From 957ff00cd4b903b103969a072136fdd41360f287 Mon Sep 17 00:00:00 2001 From: Eric Furst <86606193+emfurst@users.noreply.github.com> Date: Thu, 29 Aug 2024 16:58:49 -0400 Subject: [PATCH] Add files via upload --- ...east_squares_fitting_example_CHEG231.ipynb | 338 ++++++++++++++++++ 1 file changed, 338 insertions(+) create mode 100644 preliminaries/Least_squares_fitting_example_CHEG231.ipynb diff --git a/preliminaries/Least_squares_fitting_example_CHEG231.ipynb b/preliminaries/Least_squares_fitting_example_CHEG231.ipynb new file mode 100644 index 0000000..b3179c8 --- /dev/null +++ b/preliminaries/Least_squares_fitting_example_CHEG231.ipynb @@ -0,0 +1,338 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f225380f", + "metadata": {}, + "source": [ + "\n", + "# Least Square Fitting of Parameters to Data: Notebook Example\n", + "\n", + "In this example we will use least squares to fit the parameters of the Arrhenius form of the rate constant to experimental data.\n", + "\n", + "The form of the Arrhenius equation is the following:\n", + "\n", + "$$ k(T) = A \\exp \\left ( - \\frac{E_a}{RT} \\right )$$\n", + "\n", + "where $A$ is the pre-exponential factor, $E_a$ is the activation energy, $R$ is the ideal gas constant, and $T$ is the (absolute) temperature of the measurement (in K). $k(T)$ has units of reciprocal time for first order reactions and units of reciprocal time * reciprocal concentration for second order reactions.\n", + "\n", + "The goal of this notebook is to demostrate how to use Jupyter to obtain least-squares estimates of $A$ and $E_a$.\n", + "\n", + "To this end we need to linearize the Arrhenius equation by taking the logarithm of the equation above:\n", + "$$\\ln\\left ( k(T)\\right ) = \\ln(A) - \\frac{E_a}{RT}$$\n", + "This equation is analogous to the familiar linear equation:\n", + "$$y = b + mx$$\n", + "where \n", + "$$y = \\ln A$$\n", + "$$m = \\frac{-E_a}{R}$$\n", + "$$x = \\frac{1}{T}$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "795db611", + "metadata": {}, + "source": [ + "\n", + "## Experimental Data\n", + "\n", + "We will fit data for the isomerization of bi-cyclo[4.2.0]oct-7-ene into cyclo-octadiene. This is a first order reaction and the data were otained from the textbook *Physical Organic Chemistry* by H. Maskill (1985).\n", + "\n", + " \n", + "\n", + "|Temperature, K| Rate Constant k(T) x 104, s-1|\n", + "|:----:|:----:|\n", + "|508.7|0.376|\n", + "|517.1|0.736|\n", + "|521.5|1.08|\n", + "|526|1.53|\n", + "|529|1.93|\n", + "|532.4|2.44\n", + "|535.5|3.32|\n", + "|540.3|4.61|\n", + "|552.8|10.5|\n", + "|558.1|16.6|\n", + "\n", + "\n", + "To fit these data to the Arrhenius equation we will need two libraries; ``numpy`` and ``matplotlib``. These are entered is Python code in the next cell:\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "8ba8e9f4", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "e8c16808", + "metadata": {}, + "source": [ + "The next step is to input the data into two arrays:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "8d3367ea", + "metadata": {}, + "outputs": [], + "source": [ + "# Data, T in K and k in s^-1\n", + "\n", + "T = np.array([508.7, 517.1, 521.5, 526, 529, 532.4, 535.5,\n", + " 540.3, 551.8, 558.1])\n", + "kexp = np.array([.376, .763, 1.08, 1.53, 1.93, 2.44, 3.32,\n", + " 4.61, 10.5, 16.6])*1e-4\n" + ] + }, + { + "cell_type": "markdown", + "id": "4087c1fc", + "metadata": {}, + "source": [ + "Now we need to plot the data. From the equations above, we see that the relationship between $\\ln k(T)$ and $1/T$ is linear. This can be confirmed by