metadata": {},
   "source": [
    "Henry's law: at a constant temperature, the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid.\n",
    "\n",
    "![Henrys-law-2.png](attachment:Henrys-law-2.png)\n",
    "\n",
    "source:  https://www.chemistrylearner.com/henrys-law.html"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "601d5ec8",
   "metadata": {},
   "source": [
    "# Henry's law \n",
    "In physical chemistry, Henry's law states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid.\n",
    "\n",
    "\n",
    "For the constants and temperature dependece there is a beautiful webiste reporting how the constants evolved over time \n",
    "http://www.henrys-law.org/henry/\n",
    "\n",
    "For the CO2 constants see https://henrys-law.org/henry/casrn/124-38-9\n",
    "\n",
    "$H^{cp}$ = Henry solubility (defined as c/p) [mol m$_{aq}^{−3}$ Pa$^{−1}$]\n",
    "\n",
    "$${\\displaystyle H_{\\rm {s}}^{cp}={\\frac {c_{\\text{a}}}{p}}}$$\n",
    "\n",
    "\n",
    "## Temperature dependence of Henry’s law constants\n",
    "\n",
    "The temperature dependence of equilibrium constants can generally be described with the van ’t Hoff equation (e.g., Atkins, 1986). It also applies to Henry’s law constants:\n",
    "\n",
    "\n",
    "$${\\displaystyle {\\frac {\\mathrm {d} \\ln H}{\\mathrm {d} (1/T)}}={\\frac {-\\Delta _{\\text{sol}}H}{R}}}$$\n",
    "\n",
    "where ${-\\Delta _{\\text{sol}}H} $ = enthalpy of dissolution. Note that the letter $H$ in the symbol ${-\\Delta _{\\text{sol}}H} $ refers to enthalpy and is not related to the $H$ of Henry’s law constants. Integrating the above equation leads to\n",
    "\n",
    "Integrating the above equation leads to:\n",
    "\n",
    "$H(T)= A \\cdot exp(\\frac{B}{T})$\n",
    "\n",
    "Alternatively, one can create an expression based on H \t at the reference temperature T \t = 298.15 K:\n",
    "\n",
    "$${\\displaystyle H(T)=H^{\\circ }\\exp \\left[{\\frac {-\\Delta _{\\text{sol}}H}{R}}\\left({\\frac {1}{T}}-{\\frac {1}{T^{\\circ }}}\\right)\\right]}$$\n",
    "\n",
    "\n",
    "$${\\displaystyle \\frac {-\\Delta _{\\text{sol}}H}{R} = 2400 K}$$\n",
    "\n",
    "The $H^{cp}$ at reference temperature T= 298.15 K:\n",
    "\n",
    "${\\displaystyle H^{\\circ}=3.3  \\cdot 10^{-4}}$  mol m$_{aq}^{−3}$ Pa$^{−1}$ \n",
    "\n",
    "The conversion to  are calculated at a temperature of T = 298.15 K and a solution density of ϱ = 997 kg/m3.\n",
    "Conversion to mol kg$^{-1}$ Pa$^{−1}$:\n",
    "\n",
    "\n",
    "$conv=1.00301 \\cdot 10^{-3}$\n",
    "\n",
    "\n",
    "${\\displaystyle H^{\\circ}=3.3  \\cdot 10^{-4}} \\cdot 1.00301 \\cdot 10^{-3} = 3.309933 \\cdot 10^{-7}$  mol kg$^{-1}$ Pa$^{−1}$ \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "711e4200",
   "metadata": {},
   "source": [
    "# Dalton's law of partial pressures\n",
    "\n",
    "https://en.wikipedia.org/wiki/Partial_pressure\n",
    "\n",
    "Dalton's law expresses the fact that the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the individual gases in the mixture. This equality arises from the fact that in an ideal gas, the molecules are so far apart that they do not interact with each other. Most actual real-world gases come very close to this ideal.\n",
    "\n",
    "$${\\displaystyle p=p_{{{A}}}+p_{{{B}}}+p_{{{C}}}}$$\n",
    "\n",
    "- $p=$  total pressure of the gas mixture\n",
    " \n",
    "- $A, B, C$=different gases\n",
    " \n",
    "# Partial Pressure of CO2\n",
    "\n",
    "The Carbon Dioxide Concentration in the atmsophere.\n",
    "https://gml.noaa.gov/ccgg/trends/\n",
    "\n",
    "$c(CO2)=418 ppm = 418 \\cdot 10^{-6} $\n",
    "\n",
    "\n",
    "The standard pressure of the atmosphere.\n",
    "https://en.wikipedia.org/wiki/Standard_atmosphere_(unit)\n",
    "https://en.wikipedia.org/wiki/Atmospheric_pressure\n",
    "\n",
    "$p_{atm}= 101325 Pa $\n",
    "\n",
    "Taking the total pressure $p_{atm}$ and the concentration $c(CO_2)$ we can get the atmospheric partial pressure of CO2\n",
    "\n",
    "\n",
