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   "source": [
    "# Exercise 1. Fitting functions to data."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The change of the standard Gibbs function $\\Delta G$ of a reaction was determined by measuring equilibrium constants at various temperatures. The following values were obtained:\n",
    "\n",
    "| $T$ [K] | $\\Delta G$ [kJ $\\mathrm{mol}^{-1}$] |\n",
    "| :--:     | :--: |\n",
    "|270 | 40.3 |\n",
    "|280 | 38.2 |\n",
    "|290 | 36.1 |\n",
    "|300 | 32.2 |\n",
    "|310 | 29.1 |\n",
    "|320 | 28.0 |\n",
    "|330 | 25.3 |\n",
    "\n",
    "The uncertainty in $T$ is negligible and the weight factors are equal for\n",
    "all cases. \n",
    "\n",
    "1. Determine the reaction entropy $S = −d \\Delta G/dT$ by fitting the values of $\\Delta G$ to a linear function of $T$. \n",
    "2. What is the uncertainty in $S$ to a 90% confidence? \n",
    "3. Extrapolate $\\Delta G$ to $T = 350 \\mathrm{K}$ and give the uncertainty at 90% confidence level. Compare with the uncertainty at 90% for $\\Delta G$ at $T = 290 \\mathrm{K}$. Discuss the differences in the uncertainties and what can you conclude?\n",
    "4. Import the seaborn library, use the [regplot][1] function to plot the data. Try 90% and 99% confidence intervals when plotting. Compare and conclude.\n",
    "\n",
    "[1]: https://stanford.edu/~mwaskom/software/seaborn/generated/seaborn.regplot.html \"seaborn.regplot — seaborn 0.7.0 documentation\""
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "\n",
    "\n",
    "T = np.array([270, 280, 290, 300, 310, 320, 330])\n",
    "x = T\n",
    "DeltaG = np.array([40.3, 38.2, 36.1, 32.2, 29.1, 28.0, 25.3])\n",
    "y = DeltaG\n"
   ]
  }
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