plotting the data using these instructions:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "1cb80f8e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Arrhenius Plot of ln(k) vs 1/T, Original Data')" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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18uRJp+q///775eXlpfnz5ys3N1fvv/+++vTpo7p169rb1KhRQ88884wSEhJ04sQJLVmyREePHlX37t0LfOGhtFasWKHOnTs7bLc8dO3aVZKKHCcrf1mNGjUKjOHkzOu4bt26stls+uOPPwosy79hvCwkJiZq3759mj59up566il17NhRN954Y6F/gJWVtWvXKjc3135c0tLStGbNGo0dO1bjx4/XHXfcoRtvvFHNmzcv8jnsCvtRnRCWUG5yc3O1YMECNWnSRJs3by4wjR49WsnJyfrss88qpJ5evXopMTFRTZo0UZs2bQpMF/+VdynCwsL0n//8x2Hepk2blJmZWWSfwMBADRkyRPfff78OHjxYZh+cF6tVq5Zuuukmffzxxw5/Zebl5WnRokVq2LCh/VtNJTmLVpL1VhRPT081btxYP/30U5FtWrZsqa1bt+q3335Tx44dCx0o8NixY8rKylJkZGSx26xbt6769OmjhQsXas2aNUpJSXG4BPdXderU0b333qv/+Z//0YkTJ8pkkMGsrCytW7euQi7B9e3bV5GRkXr55Zd16NChAsuXLVumDRs26LHHHlNQUFCJ11+rVi21adNGn3zyic6dO2efn5mZqTVr1lxS7RfLD25/HZ7k4m+qlaVff/1VY8aMkb+/v4YPH26vwRhToIZ///vfBf6YLOq1WdH7Ud0wzhLKzWeffaZjx45p6tSphY4OHBUVpVmzZmnu3LkVMgL3iy++qI0bN6p9+/b629/+pmbNmikrK0tHjhzRunXr9NZbb5XJmEmDBw/W888/rxdeeEEdOnTQgQMHNGvWLPn7+zu0u+mmm9SrVy+1aNFCdevW1ffff6/3339f7dq1K7fxo6ZMmaKuXbuqU6dOGjNmjDw9PfXmm28qMTFRS5Yssb/h5o/j884778jX11fe3t4KDw8v8q9UZ9dbkTp27FhsEL/22mv11VdfqUuXLrr99tv1+eefOzwH8i9hdOrUyaltPvroo1q2bJlGjhyphg0bFhh0MDo62j72zhVXXKFffvlFM2fOVKNGjXT11VdbrnvXrl32QJWenm4/YytJN954oxo1aqS4uDidOXPG8nJscbZs2aJOnTopJiam0CEw8rm7u2vFihXq2rWr2rVrp9GjR6tdu3bKzs7W6tWr9c4776hDhw6aMWNGqWt58cUX1bNnT3Xv3l1PP/20cnNzNX36dNWuXdvpMy7FiYiIUJMmTTR+/HgZY1SvXj2tXr3a/m2/S5GYmGi/NzI1NVVfffWV5s2bJ3d3d61cudL+zVU/Pz/dfvvtmj59ugICAhQWFqatW7dq7ty5Bb7NWdRrszz3A5xZQjmaO3euPD097V+b/quAgAD17dtXa9asKfRUe1kLDg7Wrl271K1bN02fPl09evTQ4MGD9d577+mGG24os8sW//jHP/SPf/xD8+fPV3R0tFasWKEPP/ywwJte586dtWrVKj3yyCPq1q2bpk2bpoceesip0ZlLq0OHDtq0aZNq1aqlIUOGaODAgUpLS9OqVascxiMKDw/XzJkztW/fPvvpfKu6nF1vRXrggQeUnJysnTt3WrZr3LixvvrqK9lsNt122236+eef7cs++eQTNW/eXM2bN3dqm126dFFoaKh+++03PfzwwwXGRurUqZO+/PJLPfHEE+ratauee+453XHHHdq6dWuxNzzPmjVL/fv3V//+/XX06FEdOHDA/njz5s2SLlyCu+2224q8sd0Z+WdAnbmvKCIiQnv37tWwYcP0/vvv66677lL//v21a9cuzZw5Uxs3bryk4N+jRw+tWLFCf/75pwYMGKBnnnlGffv2Ve/evYsdEsJZHh4eWr16ta655hoNHz5c999/v1JTU/X5559f8rofeeQRtWvXTnfccYdGjBihPXv2aNy4cfrhhx8KBPDFixerU6dOGjt2rPr166ddu3Zp48aNBf7IKuq1WZ77Aclm/npLPgBUES1atNAtt9yiOXPmlLhvenq6QkJC9NprrxU6DperOXfunBo0aKCXXnpJTz31VKnXM3bsWC1ZskSHDx8u8gb5ypSTk6MbbrhBV155pTZs2FDZ5aCaICwBqLLi4uLUt29fHT58uMSXWCdNmqRly5bpP//5j2rUqD53LNx44416/PHHNWzYsMouRZI0dOhQde3aVcHBwUpJSdFbb72lrVu3asOGDaX6bTWgNKrPOwCAaqdHjx6aPn26kpKSShyW/Pz8NH/+/GoVlCQVe9myomVkZGjMmDH63//9X3l4eKhVq1Zat24dQQkVijNLAAAAFrjBGwAAwAJhCQAAwAJhCQAAwEL1unOxnOTl5enYsWPy9fWtlMH3AABAyRljlJGRoZCQkALjol2MsFQGjh075tRvcwEAANdz9OhRy2/MEpbKgK+vr6QLB9vPz6+SqwEAAM5IT09XaGio/XO8KISlMpB/6c3Pz4+wBADAZaa4W2i4wRsAAMACYQkAAMACYQkAAMACYQkAAMACYQkAAMACYQkAAMACYQkAAMACYQkAAMACYQkAAMACI3i7qNw8o/ikE0rNyFIDX2+1Da8ndzd+pBcAgIpGWHJBcYnJmrT6gJLTsuzzgv29FRMdqR5RwZVYGQAA1Q+X4VxMXGKyRixKcAhKkpSSlqURixIUl5hcSZUBAFA9EZZcSG6e0aTVB2QKWZY/b9LqA8rNK6wFAAAoD4QlFxKfdKLAGaWLGUnJaVmKTzpRcUUBAFDNEZZcSGpG0UGpNO0AAMClIyy5kAa+3mXaDgAAXDrCkgtpG15Pwf7eKmqAAJsufCuubXi9iiwLAIBqjbDkQtzdbIqJjpSkAoEp/3FMdCTjLQEAUIGqXFhau3atbrrpJvn4+CggIED9+vWzbD9kyBDZbDaH6eabb66gagvqERWsOQ+2UpC/46W2IH9vzXmwFeMsAQBQwarUoJQrVqzQ448/rsmTJ6tz584yxui7774rtl+PHj00b948+2NPT8/yLLNYPaKC1TUyiBG8AQBwAVUmLJ0/f15PP/20pk+frqFDh9rnN2vWrNi+Xl5eCgoKKs/ySszdzaZ2TepXdhkAAFR7VeYyXEJCgn7//Xe5ubmpZcuWCg4O1p133qn9+/cX23fLli1q0KCBrrnmGj3++ONKTU2tgIoBAMDloMqEpZ9//lmSFBsbq+eee05r1qxR3bp11aFDB504UfQgjnfeeac++OADbdq0STNmzNDOnTvVuXNnZWdnF9knOztb6enpDhMAAKiaXD4sxcbGFrgB+6/Trl27lJeXJ0maOHGi7rnnHrVu3Vrz5s2TzWbT8uXLi1z/gAED1LNnT0VFRSk6OlqfffaZDh06pLVr1xbZZ8qUKfL397dPoaGhZb7fAADANbj8PUsjR47UwIEDLduEhYUpIyNDkhQZGWmf7+XlpcaNG+vXX391envBwcFq1KiRDh8+XGSbCRMm6JlnnrE/Tk9PJzABAFBFuXxYCggIUEBAQLHtWrduLS8vLx08eFC33nqrJCknJ0dHjhxRo0aNnN7en3/+qaNHjyo4uOiv6Ht5ecnLy8vpdQIAgMuXy1+Gc5afn5+eeOIJxcTEaMOGDTp48KBGjBghSerfv7+9XUREhFauXClJyszM1JgxY7R9+3YdOXJEW7ZsUXR0tAICAtS3b99K2Q8AAOBaXP7MUklMnz5dNWrU0ODBg3X27FnddNNN2rRpk+rWrWtvc/DgQaWlpUmS3N3d9d1332nhwoU6deqUgoOD1alTJy1btky+vr6VtRsAAMCF2IwxprKLuNylp6fL399faWlp8vPzq+xyAACAE5z9/K4yl+EAAADKA2EJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAQo3KLgDVR26eUXzSCaVmZKmBr7fahteTu5utsssCAMASYQkVIi4xWZNWH1ByWpZ9XrC/t2KiI9UjKrgSKwMAwBqX4VDu4hKTNWJRgkNQkqSUtCyNWJSguMTkSqoMAIDiEZZQrnLzjCatPiBTyLL8eZNWH1BuXmEtAACofIQllKv4pBMFzihdzEhKTstSfNKJiisKAIASICyhXKVmFB2UStMOAICKRlhCuWrg612m7QAAqGiEJZSrtuH1FOzvraIGCLDpwrfi2obXq8iyAABwGmEJ5crdzaaY6EhJKhCY8h/HREcy3hIAwGURllDuekQFa86DrRTk73ipLcjfW3MebMU4SwAAl8aglKgQPaKC1TUyiBG8AQCXHcISKoy7m03tmtSv7DIAACgRLsMBAABYqDJhacuWLbLZbIVOO3fuLLKfMUaxsbEKCQmRj4+POnbsqP3791dg5QAAwJVVmbDUvn17JScnO0yPPfaYwsLC1KZNmyL7TZs2Ta+++qpmzZqlnTt3KigoSF27dlVGRkYFVg8AAFxVlQlLnp6eCgoKsk/169fXqlWr9Oijj8pmK/wmYmOMZs6cqYkTJ6pfv36KiorSggULdObMGS1evLiC9wAAALiiKhOW/mrVqlU6fvy4hgwZUmSbpKQkpaSkqFu3bvZ5Xl5e6tChg7755psi+2VnZys9Pd1hAgAAVVOVDUtz585V9+7dFRoaWmSblJQUSVJgYKDD/MDAQPuywkyZMkX+/v72yWobAADg8ubyYSk2NrbIG7fzp127djn0+e2337R+/XoNHTrUqW389TKdMabIS3eSNGHCBKWlpdmno0ePlnzHAADAZcHlx1kaOXKkBg4caNkmLCzM4fG8efNUv3593X333Zb9goKCJF04wxQc/N9RpFNTUwucbbqYl5eXvLy8iqkcAABUBS4flgICAhQQEOB0e2OM5s2bp4ceekgeHh6WbcPDwxUUFKSNGzeqZcuWkqRz585p69atmjp16iXVDQAAqgaXvwxXUps2bVJSUlKRl+AiIiK0cuVKSRcuv40aNUqTJ0/WypUrlZiYqCFDhqhmzZoaNGhQRZYNAABclMufWSqpuXPnqn379rr22msLXX7w4EGlpaXZH48dO1Znz57Vk08+qZMnT+qmm27Shg0b5OvrW1ElAwAAF2YzxpjKLuJyl56eLn9/f6WlpcnPz6+yywEAAE5w9vO7yl2GAwAAKEuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAuEJQAAAAtVJixt2bJFNput0Gnnzp1F9hsyZEiB9jfffHMFVg4AAFxZjcouoKy0b99eycnJDvOef/55ff7552rTpo1l3x49emjevHn2x56enuVSIwAAuPxUmbDk6empoKAg++OcnBytWrVKI0eOlM1ms+zr5eXl0BcAACBflbkM91erVq3S8ePHNWTIkGLbbtmyRQ0aNNA111yjxx9/XKmpqZbts7OzlZ6e7jABAICqyWaMMZVdRHm46667JEnr1q2zbLds2TLVrl1bjRo1UlJSkp5//nmdP39eu3fvlpeXV6F9YmNjNWnSpALz09LS5Ofnd+nFAwCAcpeeni5/f/9iP79dPiwVFUwutnPnTof7kn777Tc1atRIH374oe65554SbS85OVmNGjXS0qVL1a9fv0LbZGdnKzs72/44PT1doaGhhCUAAC4jzoYll79naeTIkRo4cKBlm7CwMIfH8+bNU/369XX33XeXeHvBwcFq1KiRDh8+XGQbLy+vIs86AQCAqsXlw1JAQIACAgKcbm+M0bx58/TQQw/Jw8OjxNv7888/dfToUQUHB5e4LwAAqHqq3A3emzZtUlJSkoYOHVro8oiICK1cuVKSlJmZqTFjxmj79u06cuSItmzZoujoaAUEBKhv374VWTYAAHBRLn9mqaTmzp2r9u3b69prry10+cGDB5WWliZJcnd313fffaeFCxfq1KlTCg4OVqdOnbRs2TL5+vpWZNkAAMBFufwN3pcDZ28QAwAArsPZz+8qdxkOAACgLBGWAAAALBCWAAAALBCWAAAALBCWAAAALFS5oQMAOCc3zyg+6YRSM7LUwNdbbcPryd3NVtllAYDLISwB1VBcYrImrT6g5LQs+7xgf2/FREeqRxSj1wPAxbgMB1QzcYnJGrEowSEoSVJKWpZGLEpQXGJyJVUGAK6JsARUI7l5RpNWH1BhI9Hmz5u0+oBy8xirFgDyEZaAaiQ+6USBM0oXM5KS07IUn3Si4ooCABdHWAKqkdSMooNSadoBQHVAWAKqkQa+3mXaDgCqA8ISUI20Da+nYH9vFTVAgE0XvhXXNrxeRZYFAC6NsARUI+5uNsVER0pSgcCU/zgmOpLxlgDgIoQloJrpERWsOQ+2UpC/46W2IH9vzXmwFeMsAcBfMCglUA31iApW18ggRvAGACcQloBqyt3NpnZN6ld2GQDg8rgMBwAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYIGwBAAAYKFKhaVDhw6pd+/eCggIkJ+fn2655RZt3rzZso8xRrGxsQoJCZGPj486duyo/fv3V1DFAADA1VWpsNSzZ0+dP39emzZt0u7du3XDDTeoV69eSklJKbLPtGnT9Oqrr2rWrFnauXOngoKC1LVrV2VkZFRg5QCs5OYZbf/pT32693dt/+lP5eaZyi4JQDViM8ZUiXed48eP64orrtCXX36p2267TZKUkZEhPz8/ff7557rjjjsK9DHGKCQkRKNGjdK4ceMkSdnZ2QoMDNTUqVM1fPhwp7adnp4uf39/paWlyc/Pr+x2CoDiEpM1afUBJadl2ecF+3srJjpSPaKCK7EyAJc7Zz+/q8yZpfr16+vaa6/VwoULdfr0aZ0/f15vv/22AgMD1bp160L7JCUlKSUlRd26dbPP8/LyUocOHfTNN99UVOkAihCXmKwRixIcgpIkpaRlacSiBMUlJldSZQCqkxqVXUBZsdls2rhxo3r37i1fX1+5ubkpMDBQcXFxqlOnTqF98i/PBQYGOswPDAzUL7/8UuS2srOzlZ2dbX+cnp5+6TsAwEFuntGk1QdU2KlvI8kmadLqA+oaGSR3N1sFVwegOinxmaUjR47o/fff10svvaQJEybo1Vdf1ebNm5WVlVV851KIjY2VzWaznHbt2iVjjJ588kk1aNBAX331leLj49W7d2/16tVLycnWf33abI5vtMaYAvMuNmXKFPn7+9un0NDQMtlXAP8Vn3SiwBmlixlJyWlZik86UXFFAaiWnD6ztHjxYr3xxhuKj49XgwYNdOWVV8rHx0cnTpzQTz/9JG9vbz3wwAMaN26cGjVqVGYFjhw5UgMHDrRsExYWpk2bNmnNmjU6efKk/brjm2++qY0bN2rBggUaP358gX5BQUGSLpxhCg7+770PqampBc42XWzChAl65pln7I/T09MJTEAZS81w7g8wZ9sBQGk5FZZatWolNzc3DRkyRB9++KGuuuoqh+XZ2dnavn27li5dqjZt2ujNN99U//79y6TAgIAABQQEFNvuzJkzkiQ3N8eTZW5ubsrLyyu0T3h4uIKCgrRx40a1bNlSknTu3Dlt3bpVU6dOLXJbXl5e8vLycnYXAJRCA1/vMm0HAKXl1GW4l156Sbt27dLIkSMLBCXpQnjo2LGj3nrrLX3//fcKCwsr6zqL1a5dO9WtW1cPP/yw9u3bp0OHDukf//iHkpKS1LNnT3u7iIgIrVy5UtKFy2+jRo3S5MmTtXLlSiUmJmrIkCGqWbOmBg0aVOH7AOC/2obXU7C/t4q6IG7ThW/FtQ2vV5FlAaiGnDqzdHHYKI6zZ4LKWkBAgOLi4jRx4kR17txZOTk5uu666/Tpp5/q+uuvt7c7ePCg0tLS7I/Hjh2rs2fP6sknn9TJkyd10003acOGDfL19a3wfQDwX+5uNsVER2rEogTZJIcbvfMDVEx0JDd3Ayh3JR5nKSEhQR4eHmrevLkk6dNPP9W8efMUGRmp2NhYeXp6lkuhroxxloDywzhLAMqLs5/fJR46YPjw4Ro/fryaN2+un3/+WQMHDlTfvn21fPlynTlzRjNnzryUugHAQY+oYHWNDFJ80gmlZmSpge+FS2+cUQJQUUoclg4dOqQbbrhBkrR8+XLdfvvtWrx4sb7++msNHDiQsASgzLm72dSuSf3KLgNANVXicZaMMfZvl33++ee66667JEmhoaE6fvx42VYHAABQyUocltq0aaN//vOfev/997V161b7zd9JSUmWYxMBAABcjkoclmbOnKmEhASNHDlSEydOVNOmTSVJH330kdq3b1/mBQIAAFSmEn8brihZWVlyd3eXh4dHWazussK34QAAuPyU27fhiuLtzSi6AACg6inxZTgAAIDqhLAEAABggbAEAABggbAEAABggbAEAABgoVRh6ciRI3rooYf00EMP6eeffy7rmgAAAFxGqYYOuPfee7Vnzx5J0vfff6+dO3eWaVEAAACuolRnln766SdJF34n7scffyzTggAAAFxJqcLSmDFjlD/w9+jRo8u0IAAAAFdS6p87+emnn2SMsf82XHXGz50AAHD5KfefO2nSpElpuwKAy8vNM4pPOqHUjCw18PVW2/B6cnezVXZZACpBmf02HABUFXGJyZq0+oCS07Ls84L9vRUTHakeUcGVWBmAysA4SwBwkbjEZI1YlOAQlCQpJS1LIxYlKC4xuZIqA1BZCEsA8H9y84wmrT6gwm7kzJ83afUB5eaV6lZPAJcpwhIA/J/4pBMFzihdzEhKTstSfNKJiisKQKUr07BUyi/WAYBLSM0oOiiVph2AqqHEYWnKlCmFzs/NzdWgQYMuuSAAqCwNfL3LtB2AqqHEYWnmzJl65513HObl5uZq4MCB2rt3b1nVBQAVrm14PQX7e6uoAQJsuvCtuLbh9SqyLACVrMRhad26dRo3bpw+/PBDSVJOTo769++v/fv3a/PmzWVeIABUFHc3m2KiIyWpQGDKfxwTHcl4S0A1U+Jxllq3bq2VK1eqd+/e8vLy0ty5c/XTTz9p8+bNCgwMLI8aAaDC9IgK1pwHWxUYZymIcZaAaqvUP3eyatUq3XPPPbr22mu1adMmBQQElHVtlw1+7gSoehjBG6j6yvTnTvr161fo/CuuuEJ16tTRsGHD7PM+/vjjEpYKAK7H3c2mdk3qV3YZAFyAU2HJ39+/0Pndu3cv02IAAABcjVNhad68eeVdBwAAgEtiBG8AAAALToWlHj166Jtvvim2XUZGhqZOnarZs2dfcmEAAACuwKnLcP3799d9990nX19f3X333WrTpo1CQkLk7e2tkydP6sCBA9q2bZvWrVunXr16afr06eVdNwAAQIVw6szS0KFD9fPPP+v555/XDz/8oOHDh+u2227TjTfeqO7du+vdd9/VVVddpd27d2vp0qUKDQ0t77oLdejQIfXu3VsBAQHy8/PTLbfcUuxAmUOGDJHNZnOYbr755gqqGAAAuDqnB6X09PTUoEGD7L//lpaWprNnz6p+/fry8PAotwJLomfPnrrmmmu0adMm+fj4aObMmerVq5d++uknBQUFFdmvR48eDjexe3p6VkS5AADgMlDiEbzz+fv7FzmkQGU4fvy4fvzxR7333ntq0aKFJOnll1/Wm2++qf3791uGJS8vL8vlAACg+ipVWDp06JC2bNmi1NRU5eXlOSx74YUXyqSwkqpfv76uvfZaLVy4UK1atZKXl5fefvttBQYGqnXr1pZ9t2zZogYNGqhOnTrq0KGD/vWvf6lBgwZFts/OzlZ2drb9cXp6epntBwAAcC0l/rmTd999VyNGjFBAQICCgoJks/13+H+bzaaEhIQyL9JZv//+u3r37q2EhAS5ubkpMDBQa9eu1Q033FBkn2XLlql27dpq1KiRkpKS9Pzzz+v8+fPavXu3vLy8Cu0TGxurSZMmFZjPz50AKAv81ApQMZz9uZMSh6VGjRrpySef1Lhx4y65SGcUFUwutnPnTrVu3Vp9+vRRTk6OJk6cKB8fH/373//WqlWrtHPnTgUHO/fjl8nJyWrUqJGWLl1a5M+8FHZmKTQ0lLAE4JLFJSYX+BHfYH7EFygX5RaW/Pz8tHfvXjVu3PiSi3TG8ePHdfz4ccs2YWFh+vrrr9WtWzedPHnSYYevvvpqDR06VOPHj3d6m1dffbUee+wxpwMhP6QLoCzEJSZrxKIE/fVNOf+c0pwHWxGYgDJUpj+ke7H+/ftrw4YNeuKJJy6pQGcFBAQoICCg2HZnzpyRJLm5OY6G4ObmVuC+Kit//vmnjh496vSZKAAoC7l5RpNWHygQlCTJ6EJgmrT6gLpGBnFJDqhgJQ5LTZs21fPPP69vv/1WzZs3LzBswN/+9rcyK64k2rVrp7p16+rhhx/WCy+8IB8fH7377rtKSkpSz5497e0iIiI0ZcoU9e3bV5mZmYqNjdU999yj4OBgHTlyRM8++6wCAgLUt2/fStkPANVTfNIJh0tvf2UkJadlKT7phNo1qV9xhQEoeVh65513VLt2bW3dulVbt251WGaz2SotLAUEBCguLk4TJ05U586dlZOTo+uuu06ffvqprr/+enu7gwcPKi0tTZLk7u6u7777TgsXLtSpU6cUHBysTp06admyZfL19a2U/QBQPaVmFB2UStMOQNkpcVhKSkoqjzrKRJs2bbR+/XrLNhffouXj41NsewCoCA18vcu0HYCy49TPnQAAylfb8HoK9vdWUXcj2XThW3Ftw+tVZFkA5OSZpWeeecbpFb766qulLgYAqit3N5tioiM1YlGCbJLDjd75ASomOpKbu4FK4FRY2rNnj1Mru3iASgBAyfSICtacB1sVGGcpiHGWgEpV4nGWUBDjLAEoS4zgDVSMchtnCQBQvtzdbAwPALgQbvAGAACwQFgCAACwQFgCAACwQFgCAACwQFgCAACwQFgCAACwQFgCAACwQFgCAACwwKCUAFDNMWI4YI2wBADVWFxicoHfogvmt+gAB1yGA4BqKi4xWSMWJTgEJUlKScvSiEUJiktMrqTKANdCWAKAaig3z2jS6gMq7JfU8+dNWn1AuXn81jpAWAKAaig+6USBM0oXM5KS07IUn3Si4ooCXBRhCQCqodSMooNSadoBVRlhCQCqoQa+3mXaDqjKCEsAUA21Da+nYH9vFTVAgE0XvhXXNrxeRZYFuCTCEgBUQ+5uNsVER0pSgcCU/zgmOpLxlgARlgCg2uoRFaw5D7ZSkL/jpbYgf2/NebAV4ywB/4dBKQGgGusRFayukUGM4A1YICwBQDXn7mZTuyb1K7sMwGVxGQ4AAMACYQkAAMACYQkAAMACYQkAAMACYQkAAMACYQkAAMACYQkAAMACYQkAAMBClQpLCQkJ6tq1q+rUqaP69etr2LBhyszMtOxjjFFsbKxCQkLk4+Ojjh07av/+/RVUMQAAcHVVJiwdO3ZMXbp0UdOmTbVjxw7FxcVp//79GjJkiGW/adOm6dVXX9WsWbO0c+dOBQUFqWvXrsrIyKiYwgEAgEurMj93smbNGnl4eGj27Nlyc7uQAWfPnq2WLVvqxx9/VNOmTQv0McZo5syZmjhxovr16ydJWrBggQIDA7V48WINHz68QvcBAAC4nipzZik7O1uenp72oCRJPj4+kqRt27YV2icpKUkpKSnq1q2bfZ6Xl5c6dOigb775xnJb6enpDhMAAKiaqkxY6ty5s1JSUjR9+nSdO3dOJ0+e1LPPPitJSk5OLrRPSkqKJCkwMNBhfmBgoH1ZYaZMmSJ/f3/7FBoaWkZ7AQAAXI3Lh6XY2FjZbDbLadeuXbruuuu0YMECzZgxQzVr1lRQUJAaN26swMBAubu7W27DZrM5PDbGFJh3sQkTJigtLc0+HT16tEz2FQAAuB6Xv2dp5MiRGjhwoGWbsLAwSdKgQYM0aNAg/fHHH6pVq5ZsNpteffVVhYeHF9ovKChI0oUzTMHBwfb5qampBc42XczLy0teXl4l3BMAAHA5cvmwFBAQoICAgBL1yQ867733nry9vdW1a9dC24WHhysoKEgbN25Uy5YtJUnnzp3T1q1bNXXq1EsrHAAAVAkufxmuJGbNmqWEhAQdOnRIs2fP1siRIzVlyhTVqVPH3iYiIkIrV66UdOHy26hRozR58mStXLlSiYmJGjJkiGrWrKlBgwZV0l4AAABX4vJnlkoiPj5eMTExyszMVEREhN5++20NHjzYoc3BgweVlpZmfzx27FidPXtWTz75pE6ePKmbbrpJGzZskK+vb0WXDwAAXJDNGGMqu4jLXXp6uvz9/ZWWliY/P7/KLgcAADjB2c/vKnVmCQBQdeXmGcUnnVBqRpYa+HqrbXg9ubsV/c1loKwQlgAALi8uMVmTVh9QclqWfV6wv7dioiPVIyrYoidw6arUDd4AgKonLjFZIxYlOAQlSUpJy9KIRQmKSyx84GGgrBCWAAAuKzfPaNLqAyrs5tr8eZNWH1BuHrffovwQlgAALis+6USBM0oXM5KS07IUn3Si4opCtUNYAgC4rNSMooNSadoBpUFYAgC4rAa+3mXaDigNwhIAwGW1Da+nYH9vFTVAgE0XvhXXNrxeRZaFaoawBABwWe5uNsVER0pSgcCU/zgmOpLxllCuCEsAAJfWIypYcx5spSB/x0ttQf7emvNgK8ZZQrljUEoAgMvrERWsrpFBjOCNSkFYAgBcFtzdbGrXpH5ll4FqiMtwAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFghLAAAAFmpUdgEAAFQ1uXlG8UknlJqRpQa+3mobXk/ubrbKLgulRFgCAKAMxSUma9LqA0pOy7LPC/b3Vkx0pHpEBVdiZSgtLsMBAFBG4hKTNWJRgkNQkqSUtCyNWJSguMTkSqoMl6JKhaWEhAR17dpVderUUf369TVs2DBlZmZa9hkyZIhsNpvDdPPNN1dQxQCAqiI3z2jS6gMyhSzLnzdp9QHl5hXWAq6syoSlY8eOqUuXLmratKl27NihuLg47d+/X0OGDCm2b48ePZScnGyf1q1bV/4FAwCqlPikEwXOKF3MSEpOy1J80omKKwplosrcs7RmzRp5eHho9uzZcnO7kAFnz56tli1b6scff1TTpk2L7Ovl5aWgoKCKKhUAUAWlZhQdlErTDq6jypxZys7Olqenpz0oSZKPj48kadu2bZZ9t2zZogYNGuiaa67R448/rtTU1GK3lZ6e7jABAKq3Br7eZdoOrqPKhKXOnTsrJSVF06dP17lz53Ty5Ek9++yzkqTk5KJvqLvzzjv1wQcfaNOmTZoxY4Z27typzp07Kzs7u8g+U6ZMkb+/v30KDQ0t8/0BAFxe2obXU7C/t4oaIMCmC9+KaxteryLLQhlw+bAUGxtb4Absv067du3SddddpwULFmjGjBmqWbOmgoKC1LhxYwUGBsrd3b3I9Q8YMEA9e/ZUVFSUoqOj9dlnn+nQoUNau3ZtkX0mTJigtLQ0+3T06NHy2HUAwGXE3c2mmOhISSoQmPIfx0RHMt7SZchmjHHp2/KPHz+u48ePW7YJCwuTt/d/T2v+8ccfqlWrlmw2m/z8/LR06VL179/f6W1effXVeuyxxzRu3Din2qenp8vf319paWny8/NzejsAgKqHcZYuH85+frv8Dd4BAQEKCAgoUZ/AwEBJ0nvvvSdvb2917drV6b5//vmnjh49quBgntAAgJLrERWsrpFBjOBdhbj8ZbiSmDVrlhISEnTo0CHNnj1bI0eO1JQpU1SnTh17m4iICK1cuVKSlJmZqTFjxmj79u06cuSItmzZoujoaAUEBKhv376VtBcAgMudu5tN7ZrUV+8brlS7JvUJSpc5lz+zVBLx8fGKiYlRZmamIiIi9Pbbb2vw4MEObQ4ePKi0tDRJkru7u7777jstXLhQp06dUnBwsDp16qRly5bJ19e3MnYBAAC4GJe/Z+lywD1LAABcfpz9/K5Sl+EAAADKGmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAAmEJAADAwmUTlv71r3+pffv2qlmzpurUqVNom19//VXR0dGqVauWAgIC9Le//U3nzp2zXG92draeeuopBQQEqFatWrr77rv122+/lcMeAACAy9FlE5bOnTun/v37a8SIEYUuz83NVc+ePXX69Glt27ZNS5cu1YoVKzR69GjL9Y4aNUorV67U0qVLtW3bNmVmZqpXr17Kzc0tj90AAACXGZsxxlR2ESUxf/58jRo1SqdOnXKY/9lnn6lXr146evSoQkJCJElLly7VkCFDlJqaKj8/vwLrSktL0xVXXKH3339fAwYMkCQdO3ZMoaGhWrdunbp37+5UTenp6fL391daWlqh2wEAAK7H2c/vy+bMUnG2b9+uqKgoe1CSpO7duys7O1u7d+8utM/u3buVk5Ojbt262eeFhIQoKipK33zzTZHbys7OVnp6usMEAACqpioTllJSUhQYGOgwr27duvL09FRKSkqRfTw9PVW3bl2H+YGBgUX2kaQpU6bI39/fPoWGhl76DgAAAJdUqWEpNjZWNpvNctq1a5fT67PZbAXmGWMKnW+luD4TJkxQWlqafTp69GiJ1g8AAC4fNSpz4yNHjtTAgQMt24SFhTm1rqCgIO3YscNh3smTJ5WTk1PgjNPFfc6dO6eTJ086nF1KTU1V+/bti9yWl5eXvLy8nKoLAABc3io1LAUEBCggIKBM1tWuXTv961//UnJysoKDgyVJGzZskJeXl1q3bl1on9atW8vDw0MbN27UfffdJ0lKTk5WYmKipk2bViZ1AQCAy9tlc8/Sr7/+qr179+rXX39Vbm6u9u7dq7179yozM1OS1K1bN0VGRmrw4MHas2ePvvjiC40ZM0aPP/64/Q7333//XREREYqPj5ck+fv7a+jQoRo9erS++OIL7dmzRw8++KCaN2+uLl26VNq+AgAA11GpZ5ZK4oUXXtCCBQvsj1u2bClJ2rx5szp27Ch3d3etXbtWTz75pG655Rb5+Pho0KBBeuWVV+x9cnJydPDgQZ05c8Y+77XXXlONGjV033336ezZs7rjjjs0f/58ubu7V9zOAQAAl3XZjbPkihhnCQCAy0+1G2cJAACgPBCWAAAALBCWAAAALBCWAAAALBCWAAAALFw2QwcAAIDqJTfPKD7phFIzstTA11ttw+vJ3a1kP2FWFghLAADA5cQlJmvS6gNKTsuyzwv291ZMdKR6RAVXaC1chgMAAC4lLjFZIxYlOAQlSUpJy9KIRQmKS0yu0HoISwAAwGXk5hlNWn1AhY2YnT9v0uoDys2ruDG1CUsAAMBlxCedKHBG6WJGUnJaluKTTlRYTYQlAADgMlIzig5KpWlXFghLAADAZTTw9S7TdmWBsAQAAFxG2/B6Cvb3VlEDBNh04VtxbcPrVVhNhCUAAOAy3N1siomOlKQCgSn/cUx0ZIWOt0RYAgAALqVHVLDmPNhKQf6Ol9qC/L0158FWFT7OEoNSAgAAl9MjKlhdI4MYwRsAAKAo7m42tWtSv7LL4DIcAACAFcISAACABcISAACABcISAACABcISAACABcISAACABcISAACABcISAACABcISAACABUbwLgPGGElSenp6JVcCAACclf+5nf85XhTCUhnIyMiQJIWGhlZyJQAAoKQyMjLk7+9f5HKbKS5OoVh5eXk6duyYfH19ZbNV/A/8lVR6erpCQ0N19OhR+fn5VXY5Fa6677/EMZA4BhLHQOIYVPf9N8YoIyNDISEhcnMr+s4kziyVATc3NzVs2LCyyygxPz+/avniyFfd91/iGEgcA4ljIHEMqvP+W51RyscN3gAAABYISwAAABYIS9WQl5eXYmJi5OXlVdmlVIrqvv8Sx0DiGEgcA4ljUN3331nc4A0AAGCBM0sAAAAWCEsAAAAWCEsAAAAWCEsAAAAWCEuXkS+//FLR0dEKCQmRzWbTJ598UmyfDz74QNdff71q1qyp4OBgPfLII/rzzz8d2qxYsUKRkZHy8vJSZGSkVq5cWWA9b775psLDw+Xt7a3WrVvrq6++KqvdKpHyOAbvvvuubrvtNtWtW1d169ZVly5dFB8f77CO2NhY2Ww2hykoKKisd88p5XEM5s+fX2D/bDabsrKyHNZTlZ8HHTt2LPQY9OzZ097GVZ4Hpdn/2bNn69prr5WPj4+aNWumhQsXFmhT1d8LijsG1eG9oLhjcLm9F1QUwtJl5PTp07r++us1a9Ysp9pv27ZNDz30kIYOHar9+/dr+fLl2rlzpx577DF7m+3bt2vAgAEaPHiw9u3bp8GDB+u+++7Tjh077G2WLVumUaNGaeLEidqzZ49uu+023Xnnnfr111/LfB+LUx7HYMuWLbr//vu1efNmbd++XVdddZW6deum33//3WFd1113nZKTk+3Td999V6b75qzyOAbShRF8L96/5ORkeXt725dX9efBxx9/7LDviYmJcnd3V//+/R3W5QrPg5Lu/5w5czRhwgTFxsZq//79mjRpkv7nf/5Hq1evtrep6u8FzhyDqv5e4MwxkC6v94IKY3BZkmRWrlxp2Wb69OmmcePGDvPeeOMN07BhQ/vj++67z/To0cOhTffu3c3AgQPtj9u2bWueeOIJhzYRERFm/Pjxpay+bJTVMfir8+fPG19fX7NgwQL7vJiYGHP99ddfSrnloqyOwbx584y/v7/leqrb8+C1114zvr6+JjMz0z7PFZ8Hzux/u3btzJgxYxzmPf300+aWW26xP67q7wXOHIO/qmrvBc4cg8v5vaA8cWapCmvfvr1+++03rVu3TsYY/fHHH/roo48cLits375d3bp1c+jXvXt3ffPNN5Kkc+fOaffu3QXadOvWzd7GlTlzDP7qzJkzysnJUb169RzmHz58WCEhIQoPD9fAgQP1888/l3f5ZcLZY5CZmalGjRqpYcOG6tWrl/bs2WNfVh2fB3PnztXAgQNVq1Yth/mX4/MgOzvb4cyAJPn4+Cg+Pl45OTmSqv57gTPH4K+q2nuBs8egKr8XlBZhqQpr3769PvjgAw0YMECenp4KCgpSnTp19P/+3/+zt0lJSVFgYKBDv8DAQKWkpEiSjh8/rtzcXMs2rsyZY/BX48eP15VXXqkuXbrY5910001auHCh1q9fr3fffVcpKSlq3759gfu/XJEzxyAiIkLz58/XqlWrtGTJEnl7e+uWW27R4cOHJVW/50F8fLwSExMLXKq8XJ8H3bt317///W/t3r1bxhjt2rVL7733nnJycnT8+HFJVf+9wJlj8FdV7b3AmWNQ1d8LSq0Sz2rhEsiJU6779+83wcHBZtq0aWbfvn0mLi7ONG/e3Dz66KP2Nh4eHmbx4sUO/RYtWmS8vLyMMcb8/vvvRpL55ptvHNr885//NM2aNSubnSmlsjoGF5s6daqpW7eu2bdvn+V6MzMzTWBgoJkxY0Zpyy8T5XEMjDEmNzfXXH/99eapp54yxlS/58GwYcNMVFRUsdt2heeBM/t/5swZ88gjj5gaNWoYd3d3ExISYsaOHWskmT/++MMYU/XfC5w5Bheriu8FJT0Gxlxe7wXliTNLVdiUKVN0yy236B//+IdatGih7t27680339R7772n5ORkSVJQUFCBvwZSU1PtfzUEBATI3d3dso0rc+YY5HvllVc0efJkbdiwQS1atLBcb61atdS8eXP7X1uurCTHIJ+bm5tuvPFG+/5Vp+fBmTNntHTp0gJnlQpzuTwPfHx89N577+nMmTM6cuSIfv31V4WFhcnX11cBAQGSqv57gTPHIF9VfS8oyTHIV9XeC0qLsFSFnTlzRm5ujv/F7u7ukiTzfz8J2K5dO23cuNGhzYYNG9S+fXtJkqenp1q3bl2gzcaNG+1tXJkzx0CSpk+frpdeeklxcXFq06ZNsevNzs7W999/r+Dg4LItuBw4ewwuZozR3r177ftXXZ4HkvThhx8qOztbDz74YLHrvZyeB5Lk4eGhhg0byt3dXUuXLlWvXr3sx6WqvxfkszoGUtV+L8hX3DG4WFV7Lyi1yjythZLJyMgwe/bsMXv27DGSzKuvvmr27NljfvnlF2OMMePHjzeDBw+2t583b56pUaOGefPNN81PP/1ktm3bZtq0aWPatm1rb/P1118bd3d38/LLL5vvv//evPzyy6ZGjRrm22+/tbdZunSp8fDwMHPnzjUHDhwwo0aNMrVq1TJHjhypuJ3/P+VxDKZOnWo8PT3NRx99ZJKTk+1TRkaGvc3o0aPNli1bzM8//2y+/fZb06tXL+Pr61tljkFsbKyJi4szP/30k9mzZ4/9VP2OHTvsbar68yDfrbfeagYMGFDodl3leVDS/T948KB5//33zaFDh8yOHTvMgAEDTL169UxSUpK9TVV/L3DmGFT19wJnjsHl9l5QUQhLl5HNmzcbSQWmhx9+2BhjzMMPP2w6dOjg0OeNN94wkZGRxsfHxwQHB5sHHnjA/Pbbbw5tli9fbpo1a2Y8PDxMRESEWbFiRYFtz5492zRq1Mh4enqaVq1ama1bt5bXbloqj2PQqFGjQtcZExNjbzNgwAATHBxsPDw8TEhIiOnXr5/Zv39/BexxQeVxDEaNGmWuuuoq4+npaa644grTrVu3AvckGFO1nwfGXPgwkWQ2bNhQ6HZd5XlQ0v0/cOCAueGGG4yPj4/x8/MzvXv3Nj/88EOB9Vbl9wJnjkFVfy9w5hhcbu8FFcVmTBHn4QEAAMA9SwAAAFYISwAAABYISwAAABYISwAAABYISwAAABYISwAAABYISwAAABYISwAAABYISwAuK88//7yGDRtW7ttJTU3VFVdcod9//73ct1UWnnnmGdlsNvXr10+5ubmVXQ5QpRCWAFySL7/8UtHR0QoJCZHNZtMnn3xSZNuOHTsqKChINpvNcjpy5Eih/f/44w+9/vrrevbZZ0u9/bfeektHjhyRzWbT3r177csyMjLUsWNHRURE6OjRo2rQoIEGDx6smJiYEh6R4jlTszFGsbGxCgkJkY+Pjzp27Kj9+/cXur5//etfevfdd/X2229r+/btGj58eIE2Bw8eVKdOnRQYGChvb281btxYzz33nHJycsp694Aqh7AE4JKcPn1a119/vWbNmmXZ7sSJE/rmm2+0Y8cOJScn26eGDRvqxRdfdJgXGhpa6Drmzp2rdu3aKSwsrNTbj46OLrDsf//3f9WpUydlZmZq27Zt9u0/8sgj+uCDD3Ty5MlijkLJOFPztGnT9Oqrr2rWrFnauXOngoKC1LVrV2VkZDi0e+eddzRjxgxt3LhRw4YN05dffqmNGzdq3LhxDu08PDz00EMPacOGDTp48KBmzpypd999t1zCIFDlVPJv0wGoQiSZlStXFrps4cKFpk2bNgXmN2rUyLz22mtOrb958+Zm1qxZl7z9pKQkI8ns2bPH/Prrr6ZZs2amY8eOJj09vUC/sLAwM3fu3CK3+cgjj5jmzZubrKwsY4wx586dM61atTKDBg1yap8KqzkvL88EBQWZl19+2T4vKyvL+Pv7m7feess+b/ny5SYoKMjs2bPHof8vv/ximjZtaqZOnWq57b///e/m1ltvdapOoDrjzBKACrFq1Sr17t271P1PnjypxMREtWnTpsy2f/DgQd1yyy2KiIhQXFycfH19C/Rr27atvvrqqyLX+8Ybb+j06dMaP368pAv3VB0/flxvvvlmqeqUpKSkJKWkpKhbt272eV5eXurQoYO++eYb+7x7771XycnJuuGGGxz6X3XVVTp8+LDGjh1b5DZ+/PFHxcXFqUOHDqWuE6guCEsAyl12drbWr19/SWHpl19+kTFGISEhZbb9hx56SE2aNNGKFSvk5eVVaN8rr7yyyHuoJKl27dpatGiRZs+erRdeeEEzZszQ+++/L39//xLXmS8lJUWSFBgY6DA/MDDQvqy02rdvL29vb1199dW67bbb9OKLL17S+oDqgLAEoNxt2rRJ9evXV/PmzUu9jrNnz0qSvL29y2z7vXv31rZt27RixYoi+/r4+OjMmTOW62/Xrp3GjBmjl156SaNHj9btt99e4hoLY7PZHB4bYwrMK6lly5YpISFBixcv1tq1a/XKK69c0vqA6qBGZRcAoOq71EtwkhQQECDpwuW4K664oky2/+yzz6pFixZ64IEHZIzRgAEDCrQ5ceJEsdvLy8vT119/LXd3dx0+fLhEtRUmKChI0oUzTMHBwfb5qampBc42lVT+zeuRkZHKzc3VsGHDNHr0aLm7u1/SeoGqjDNLAMqVMUarV6/W3XfffUnradKkifz8/HTgwIEy3f5zzz2nl156SQ888ICWLFlSYHliYqJatmxpuY3p06fr+++/19atW7V+/XrNmzevRDX+VXh4uIKCgrRx40b7vHPnzmnr1q1q3779Ja37YsYY5eTkyBhTZusEqiLOLAG4JJmZmfrxxx/tj5OSkrR3717Vq1dPV111lXbv3q3Tp09f8qUpNzc3denSRdu2bVOfPn3KdPvjx4+Xu7u7Bg8erLy8PD3wwAOSpDNnzmj37t2aPHlykX337t2rF154QR999JFuueUWvf7663r66afVoUMHNW7cuNA+xdVss9k0atQoTZ48WVdffbWuvvpqTZ48WTVr1tSgQYOcPWQOPvjgA3l4eKh58+by8vLS7t27NWHCBA0YMEA1avBRAFiqxG/iAagCNm/ebCQVmB5++GFjjDHPPfeceeCBB4rsX5KhA+Li4syVV15pcnNzL2n7Fw8dcLEZM2YYd3d3s3DhQmOMMYsXLzbNmjUrsp6zZ8+ayMhIM2zYMIf5ffv2Ne3btzfnz58vtF9xNRtzYfiAmJgYExQUZLy8vMztt99uvvvuu+IOUZGWLl1qWrVqZWrXrm1q1aplIiMjzeTJk83Zs2dLvU6gurAZw/lXAOWnRYsWeu6553Tfffdd8rqMMbr55ps1atQo3X///eW+/bZt22rUqFGlPpsDoGrgniUA5ebcuXO65557dOedd5bJ+mw2m9555x2dP3++3Lefmpqqe++91+lQBqDq4swSAACABc4sAQAAWCAsAQAAWCAsAQAAWCAsAQAAWCAsAQAAWCAsAQAAWCAsAQAAWCAsAQAAWCAsAQAAWPj/EuRex31DrPsAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# Plot the data\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(1/T * 1e3, np.log(kexp), 'o')\n", + "plt.xlabel('1/T (1/K) x 10^3')\n", + "plt.ylabel('ln(k • s)')\n", + "plt.title('Arrhenius Plot of ln(k) vs 1/T, Original Data')\n" + ] + }, + { + "cell_type": "markdown", + "id": "a826bed5", + "metadata": {}, + "source": [ + "The plot is, in fact, very linear and the fitting will give reliable values of the slope and intercept. Note that we have kept the units inside the logarithm since these operate on dimensionless quantities.