    "$pCO2= 101325 \\cdot 418 \\cdot 10^{-6}= 42.35385 Pa$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "502d1324",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import fsolve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "87c03a8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "p_atm=101325 #Pa\n",
    "\n",
    "c_CO2=418e-6 # 1\n",
    "\n",
    "pCO2_atm=p_atm*c_CO2 # Pa\n",
    "\n",
    "#henrys law constant at reference T \n",
    "H_ref=3.3e-4\n",
    "\n",
    "conv=1.00301e-3\n",
    "\n",
    "H_ref=H_ref*conv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5ea2d3f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#temperature dependece factor for CO2\n",
    "f_CO2=2400 \n",
    "\n",
    "T_ref=298.15\n",
    "\n",
    "H_ref=3.31*1e-7\n",
    "\n",
    "# Henry's law temperature dependence\n",
    "# T in celsius\n",
    "\n",
    "def Henry(T):\n",
    "    \n",
    "    #convert to Kelvin\n",
    "    T_K=273.15+T\n",
    "    \n",
    "    res=H_ref*np.exp(f_CO2*((1/T_K)-(1/T_ref)))\n",
    "    \n",
    "    \n",
    "    return res\n",
    "\n",
    "\n",
    "test=Henry(25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b812d226",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CO2_aq-concentration [mol/kg]= 1.401912435e-05\n"
     ]
    }
   ],
   "source": [
    "\n",
    "#concentration of CO2aq in the water \n",
    "c_CO2_aq=pCO2_atm*Henry(25)  # mol/kg\n",
    "print('CO2_aq-concentration [mol/kg]=',c_CO2_aq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "28534bed",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "3ae64936",
   "metadata": {},
   "source": [
    "# Dissociation constants\n",
    "Those dissociation constants are dependent on Ionic strength (all dissolved ions charge summed up) of the solution. This dependence will be neglected here. It will make the calculation much more complicated.\n",
    "\n",
    "$${\\displaystyle I={\\begin{matrix}{\\frac {1}{2}}\\end{matrix}}\\sum _{i=1}^{n}c_{i}z_{i}^{2}} $$\n",
    "\n",
    "both cations and anions, $c_{i}$ is the molar concentration of ion i (M, mol/L), $z_{i}$ is the charge number of that ion\n",
    "\n",
    "https://en.wikipedia.org/wiki/Carbonic_acid\n",
    "\n",
    "\n",
    "The squared brackets imply the concentration is meant:\n",
    "\n",
    "$$ c( CO_3^{-2} ) = [ CO_3^{-2} ]. $$\n",
    "\n",
    "Because the $CO_2(aq)$ reacts fdast to $H_2 CO_3$\n",
    "$$ [CO_2 ] = [CO_2(aq) ]+ [H_2 CO_3 ].$$\n",
    "\n",
    "## 1. dissociation constant carbonic acid\n",
    "\n",
    "$$ CO_2 + H_2O ->H^{+} + HCO_3^{-}$$\n",
    "\n",
    "$$ K_1^{'} = \\frac{ [HCO_3^{-} ] \\cdot [H^{+}] }{ [CO_2 ] } $$\n",
    "\n",
    "## 2. dissociation constant carbonic acid\n",
    "\n",
    "$$ HCO_3^{-} -> H^{+} + CO_3^{-2} $$\n",
    "\n",
    "$$ K_2^{'}=\\frac{ [CO_3^{-2} ] \\cdot [H^{+} ] }{ [ HCO_3^{-} ] } $$\n",
    "\n",
    "## disscociation constant of water\n",
    "\n",
    "$$ H_2O -> H^{+} + OH^{-} $$\n",
    "\n",
    "$$ K_w = [H^{+} ] [OH^{-} ] $$\n"
   ]
  },
  {
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    }
   },
   "cell_type": "markdown",
   "id": "a5431c91",
   "metadata": {},
   "source": [
    "## Variation of the dissociation constants \n",
    "The dissociation constants vary with Salinity (the Ionic strenght of the solution), pressure of the system and temperature\n",
    "\n",
    "![bjerum_plot_pK_variation-3.png](attachment:bjerum_plot_pK_variation-3.png)\n",
    "\n",
    "source: (Zeebe and Wolf-Gladrow, 2001)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aebaae68",
   "metadata": {},
   "source": [
    "# Simple Alkalinity (TA) expression\n",
    "Acid buffering capaity of a carbonate solution.\n",
    "\n",
    "Carbonate alkalinity\n",
    "\n",
    "The alkalinity can be introduced  by any alkaline substance added to the solution for example:\n",
    "\n",
    "Some Hydroxides (strong quick reacting base):\n",
    "- NaOH, Ca(OH)2), Mg(OH)2...\n",
    "\n",
    "some Carbonates:\n",
    "- NaHCO3, Na2CO3, CaCO3, MgCO3 ...\n",
    "\n",
    "The hydroxides will react with the CO2 the Carbonic acid from the atmosphere to from an new equilibrium state.\n",
    "\n",
    "$$OH^{-} + CO_2 -> HCO_3^- $$\n",
    "\n",
    "\n",
