{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains course material from [CBE20255](https://jckantor.github.io/CBE20255)\n", "by Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE20255.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Henry Law Constants](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/07.05-Henry-Law-Constants.ipynb) | [Contents](toc.ipynb) | [Bubble and Dew Points for Binary Mixtures](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/07.07-Bubble-and-Dew-Points-for-Binary-Mixtures.ipynb) >
"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "Ul6-TcGgTzMN"
},
"source": [
"# Binary Phase Diagrams for Ideal Mixtures"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "Ul6-TcGgTzMN"
},
"source": [
"## Summary\n",
"\n",
"This notebook shows how to use Raoult's Law and Antoine's equations to calculate Pxy, Txy, and xy diagrams for binary mixtures. The video is used with permission from [LearnChemE](http://learncheme.com/), a project at the University of Colorado funded by the National Science Foundation and the Shell Corporation."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "vP0hlXLwTzMP"
},
"source": [
"## Introduction\n",
"\n",
"For binary mixtures, Raoult's law provides a very useful equilibrium relationship between pressure, temperature, and composition of liquid and vapor phases. This relationship can be expressed as a set of equations, or graphically as\n",
"\n",
"* **Pxy Diagram** relationship of pressure, liquid, and vapor composition at fixed temperature.\n",
"* **Txy Diagram** relationship of temperature, liquid, and vapor composition at fixed pressure.\n",
"* **xy Diagram** relationhip between liquid and vapor phase composition, usually plotted at fixed pressure.\n",
"\n",
"The following [video](https://www.youtube.com/watch?v=E_Vuz8cfbEo&feature=youtu.be) from [LearnChemE](http://www.learncheme.com/) gives a brief introduction."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 321
},
"colab_type": "code",
"executionInfo": {
"elapsed": 351,
"status": "ok",
"timestamp": 1541104787059,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "m_yfuELiTzMQ",
"outputId": "3fceb434-33fa-4d5c-b0f9-a3d3f9197650"
},
"outputs": [
{
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52MzjGVK/JIiLA1j537u3Hcrz3qVmly2ixHv2tZ4hqLl6DhmbjY3AM6KaeNkrwdLHOAc7\nw9gqpuJYw9jRFzmCfXfK1DV989vgvMPeXygDd1fmkntr9LjqBbtusbW3GNPf8WghyBwvm5sGPpbZ\nEprU3w3Xr0+qyz+0eLH7Tsfq1YvK5JkaLAN3fw6D6rzufxSfiUWMcpsQEDS1mhpHWutk+QXKle50\nm+23TyUtdXsMiaPGdl5WT7QyTwus40OLkHWb6Db5Bc85uOfYM4hyI/ejLfK1DVXMvp8F59gNEjqd\ngkaCXU3fsiU9hwTKxx7LPgwuIY+Dn6iZHzEA9fXr4dr3VPtPnYuV7O4UEGezLmY4azq8bvCQXEdR\nZ/qvMTRiN4Zqt3U+QQWta27vypCnrfak4fFuGwZ2PxCAGGI/sS4a3E1tV7HZac6ThnEXcJ4g7icM\nTMWi6Mkaybaaq9twvEintIa06hv8klkUfNCnuPtPBHtr7wcuAY/u2nm6xpvytcbhHFYcD2rycqV1\nwSySsL27gNL7DvXoFxYonSPOoUB1VuQGR6ZNOw2oKWur10uVFiuysrK48Z4HWceLHnOs2bAr8l5h\nubE77xLT6i1zS5t0CLQTa1GUwzOLsMex4tjg4eiZchrtO4sOHcK5mbK0U6nepW4zZnF0mffb8VuI\nXGiz2FzdbS3fqN11GZMMn3ZG35E0VqJhmYlYlKax5qCFbZohSkJ0pSyiHokIVhSFLKVhycOVYTCl\nzdVgcnBVQThBYHJw4KkFSCgu1BYpD+0f/iK0grFIf2jviUDWptU6vRTq9CgttTapMoUc1tblBfqC\nNYVHPjHU/RVvzG/ut+ZKDXrb6oDgehXOdkucdnV8EolkB2cbVR1bQufFmHo/6q05Ibud1FprVcs8\ncX3jv5BZH5bjXLOkeqzudq1E9B+allNLs4knlt29VScmR2xcXH8lS0kitgpmHJa0b27qixCwzeGu\n/cqGR20uqm/mSqw11WdlY55GODe58I/VZaj+2vhPCcni80keM6Fr426nCRxA/IFbsv2P4vBC+XTB\nMAL0QvJdXwIC0/8Ah9/+Vy768kf/ALKv2Rmmh9pHwxWIpnScxo6bAm/jdKsubwTg03F3ZLYpWR+7\ntDjrBN3f6LjtlBAdvVL3mDw3ByPaX2gbNiwTNjDCwSRh2klpLqvpv/Rcf2YhJ4U+TC4L77nahU+Q\nG8lg22FkHp5b7rSPPAtemEZa4W4BvmV672n4fixYXDcx+NDjTzSNjyDj/doi3EV1qtiutJgFnEMT\nHw+F4UvCXx3LK5jXE9e5Pw7G7Usp4iWLMxtHNbPGHN1AyAjUPS1TJkSB7HCR2489l7PC924r7W8Q\nhmczNx447jEoD2sPhvTe3W1y2z8LzuNxQQ8Hlnx8dpjZDEG+Mg1qdZAr4nyUacRnEpQ4sexpIVvv\nzqILQ357/RewfgHN4TnfaXDMXFljYXxcnTqbsasgnfb5rl4DcLE9jI+JycOx8nIbIQDI0WfGQLNW\nQPJLSoeadI+dxtxIP5JL0nw7V5r3HEp+H4eNw/ibeGY5ky2tBaRsAQD0qie1rie2+HBh8Vi92ibE\n2SLU5rRQuzvX0UVxsdw1Edz3TPZzJgejQPyVELtJBPa0PmIoNcVPtq+FssmtwDOgVL71WepSDomY\nC99Il2vi3aGt3J6nyVzGNgjPTUUkMYjaXOJvf5BVTTa3+DoOijccEn6699+qhjXPdTRZUsNHUdye\ngWppY22trUdzQS0iLQyBrO9u7lZ8g/tdtqFK8vYPCXE1usuzn240D1KQstsDDHGAep3KaQNkjLXb\nDupLqFqmUgx/eoFZa6hgcwXfQ9ihr6NO6/1TOt1kpXCxRXRxmD2mCrZY2JVmsmvRRYS0GxQvdX9F\nSyToa381cTZuuyi8HaNUZIduOyaPXTnNeRp8iqA6nbJua4WWuIvruhUND58hrQ57zXxVYypA6xIf\nnukfK8s8QBB6Ko2NzStyk4w2e/SfhaoOc/8AC1Y781BtXaU1h1QnCzGU/uj5lRzX+a0jXsFIc3zH\n1WIuv7zkttvqqjohMucJS3o818U3vB/EVRvWKT+8d8SlOQ/sSsTp3Oc6z3UGt0rW+vwVT5i7psFn\n1m+iC8dyEFus9ioc4u7qkvaO6jmj0QWk7UkIoJOZaeM69QtraF240l0VaACTsntIdRfo1NvzB2Ve\nqv3k2speHgHcKHPJb3odVSJG2LcExkb+6dlmVhOpGrbqq9bVW4lp2NjslWNLXtDgXC67KXOL3a3d\nT0KoaHVbhsrXPe4eInb8lJVJJJoWQlEl/JBcQR0HwVZFbt+YSEeh9luMY3BpMjIymyODm6f2YBPU\nevot8PtFwbh0c0vB+HTHKkveY7bnzsmu9DyXkA8FtFpUtcDsFR6L2f45Dw7J4hLnmWSTKAtzAD4v\nET39Vfg8Y4V/Zn7KzDkQtb0dCN3jVf8Au15miBZ6qDG8hS1p6x/GcPisXCuHYOO9j4p2aWTAaKAI\nonutnHsjhEvE5Ic/hXEJZAAzVEXBrxXYBwvr5Lw4uNzXAFpBsEHcLoD2k4y1ukcRmr5E/WrQelP2\nd7I8ec5vOdDNjf3bfE5h1ep6bLj+zPGYOEcSyJcmNximFamiy3e+i4Us8s8rpZpXySONl7nEk/NQ\nHWwtPc2g9Vhcd4LgQ8SgxW5snvQJM0gBLnEEemwvvvuVhHF8YeyA4W5svPD9V0NP3763/ouECBsB\nSlzi4oO9xbjeNncK4XiQMla/FDOZqArZoG2+/RR7VcWxuMZsM2M2RrY49B1gA3d9iVwRshQMRe1g\nKkPp1FOqiaf0taglc03QC1fsmfdN+e/VZ4mMohz9IQSsrHCyZ73BvWnXsEjHFood+yXURVdQjqel\nIp2AOJ1O0gd1aX20hg8PcnclUEgHY2ApMx00NgoANtws9VA2NHcA9FDSQbBpM1w3ttknZUaHTF9a\nRt6pHNJPjJsqtsjo3We/UFXB0cuzpHNPcFZatRIwxm+rfNKtfKJNHdo8lmfE6M2N2dPgrEszBUIH\nn2QqhmG6AFlaDsLWUbOHxWyOPWfGaHmpKwr63RpNo1CgQ3yBQXaXENAq+6drmmMgg13rsosEbudD\n9/L0UEtPbo3fdLI3T0uuoKW7G3xKqHIvrQA6/oleQTYquyTr0UIJ5p7Md9Uc5w/c/NVaiN7v0Uh7\nthe63bCwTPPRgSumeEBzhvZ3UF7gaJN/BLKBml7f0