\n", + "\n", + "Next we will fit the data to the equation: $y = m x + b$ using the ``np.polyfit`` function, and calculate the **estimated** values of $\\ln(k_\\mathrm{exp})$ as ``y_est``" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "60aa3c41", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "*******************************\n", + "\n", + "Fitting Data to a first order kinetic model\n", + "\n", + " y = b + m x\n", + "\n", + "\n", + " m = 21726 K\n", + " b = 33 \n", + " A = 1.33e+14 1/s\n", + " Ea = 181 kJ/mol\n", + "\n", + "\n", + "*******************************\n" + ] + } + ], + "source": [ + "\n", + "# fit a linear curve an estimate its y-values and their error. deg=1 fits data to a linear equation y = b + m x\n", + "m, b = np.polyfit(1/T, np.log(kexp), deg=1)\n", + "\n", + "\n", + "# Calculate estimated values of y where y_est = ln(k)_est\n", + "y_est = m * 1/T + b\n", + "\n", + "#and write the value of the results: \n", + " \n", + "print('\\n*******************************\\n')\n", + "print('Fitting Data to a first order kinetic model\\n')\n", + "print(' y = b + m x\\n\\n')\n", + "print(' m = %6.0f K'%(-m))\n", + "print(' b = %6.0f '%(b))\n", + "print(' A = %3.2e 1/s'%np.exp(b))\n", + "print(' Ea = %6.0f kJ/mol\\n\\n'%(-m * 8.314/1000))\n", + "print('*******************************')\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "7797ed49", + "metadata": {}, + "source": [ + "Now we plot both the experimental data (as points) and the fit of the data to a linear equation:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ed10e678", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax1 = plt.subplots()\n", + "ax1.plot(1/T * 1e3, y_est, '-', label='Fitted line')\n", + "ax1.plot(1/T * 1e3, np.log(kexp), 'o', label='Original data', markersize=10)\n", + "plt.xlabel('1/T (1/K) * 10^3')\n", + "plt.ylabel('ln(k • s)')\n", + "plt.title('Least-Squares Fitting of Arrhenius Plot of ln(k) vs 1/T')\n", + "plt.legend()\n" + ] + }, + { + "cell_type": "markdown", + "id": "c27b5e6c", + "metadata": {}, + "source": [ + "And we also plot the residuals, that is:\n", + "\n", + "residuals = y(estimated)-y(experiment)\n", + "\n", + "to verify that a linear equation is a good model to fit these data." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "d428a13f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Residuals y_est-y_exp')" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# Plot the residuals\n", + "\n", + "fig, ax2 = plt.subplots()\n", + "ax2.plot(1/T * 1e3, np.log(kexp)-y_est, 'o')\n", + "plt.title('Plot of Residuals')\n", + "plt.xlabel('1/T (1/K) x 10^3')\n", + "plt.ylabel('Residuals y_est-y_exp')\n" + ] + }, + { + "cell_type": "markdown", + "id": "69e5cfeb", + "metadata": {}, + "source": [ + "The residuals are all small in magnitude and show no obvious 'trend', that is, the model is a good fit to the data.\n", + "\n", + "## End of Notebook Example\n", + "rfl. emf modified 8/24" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2cae855e-e3ea-4acb-981c-b0b53fb82af7", + "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": "3.12.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}