    "Alkalinity expression for a pure carbonate and hydroxide acid-base system. There are no other acid-base pairs involved like other inorganic bases or organic acids\n",
    "\n",
    "$$ TA = [HCO_3^-]+2 \\cdot [CO_3^{-2}]+[OH^-]-[H^+]$$\n",
    "\n",
    "\n",
    "\n",
    "set in everything:\n",
    "\n",
    "\n",
    "$$ TA=   \\frac{  [CO_2] \\cdot K_1^{'} }{ [H^{+}]  } +2 \\cdot \\frac{ [HCO_3^-] \\cdot  K_2^{'}}{ [H^{+}] } + \\frac{K_w}{[H^{+} ]} -[H^+] $$\n",
    "\n",
    "set in $[HCO_3^-]$ again:\n",
    "\n",
    "$$ TA=   \\frac{  [CO_2] \\cdot K_1^{'} }{ [H^{+}]  } +2 \\cdot \\frac{  [CO_2] \\cdot K_1^{'} }{ [H^{+}]  } \\cdot \\frac{ K_2^{'}}{ [H^{+}] } + \\frac{K_w}{[H^{+} ]} -[H^+] $$\n",
    "\n",
    "simplfy it:\n",
    "\n",
    "$$  TA=   \\frac{  [CO_2] \\cdot K_1^{'} }{ [H^{+}]  } + 2 \\cdot \\frac{  [CO_2] \\cdot K_1^{'} \\cdot K_2^{'} }{ [H^{+}]^2 } + \\frac{K_w}{[H^{+} ]} -[H^+]    $$\n",
    "\n",
    "\n",
    "solve it (find the correct $[H^+]$: \n",
    "\n",
    "$$  0= TA- \\frac{  [CO_2] \\cdot K_1^{'} }{ [H^{+}]  } + 2 \\cdot \\frac{  [CO_2] \\cdot K_1^{'} \\cdot K_2^{'} }{ [H^{+}]^2 } + \\frac{K_w}{[H^{+} ]} -[H^+]    $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8a6bc932",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import fsolve\n",
    "\n",
    "\n",
    "# I am using the constants from phreeqc.dat  database avaiable at:\n",
    "# https://wwwbrr.cr.usgs.gov/projects/GWC_coupled/phreeqc/html/final-90.html\n",
    "\n",
    "#(Parkhurst and Appelo, 2013)\n",
    "\n",
    "\n",
    "\n",
    "#first dissociation constant of carbonic acid\n",
    "pK1=6.352\n",
    "\n",
    "K1=10**-pK1\n",
    "\n",
    "#second dissociation constant of carbonic acid\n",
    "pK2=10.329\n",
    "\n",
    "K2=10**-pK2\n",
    "\n",
    "\n",
    "# dissociation of water \n",
    "\n",
    "pKw=14\n",
    "\n",
    "Kw=10**-pKw\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2158bf33",
   "metadata": {},
   "outputs": [],
   "source": [
    "#alkalinity of the solution \n",
    "# 10 mmol/kg\n",
    "TA=10*1e-3  # mol/kg  \n",
    "\n",
    "TA=5*1e-3  # mol/kg \n",
    "\n",
    "\n",
    "#define the  alklainity function\n",
    "\n",
    "# the variable is teh H+ concentration which is directly linked to the pH\n",
    "func = lambda H_ : TA - (  (K1*c_CO2_aq/H_) +2*(K1*K2*c_CO2_aq/H_**2)  + (Kw/H_) - H_)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e3f1837a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "H = np.logspace(-14,0, 100)\n",
    "\n",
    "plt.plot(H, func(H))\n",
    "plt.xlabel(\"H+ [mol/kg]\")\n",
    "plt.ylabel(\"expression value\")\n",
    "plt.xscale('log')\n",
    "plt.ylim([-1,1])\n",
    "plt.grid()\n",
    "plt.title('Find the point/ [H+]/ pH-value where TA-(...)=0')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f15f861b",
   "metadata": {},
   "source": [
    "# Find the pH at equilibrium of the solution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6c9b81f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The solution H+ concentration is   c(H+) = 1.336151e-09 mol/kg \n",
      "at which the value of the expression is -2.602085e-18\n",
      "The pH of the solution at equilibrium with the atmosphere: pH= 8.874144\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Use the numerical solver to find the roots\n",
    "\n",
    "H_initial_guess = 1e-8\n",
    "H_solution = fsolve(func, H_initial_guess)\n",
    "\n",
    "print(\"The solution H+ concentration is   c(H+) = %e mol/kg \" % H_solution)\n",
    "print(\"at which the value of the expression is %e\" % func(H_solution))\n",
    "\n",
    "\n",
    "print(\"The pH of the solution at equilibrium with the atmosphere: pH= %f\" % -np.log10(H_solution))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4eeb43a5",
   "metadata": {},
   "source": [
    "# References:\n",
    "\n",
    "Zeebe, R.E. and Wolf-Gladrow, D. (2001) CO2 in seawater: equilibrium, kinetics, isotopes. Gulf Professional Publishing (65).\n",
    "\n",
    "Parkhurst, D., Appelo, C., 2013. PHREEQC (Version 3)—A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations. Model Tech B 6, 497.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec1b0aa6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}