Uc6X8VKSSWgv6HpsrIuUyjqIP8AhV2ShE2e\nW93Aeu1oOP4jqd3Wpssf4tRWSScmQ0HDfoQue0y1UQORv1FKDC0JTN538gjnjyNpyvCBF+I180ug\n3tt805naa8O/qpfK3YFoPdXlFb706aN+dqssd1oq4ZDdwWNpHOYd6I/olzCM9EdUUXdyVaSHbiin\nZGT/AMsfHotbFKWwPd0armY7h1cAmLZWmmHbvupELiPGSszkupuVH6IHJFdEhjr7jXJJWGMC2A+t\nrParzOxvQXXmq3yMcSSAAqRuKpo9LQQR1H0WqLWa29RZ+KgvZ+Ej5qgud2CTU5WmbaS8VVD42oMo\nH3dvgsxsoorVFtHvHa1BmJ7rPSYXqFBKhLXBxJq09bK1kA073aUtJJ0xuIHUrF+NURFqC4A7g2gk\n1Yagm0KuyB5o1HuPmqGLuiXXvRH1SOuvRLZ2HZWIS15PkgjV4asqYg3Qep9FqicwbNLfmszNL2zt\na7SNifM0jezVkrcGirBG6ghuoE9QsbNUxXR9VF7rRIA5xGn8kghBHTZW0UF3khpoeI7qx2ORekBK\nICTuCVq4QXtt5qWu2sfBOYXN6MJCBC4n8PnspcKUkne7UfVaI2MA0lpJHekOxw6q2U2hVDXOAoE/\nVO2R17uNHqpfFpZsDY7+aqLXV0P0VsWDQWSOshwFi+hSA7DsoANj12Ruxw1MJCItiAfK1p6XXwWz\nLcPCxjaYPMdfVYoZY7NDSQe60vIIHlWyk9tR0rs11Q00dkpNUTt3oo7EjsiLTGJMZxAt7fVVUK60\nfXumZI5pcGnr1UUHCwAEUuwKkNOiyCfgrOTpIDjqs7nsrWubVdApMlOWK8tRTax+Fo+StM1xlvKY\nD2IG4TRyxRuJluRtdAA0rbCoSua0eFoPwpPzWl2736fkE7sxhkBjiYwAjY72lGS8P6NHqBuEEks6\nsjseZKNYv7tUERZuggSsEtdA4lDsgyuMnhj7UwUPkFKVGo34WuVJDnPPhPVWHIe37rtQ86VTpHOc\nSCT60qiSxw/dtQ1g70FAJcPvfK0FurogDoDti07phvQDXFQHVs0kFO6Z2gDmONHYX0QQ3Hlcb5ek\nfFXNxfxuHyVDS8US8NB6bp2EX45SfRSbXhppjfK/M9VPXvSzukYB4bF7bL2WDxYTezOdxB2Bgc3G\nkaxg5HhIOnrvv181mrLeWAHmiwF6hsWBxHgPDZMxwxn5WW5oMEQtznOcA30CxQ+zl5nEGzTSnHwn\nBpMMeuSQkWAB8CFNZLcO/T81VIa+8Oq9K32bb9rY2KJ5Gw5UTpY3vjp4qrDmnodws7OEYE7uIlvE\nHugwI2OkkbHeonVqAH/p2+KsYyW8/wCA/hVJjLn2BuewC9b/AGY4YczDh+0cms+PXjgRi9hZ1Hyq\nlgxOCY0WJk5vFsmSLGgyDjt5TbL3A0T8P0K3EUjhODWvoEPHYkV+SqcAHG6tepPsmxvFMqDJyTHh\nY0HvBmYNyw3Wx+Dvp6rfPwjh2Zw/geNFMWRzmQNn5QD3GrAd/T4qpLwwabofQqxsbnGmtBXoMb2b\n1ywwZU7opZ8t+O0Bt21gJLvqKU53AsXH4Tm5eHmSTyYWRyJWvjDW6tQG31CTMjjR4GujI5sbPNxq\n/gpihha7UXg103XpMb2ax8iJ7cXiE8mQ2Hmc1sX7A/yh3/VZuHcAw5sLhuTl5ssZznmNjI4wfFZA\n3PbZZ5leHJ5jNxsAPVJIG6tiLO25XayfZzDjxuKcnOllyuHDVK0xgMINkAd7ofVas3hE/FcjgmLz\nIm68TWXtjrSwBt3ubPTyU1XZ5blt5gA0k/HZWaGsaHHv6rsO4FgZMkUfC+JBznT8h7ZwGv8A8TR3\nH+7S8b4LjcOx3OilzDIyXlls8Ba2QebXAVXx/wC9pLcf9m8d/mqJdMbgHafRdfAjHD+GzcRmax0k\n1wYjXAEX+8+v5eg9V6jhMLzwHBPA4uHznSDmRzjxvdtYvsevX0ViB8/2dsQQpDS6gGnbuvRY3AXc\nQzuISzwSYEOK7x48DeY8OO+hn9elbitlePZYHi2JjDIlbj5cTpGPkip7aAsOB77pyjzcLWCWpiQw\njfT1SvEYss1HsF3MzhGL9lHPwc7nMinGPPzYwxrHWBqHpuPkVqk9msR2HlS4+ZkSPxYxK95h0xSi\nrIYfh6qcq8w07bEtH9UzHvG5BHkSu3mcEwsTg+PmnPImy2NdBC8UCTV2R2APVaX+y+I/Cy5MPNyJ\nZceLm63RVDJtdNd3+qUjzwyDdUDSZuQwjf8AIr0fEuHcJx/Z7hs0Ep5sj7jkMPimOro7yr/RWcY4\nP9oe0eYcudsOPiY7ZZpYo62o0ACT5H6JqtvNCSM/vJmlnYj5Lrj2cx5MjhhxcmR+Fn6mtkcynMIB\nNEfIpcn2dxm4ORPg50ksuLkjGla+PS3UXBu3wJG/oVNVtzgb+CKtdbinAYeGY015WYZoWglz8Y8m\nS+zXAbde5XCZkE7EC+wWZxmFtdpAHdQ3UBvulEu5DhpoX8Uon23Au96UoWWgNCo5znDw0pbP8D8k\nqUtfoCUs8gEglvp19VHP2G3Xv0SpUGBuqwBZ8lf7t4SQa38lRHM4kEtbt61a1HIaK36np6KzsjM+\nFzCLFjrdpW9aWoyuN0KA333VMxLvExvwrurEz9qIomvJLrq+y0NDQKbpr0Ko00w6hV73aOh9PRSe\nVhbqYRX5JSwk2NgpidbwNIJJr/dJ5oniy+gB0o9VF7cklxFaaruUjRYJcaTkeGw416hNpYHU06vU\n9F2hyoobbASLpS1ukm9tu6CXONBpAHkoMTy7SWm+1hKkM1ul2oUb2qlIZZ06u3ZTHC+3NNixe6Gs\nN7NJvyCA0+LSevkqneEn8N9FpGNKAKbpd6iknujnSODpB511UWpUtojp3+aY7EafomMbIJPE8mj2\nCslijbRicXXVb6v6BClOxPib0UBhrfqeiv8Ac5XhpAADhYJ2SvgMIt7dugNpa1Ko9Dtv6qCaNBSK\n7FoF/kod1NDYBGU1sOpP5LrYPFY8b2czuGSxSGXJkD2vbWkAaeu9/urkG6FEaaT6gWX0ICDss41C\nzhnCMXkyl2BmDIe4VTm6iaG/XfutsftNBJm8UZMzJjw84te18Lg2WNwAF9a7Ly7LIvq302U6Rueo\n80tXpMf2hwsTjWNkxR5kmPjwujuSTXJI4/vGzQ6dlz+H8UixMHi+M+ORzs+MNYW1Ta1dd/5h0XKd\nFq22NdfRFuJvz28kHpB7Q4/v3BMgQT6eHROjkb4bfbatu/T40iLjGBl4OZgcSiyRjTZTsiN0Va22\n69Jvb/uvPM32H1QGDxOca37JY9MfazHn4pmHLxpfccrG920RkF7Wi9/j4j+SoyOI/aUXDOG8Bxp3\nZGE8vjMrm+Ktwbv5lefBYXbUPJLHbnWNiOtIPYcc41HH7YYs7mufDgCnMjo29wOqj0O5A+RXLdx2\nAcN4tB7vKTm5vvLNVaQ3WHaXb9dq2tcZhtuluzfNK2UVRFgeaD2knthw9uaclsXEHB8HKMOpvLj+\nDb6+vouRi8cgj4fwbHMMxdw6XmSEAU4WTTd+u/elwAXNeSNj8U7iXbaqd5Ko9B9v47pOPvbDN/5k\n1rY+nhIDh4t/UdLV0ftVFDmcMyIoJCMTG93ma6hqB07t39L3XmNmhoca77JnC3b9L/JRXbmz+Bwl\njcTByJdU/OklmeGSNH4WFpsV/vqum/i8HFcd/CMObNmdlOBMmYW1jsBskEbmgO/1XkidthXkkbYa\nARfkER0ONZceXlD3Y6cXHYIoGeTB3+J6rp4HE/Z+saeTBysbLx6s4rgGyHruSbXngHBpG39UVqNk\n6fS1Felb7VNky+I+/Mlixs0CjjvqSKhQIPda+BcQxsr2nwo8Xn8mGF7eZkSlz5DW5O9D5Lx5Yw7v\nO1bkC6TtEJP7QDSegrurZT0MvGcDGwfcuH4s74zmDIyBPVGnA6RX+EdVqzPanBldxER/aD/fMcxg\nSFuiI1XhbfrZXk2lwGloJHfdDm+VdepPdSx1sri0M8XBWCB7vs5mmQPqpPu9PTwnr5rr5XtXhPlz\nXxtz3nLg5YZI5uiI1XhbfzJXlY2gsadVOI3sWqtGqTc7dTsrElO6/imFP7P4eJkMyG5WEbYWBpY/\nfvfotr/aPFn4pmzyQTe452O2CRmwkFAixvXcry7XNF6WhxvupeJHR+JpAb0IUsp6H+0OLj5XC4cW\nGc4PDy5xL65kjiCPh3/NZ/tvHkwOKYfu8zzmZhyBRAAbrDtLjdg0K2XHMY06i4hwAsV1Sh8mutRA\noAkeSD1cvtFixYWTHju4hKZ4jE2HJeHRx3sTq3cfqvJu671Vqdzerp691Dm77HcGh8UsN+8NJ2HW\n0F97AV8EpsN8JBHc31UiMNeXGzt8lA7IwDs9hI81DhpBs90pOp23hb380ffbvdItpeNOkAWQOyg7\nt/0Clrg5l1YCGMJbfb1QAALgAR1Voad3Oc3y0jqq9IFmu/VPYYG0dia+aIts7Na6muG+3l5pSZNI\nqxv1qkODdyBvW972oDiSBfyq1Fs51aegBP8A3SsDiHOs11J6X8FJaA0N8V+V91DTZ1E0OoCCRTWg\n3v1pQQQSDZJHQJJOxLtu6djn78s9ewKKy6Xs8LjRrpRUa3O/u2avNXc+MzhxO38oWtmRAATZ/wAJ\nFfNbmaWMYlzBPICQ36LSZ5Dsa1KJWxvk1Q02ze6kuEekN8ZPXsR/0TiWapHOkJDnEuLutBWF7tvD\n3+iiR51O0t3F23qAq2SvrcVfopQcyu100fO1Q6SQSHcde60t181o0V5dNlVkRs5mxt1+fROl1nsN\nkxC1vNicX/vUUznsinJxGu01vYtZnMcHUNL7H7ptTHJIzWzZprexdqp/tu99cWR1HuNj2WafIL7D\nztdgeSrbK8AnwbebUMfrvURfoFKWZsjy1zgRVpgHGPfuimNFHcAUma6PQRpJ2ob9FWaKxuqTQHMY\nP5lMrQ3SNjq38PxISuA2vsbVsXJABdZI3s9EWlTQXDZ+56CkwdsOxvoO6HeEuLR1SF2mnBvTZO06\nWtG7i7bvsp/Y6TpJaT5qtkwYbLQT1JctLMYyNdra5t9q3U6aiL6ZhsToN+FQLe7TqoevVaGQxiTQ\nHEH1/wC6JINLOY3xD4i6+CtwTjJIwxwNnSANiSoabaGRhupx6kpRGQGve3wndoI6poQ0ysY4A6ng\nWDRFpTK12PyXj3jU1obdNr6pJW45j0wGQ/4q812c32eyvfsmDF8ccT+TEZpAHSkN1FrR3NKqX2ek\njwMbLhcHtdjsmlY5wDmlxrp5eqK5BYTpb18irxEGsNvbqrpva25/Ccnho52Vyi1svKcYpAS19XRH\nbbdbZeCYrOCw8QcziMnMhMrnQ6NEfxvdDhwZnNF8uPR2A636q2GGR8dHQ41+6d1uwvZ3LfkYgyHR\niHIlETnwyB5jOkmj9FUOD8Rjj95jjaRu5kZeOY9l6dQb1qyEmCJi+WQY72ffaTd1SOS9xOlhJroS\nF0n8B4m7JggLo3vkc6OxKCGPDS4tNdDQSx8F4lzWsYYix0Qm5olHLDOl6vjss1K3i4rXauv3R5LQ\n2DUweJgA28RN/wBF0ZeAZuLhzzujY0QP0SDXuDQIrz6hN7P8N+0c18eS2VsUcLpaioucRW3frasp\nTmTM5X7Lw1W5b3StFRU373kOq9Zk+y0TxK6CV0ZMbJGxT00tJNU7yWfG9nsbHx2uzpMmKd2ScYcv\nQ5rfU32+CFPNH9yz9eqYbyabqhYWrLazh2TkYeXC2eWOQt1AkAjzWed7Oe33eMtjqqJs2lIhznu8\nqHdK1tgb0T1NK1sBjldrc2QdNnVuneyMROMbbf0ppulGtZUu8OzT4eu3VEfm4gtHQauh+ChwcGgG\n7PelYxpZGJOUKHc0UQj43cwdW9vRWRM5zizmNZ8W1a0M0mOpwW2LG52+SzSxFuQ5sHiaBu6qPwS1\npazDDmftnPa391wFh3zVb8a3N0PDh16bj4rTiSY5aGljw9pu7/3SbIDpA0se4DrRrdLWMbYpA9o0\nbhpq2gJ3x63DXE9od1vYIeHQOa626wb23WpuRzgLc1rrruQiV6572tYaja4NrqTupqgN20em1ldA\nRRtldIeXMenTpXooc2JslssCurQf6UhTIG6gKLWeigxAXoc4t9VfRsNDGkAkBrm0T633VhdDG0F0\nWl2428lFiGWFhkeA0Gmmz6DzV2XDA17THI57+5IoD5IL2c1roCLPW+n0VmW6N9lji8iwTVfIJaTC\ngWHnT4iPPskOoPFk+Lct7q+MP0mN8bgHWdwVUWjnFwtxOxHYIkwBqbud77dSUuhzXONmwe/ZOKc0\nlrXUCma0eIGyHiq8x5qFM7X76ARvuQU8ZAa93kVqvGLyW48Y+A6Kmcsk0gDQAex6pa1TnxbMO3fq\nlY8ufuaCkanEB24rsFMMJdIPATv09F0Z5MH+ItYRXmVYwWxgN3+LyS5EWg2Rpabq1Eekwm3Afhuy\njUdupLHqi5jS8lwvZxr8gsEToi0CQPJ9KCoGTM2mBzhXTdDT+1skWDvSY40uWd9OpG6B0YAL/COj\nj0XJm1OncG7+I1XddXFERZIXSRtJeerSSn5TC645N9ttABWYmm5jaOXDGtr+4KsY0uJsk+avyGFu\nRI0buYbBrr8Vr1tbjazkW7TuwNH06Lc5cOWrnOhddMsg77KBG4dFriljZY0uJfvepJHJA5x1scT1\nu7UuV1hnEZ6agLTtjABFn1Tyvhc5pia4djape2ngs6p2zMUtMYDKFn49VZHDzDp2a0bu3VEZfJM1\noFuJ0ho7rQ2N0bi0aGvBohzqUaxiETRMiqnAtJ7G1YyASgcsNA8i6ykfHIGuMskQb2HMBVFEj+8i\n2G1FIhZmL6bJMcM0WAC5wFD1W2Vk4cWlzCB5hcxskofAOZbdYFX6hdmaVup1mjt1WZaifGIRubnw\nc2idW1NW18UfMd4G9fJYM2YRZmPKSSG2aHfdQ3iEksz3NZsSAGH1NdVaS+UZmuJxcRcf7vokxs3E\niyI5p8f3gsN6SdIJ+W/VXOxw6d7sgnc2GOsALK7BgZfMdI1xJ06SC30VijKJdyD2ldPllzoGPmMz\np4XEmonFtHYdRXmqZuMzxY3JMDH/APDMxi7XR8LrtcuKGTFJmFSAbagOire/nRkaXWBfRaYdHI4v\nJxVz8eSBkQyMsZJIN6To01/qjN4g2bHw8fltMeNGY+v3hawY8DQ9skk/LI3DhvSuZj3KBzGuYN9Q\nFgqSsPSt9oTI4SPxRGWSNla0vdVhunYdhXYLmS8aka2JrMWGTIgZy2TuN6G6rA03VjzVMgcWctr3\nNvfZpOyR+NIIzofb6seBZiZamIdCP2lczKjkOFFFUrp304kOkc0tLie2x6LTj8Ynix2NYxhjZByv\nA8jXRuwRuCuHFFNKy3xlnYtI6rK2eTElfC4FoJ+78fVOSoh2G8afmSiDIxxyfexNI7W5103Rp336\neqqPE3cNzciXHgaRMyRjfERyw4/6bLmHJbETcIbv9U7c4Pj0yxh99CU+7OKbsfis+LjTGRoe/I5e\noudvTTY+vRaX+1DpHF03DopdOR7wwukd4HEeQ616rz8UPNJDXAEnbfoPJbDjx6aLns8ya3SZpKme\nRkwuzMs5EznCSZxkN9yfKla7Et9gA6XX4a32/VUsZI0Brm81gFDS6yFYCwNOt4aPVSZl0iIUOx5m\nNc40SRYvYFWtieIy6J4c+gHafL4q4aHsrmtc3yPQrPm4rXO1x2XE9D0pIn1MsfCNx5qe4kgtdRGp\nUGVrHU/UXXvZSkPa8MB0lVF0gadwRf5rdOcy2OzJMhpa4ggdDW6pDpOZ3A77rZwpolhmc9ocW0Bt\n8SqRgz8rU97RY3aN6+Kz0VMrsWblQU1zTqNnbcdldkPiEYEUrnA/u+SwuikY5jAQGefqnljcxrdT\ndQJqwsy1/KDTRRh0ZbNqF7tPRMYoCWhs7G2dqCobBO11uYdPxCrIeR0og7Eqs7NDnN16Q5w63RoK\nNNvAa46j03VL3t02dwteA6FsEfMALydj367IdswZKzLEVkOPSz0RJkPbLJFpGxIK7ctxxk6r0g9a\n6fRc1uHHkcwy3G51Frgb+Oytwaz9KI52gNcCBZ2BC3faM7RpGkjpQaAsOViDGLZIzraDe+1KhmQ7\nnB56eiVaXMcN4zpsd4eyRwvtqNLYMnJnDZRFrjc3oas/Nc0DmODnt77B2/5LVDlzxxnU5rWNFCxe\nyysSkvygJJdIFAhwq+vb/VRG6JwPMkDJGjSWlR9oyOgLRI0k7Gm7qnJpzmHQS9xtzh0V/wBrcLw3\nGjsyu2I2dZF+lIdDr3ja3RexKzhrpN5SDXZIMmWPeAua69Om1mOTZmZl77saR8Ess73utgDR5AJZ\nI29Wg2na5rWgaN66rtwzckJc4DUFI1nvQVsbQ4m/okkkrZjR18lbhOWjh8JkdN0Lgza/iLWo4ckT\nXPAaNIJ2H/T0WRs0kTCYyQXCjp6qOfkHYveBv95yxNzLpjlERTayOWWBsziCT+61m/WugCSLGypH\nuaRK1ovTqBA+XqtuHHNNwxpfK7mAnxkknr+hQcSQjxZLyPmf9VIyqW5jaIc1sBinYJmaHv6Bxrut\nsmHitY7U83XSxfRY8zHlflFji+RrBQdRIqrUcpwaQ0hwIqiOi3rty5ba8I044+61/wAdSXRAT4Yj\nfmXJo8V3d6vbA0Hv0pb1hjZmLGD/AJbVQ+JwfrOwPkuiRjtHiA2+akOhH7rf8qTEJcy5zhI1/wDw\n7nAgWDdEFas+YPyy9jntHSiW2PktBnjYDTbrsK3TtyWA7Aj6KVC3LkuOkkOL9QO/RQXhtHxb+a7f\nvjTQ3r5JRmRuYNTHNJ8wDSUXLjOk1EEEijt6LYOIOfHTneW9Wtzpcc7FrTf8qVjcOTZrI76bilKh\nblysiXmvsucT6qzHotebIILa+q3SYeO1pJBbt11fqtT8eGZpa2mtoURsQs5TTWOOy/FMOTDofqc9\no3BF/NLJhsbIOVN4CL0EArnvx8zHcXQPee/h2P0TPi5/DhkahzAHcwkkOsH9KXOnXmHSbhMIfpdo\ncK7Aqj3GeCUjHczTKNRcaF/7tccSvbiuOo/3jR19CrnzkwR1K+w3xDqPktazDNrxw9xIBjiFmt6/\n3Sux8ENcCzIxKBstFb/ksDZpZQWh+3qVdFG6N4kbK8OH4SpPDcRM9Q6k8WPDnRsdIGijYsdKKyRY\nXOc57MyRwJJDQ/pvsOqGlskw59eI+JxG6tHDNMlid7STWxKmxOEwPsy+s8h/9X/RZOKYMePhCUyO\nLtQADjf+gWSLOyRkOY2VxFkdUvjyHuje8lrCAAd+p3V5iXOcr4dNvDQ/FDchrNY2bvW3xWBnDzpd\ncoodNWyrZlTttjpHmj5kqxmSTGWvf9SlTBM4yzcl8UphO7mmiAbtdSI3pbJE5un8J/0IXMhvmveb\nLr6lXvyciQAMmLQ2zs7rurlzwY5U2Z7I4ZGyMp0dbuG25WR0sb5GiS3M6+e+6qn57oCHvLmuqrPz\n6JoIYmYzZJXU7UTf+iRHCTn4vcGAOLbFDaz/ANFQ2WJj3WXOo0CDVJ4HPkFPYQ1zbsrNIyNujTes\n9b3tSOyc57aXRNc5ryX0N6+KofABlcoWQaW0O/YuAHibR+Kytm1ytkLKrqtYpkuglbhyOj06myOs\nb16LX7xFFrcWO0VWxFlceSRzzbvvdl0nYs3uYmdGdBAr1v0Uyiu1xla3Jxnuogll2OlpZcnD5LxT\ng4ggCgVgOPI02KNdloxcCWYOIFhvXT2SsTaelgyJGwB7W+GqaD1Kpe0HU95IPr6rRkROjjOgOMbB\n96uyr9xky8VjmOAfZJa47geix2s4z0ymBpIe1y0e7w6mvhDvDvqJ6/FUzQvgEeNKKLnWHDuE75Zc\nWENaNnWbP0Wmep5bvemSGnNc4VTgCNwtmPFjyQ8y9JBqnG1wIHSRuDnt8PmD0WgZAcwhr7B+8P6K\nTjMN45+O66AhhIe0t7rJJi40jwOXGZdVOposCj+iwRZUjXCJzyI3f6qyOfkOEgbqPQE9KpSqa3tr\nfw2F8zXnU1gHiYD12Xnec8ftBem6G67eXxJzGaWDSSD/AEXHjb/w51jwHpXmtYz65519JDWvDHgk\nH97TsrXCQTRtBcW97VEIMUhLrDBtfdaZJAQQKJ8kntiA9xa8i+vfsoIIbpJ+ndVueXRBvRztqTga\npQ0dAOqlKxaXHumDN+qcA/yj5pg2/wB4n4AldLZK1purICYRjzKYR7/dd89lY2Pf7rR8d1m1iFTQ\n0EB3RXF2p9+FpaAAKPkpc3SNv6JXhxI0ULG5KRPLTt8OdfDACSSB3/xJnvEbC8gkDs0WVXw7bCIu\n6BB+tqwvawFzjQG5Pkuc9u8dMuTK2Jk2pz26pA22/wCEdVnZRC0HL5U+WwsDgG6xZ+94RtSn3dkg\na9hDHPaHae2/ku2GcY9uGeE5dMeRI6FgLasmt1Sb6ucSVqysZ/K0uIbR2JOyzWAQxx8VLrcTPDlU\nx2rvyUFWFiyztkG97eYVS1ura+3RMHg7WL+Kyav5W/RMHuAoeVKLbVrbt4m7+qBID0IWXW7zTux5\nCHPeNG2rxbX8FJmFi2kKS6lma9kfQiq38StgdzpQwEbmr+alrRxGZjy2gnUel913DZa22kUKHXbb\n6/T6LniOXGB5bRrO2vyC3QOLYgXP1WuOU307RjMdrYnbPHUVYNf7CzZmK9jntYTypOo2As7LTbdL\nv3C7qVi4nkse1hbLolaCHlp2KzETMt3EdpbG2PCYC1nLkkDQBvaoGHjZIa6BzoS66Dtxt/3WOaTH\na4BrnOaBZvzVAeI3eY7breOLGXyX21uxycLml96AOh7HsszXVvZ7HqroGz5ELmML+TtqN7DyWrFw\nYiyT3icRVVEiwRvf+i1E1xKVOXMMbdQaHAkmqFnfqrrlmjDS/U89i6z6qcjBPOLYZtUfZ1VatmxY\nQ1jWRukOkAnbrW/VZmpIiSY8WPNPC0amTGmlza09O47rTPwz3R2skEuPW+vyVGLGYpg98A0i9rp3\nTqCts0+tuiN0jWEWQ86rd8+yktY1HcMzMTH0F7gwPJ+6XKfdIb2bGfiD+iGMDdWphdqNktP+h/VS\nBQPJeCR+70/IqTMt64mONAQRpb8hSzO4dAR+zfKx31CvLpBd8tpq93gbfVLrPeWEbavvg7eeyXKT\njH25zsHKD9vF6hySTHMf96CPWtvqulzW98mP7urYOO30UGSKrdkE03Vsw9FqMpY/Xj6xw8luxnka\nD5EV/RX+6wCnMJe4PoAur59E2ZgR+4jLjedRogaKuzW+6zPDmadRtw7BJnxmeOFpgl1PEctOBpzX\nN/K1pwcbHiYTk6nSEFtAAtbffzKqw8jmTnmt2PWzVbra+WFkZdyxq7CrtZmZjhuMcZ5Vtw+Xs0M0\n/i1DdabyGRBjpg1jdgL6LmOyS424CIkVpCVkrBqaXnUdqHy6qVM9rtELsrh7pdEkcg8R7H52limn\n4Zm8tgGl4siwb2/JLrIYDY26UkoU2UbvIG/nurdcMzXcNMubLqjbRfb/AB0Oo8l05ORIGvjbvVkN\n7LlxZkUMbWOYHyknUSNlZDxOtWqIBosEtbufgs01GUR9q3vjjn5jSTOHE24fdvy+q6On3nH1hrJj\np0ku69+q5MwY+aw6wRVgpI5pomStikc1nmO6vaRkrdgZETxC933hexsUrcfEjhyWOe/oenr/ALIV\nMb3Tut5JcDW56BMGgzuskjYi+y1Mz0xUfSMhjnZLwXAMHopB5kNNaA4DTukm1C5HO/doi+qjlu0x\nmIeKt72Q+xM5zRod4iB1TDljGDX2B69Ue8tcxg6nZtq0AONkA/FZmU+2WYF7RoNtA3AS+7hlOkJ9\nR5KzIItuk0+1YTt4rHYmlqMqSuUxmAhp8Rc0fNMXinEbH8yspfyzbLLSbO3ZNG4SOPLNqysSkE9m\nAfEprd3cPkF2OAQwy8HyJMjFinfHK4jUAHHwtoauoH6rYPs7DzmRZvCYI5iWaGAc4PDnURuKB27q\nfdH083qbe7/zThp0h4adJ2utl9GjxuDHDyZfsfHYyAF7mGBm9C9qQ7G4bG0Q5vC8ElrdYbFG14Yz\nuSCBQB+v1WtbS3zkmgk1DuWjZe/gdwOaJhyOEYok0A0Mdrg0UaHT0P8AshaIcbgEuSyAcIxmyOJF\nHFZ4SC4Uf8rvT6hNC3i+Dya+dCXdW6gtWRAx0D2vk0NIou6UvVww8KOXBHi8IxgXk2/ksbTKO4+J\nFJY/cJ43nI4VC5uotawYx3IJ7uAB+72KTh9tbvBZkckmbI3HezSWA2SNxS1BwhbDJM8BrGBoDd78\nyvZOZwLU3TwrHLXkgO92b4wL6fMVuoLPZ4WHcKxxWxHuzNndNPx/L1ScUjOnh8ueKVrAx90K6ED8\n1lcP+IaV9C5fAnOaG8HgcCaA92ZZcdOw/wAw9PVXY+NwKeVoZwvGaDGXte7HaBQq/pqCRjXROV9v\nngFt1aTXmkc0OFGja+h4jOFT4E80/DMSMQWXR8oEgVY2rr/0PdJC3gxxWvm4RjMc0VIGwNLWGyOt\nDqRtt3C67S56vmMsZYfTskFkgNFk7ABfTns4G3IkjfwbFGlrSWnHZqLiary8u/dXY+NwWXJj5HCM\nQM5bpRKcdrd26em233u9LMlPC4OFHDG18jLl76v3fgt7sZuRHplHh9eq9XjHAf8A33DIGy7O0sis\ngVudwLA8xd9k8WRwqRo04LXuIFBsLfEas1fl6rjOEzN29MfLjEVEPnGVB7tmOhia11AEHQLTQs5b\ni8kaz5dAvokkvBWN5xwI3NcSGvGODrq7r4Ufpta43FYZm8XlixMaPRqGkB2kfdvp8fLzK3lMxDOE\n4304WK5zpRzNTo3bX5HstcmGGuOi43jfbcfGl0TJ+xeYbbG6rDuuyQSyvgkL3OcXGnU2zXwVj8f5\nJx2hzz/L+OMtJee4gMqIXIP2I/eabHzXMmkDi0NNnyC7WZitixpRHA6PGloM1u8Wx+PzWfg3DR//\nACp2B4JLYoz0JH3nOrsPz+RWdoiLluMJzyiMftzHROHkSTVJo4zY1C29/gvcswHFzWSZErSJNFRU\nxoGm9gAsGdgNkDDOQeZuyYCnM3219iDtud/pS4YfmfHllq7T+LNcTcuTjZbYSRE1pDiNXVpHzH+y\ntcb4cl+ltNeTQa0/Dt9f0VPs7ixTe02NjZWO2RvMe18b2gt2Y7Yj4j8l63heLhOibkZHCoboAaMJ\noAJJ6Ef73XaauIcoymOYeXmxZonUxpNHfTuP+iQQ5RNBm/lYXu5oOGStJn4WHtF2X4t9PiPzXlPb\nX3fh/FI2Y8TIQ+AOIjaBZ1HyV0X9v9OW9zmPMb5Yw8dW6wT+SUWXDxEk9wx36LOeIz6Q9mzPwkLR\ni5zXYb8jLe5gbI2MaGatyCbO422WZqD9ixkesWXyN+LCP60iXHjoC5JLPQBo/q5ZcrGzudJ+ybTH\nEauYPEALJaDRIqjsE0mLnY7mgxsJBI1OkYdBq9zfh281Lx9N5nhz+XryJm6jTSWg113WiKWEMEcl\nhukNcRuaUM4bmOmrQxjS9rXPdKzSS7cUb3sG9k03C8t0jmsiZIGuc2xKzxaetb70Nz5KznjdW5Ks\niWAuAhD9NaAXbbfVRLK10TQ1ooCia3IClnC8pryDGCNgBzWU4uFtAN04keVpo+G5MnLcWNa2XTVy\nMFNcQA4i7q1d8fS1TsgvhazU8xt6jUmEllmrcjeqVruGzjIkhGhxjJ1EPaGgA9buh9e6skwZosJ0\nstMc2QxhmppO1Ek+K++1A/TdSc8Z+zlnMur7hNE2mZPK4hzh4Qe/VX+4Q8+OJ2SI8mmEsLNvFVN1\nXu6nA1Xnuqsjh+U15jAaQNXi5jNPhNGzdNqxsT3CkZ4raubKZpLdN/1HzVZzRVNb06HupbwrOkcd\nMIsOLaMjASQATVnfYg7dkR8LyTJpMLnO1MADC1wIdZB1A+nax1ulrbD1naZLBLqaWu1H4K6GcBrW\nuBqtla3h2QKYxjDqrT+1ZTybrSb8XTtaz5GM4PxmsO2RG1+oiqskV+Sl45SvSOZHztZtxOwA7K+W\nRsL3gaqaAKSZ/DHcPnLS8v09bbpINnYiz5X16FbMzhjy6mySuc0x/eg0tfqrZrtVEjV0NdCpthxy\nQxsdYLze42+CIZQ9hALqvqrWYuQW+OPQ0mty2wNWm9N3V7X09Uz+HTRl+iMPYwuFgi3U7TYbd1fe\nlNsfVZuYIh0tg7DqqJMkufbbb2tdB3CpY9RkaNVOOljg87OAN0a6uqtz6d0juHzxgsfFEGb2XTRg\nAg0fFqoGz0u1qM8O7SpYhJIW1u4HzVzcgRVqDt2rRNiugjiJOkuc5hZX3S00f6p8zhRbkughM75m\nOeP2kQiaQ27IJduE3wkZmZzI2NbygWt6tLRTvilkyuYbZG2Om/daUM4RmSS8tjWCiAXGRuncWKN+\nLbfw2oj4ZlOkaYmBzToouexllzbAFne+3f0HRXbD1LkrJGvovsOaLPqnfkOMlBpc0+SuGDM6FjxF\nfMAIbqGqiaB03dXtdKDwzILy0MboDDIXiZmkAGj4rrY19VNsfV5VZEgjMbd9Xb09EjdMevlucAeg\n2G60HhWS/wC4wuFhrS97Wmy0OoC9zRGw3/okGHNHic+TQ1nhoF4LjqFjYbjYXvSbY+j1XsTw33zg\nORZY68lzHsfu1zdDFqyhO50TMePHjB5Ymc99OaGuvRVdt+/crhezHtNJwTBkxW4Ina+YycwzaANg\nK6H8K70vtkxrzzeHQdaBM13/AO1amImSLp6Dh72Q8NknLPDbnmh94Dv69ErncLx3mD3WJpjeCGiE\nVqoURtQNfPb0Xn/7dB7C13DGkEUQZtiP8qRntbiNjH/lcLXaxTebe2+/3eu5WomI4Kl6GSTg7gYS\n2Ikx6Ry4zek7UCB69B6ow5uEwOibAxopri2QxEVbjdmtrJP12Xm3e1+MxzXt4MwuBoHXVb3+HzWd\n3tfji428FgArctyO3l9xaSXsX5GDiSDlwftXvbtHDuXOIFk113s96SMlwIXySe6NhZrc0SiMeNwJ\nDthvtvZI6Wei8s324jlyBI/g0QfsNZn32N/gTTe12G5ziOEwSvcbeObv/wDr/wB0Ho4TwmOV0wjp\n76O8ZNbE7bVtvfl6JveuEySAiFj+Yx1uEBNi929LveyPmVxX+0WG0u/8th8Qp3j62Kr7vlss0/tP\ngxsBbwiE3sdUmkef4f8AdKXBrL0rsrAx8kQ+7Na1oBbI1gIuhQAG5NAVQ7BLGeF42SMqJvjlHLtr\nTsKG1f8ApAr4Lz49rMXJY+V3DYHS7NDedeoV/h6qg+1mKGuLuCwAkbATbmth+7skSVL1WFkcLkDY\n8aKNpfpuNsXetQuhW35LVLw/FmlfLJCwyPbpLq36V186Xh4PbiOKS4uBRRuG1ieqrb8Kud/4ivaQ\nPsthvyyb/wDgqj2YwMMM0DFgDaquWOl3/XdPHi48UnMjgiY/Tp1NYAa22+Gw+i8gz29cY2udw1rS\nexyP/qob7fkuN8OjDR395/8AqpcLT1owMMNDRiQBodqA5Yq/P4pmYeMx2pmPE1224YAdhQ/LZeLH\n/iI43/5Y2+3/ABB3/wDaoP8A4iuF3wtm3/8AZO//ALEtHszgYZu8WA3RP7Mb10XhOMZDT7XZ0Zgf\nLIKDdDq6Mv8A+RWg/wDiK8aa4U11i9sn/wCq8nxPi0ufxifPjDsYzOaS1r9VUAPS+imUXCxNPUYG\ndFkRMx8h4E8LWta4Gw8bW13qP1C2Oz8NkkoZI1odE+2F2wdtVH1329F5VkuPJzMnGf7s2MhojcRb\nifIk10TzY7I3zMkyWXE0OLQQS4elHy+C9UfP8cxzNf080/DltcNHFZmOh5hikLnvpkhft0r/AEH0\nW/gTw2DGkkeGkxuY0u+6TzHEtPltX5LzeXkMmeRAHxwAbRuds39VZwnLZHO6OablQSxua7VekO6t\nJAB7j814Plw/ZjMevf8ADnGGUX10961jhVWC0UL7UDX9a+SycQ0DGkYTRkbpYxotzyPutA8h/UrL\nH7QMc01l4DqHUue3+o3+AXO4rxaObGme3LhM5jEbBBrBALgSbIHax17r5fxfifLvG0VD1/sxx/lc\nNHCJyfbeGMEG3EOLT1dyTq387ten4lw6KF0IxsRztV6iA54FdL39fyXgfZ3Kg4fx/CysqQRQRl2p\n1XVscB09SvoH9ruBEf8A5Bv/APm/9F9icLh4Nub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