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Laboration Co-komplex, "proof-of-concept" rapport med IPython Notebook (istället för Excel)
{
"metadata": {
"name": "Labinx 2 - kinetik Co-komplex"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Labbrapport: laboration 2 - reaktionskinetik f\u00f6r ett koboltkomplex"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Utf\u00f6rd av:** L., H. \n",
"**Datum:** 2013-01-11 \n",
"**Handledare:** Taha Ahmed"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Syfte"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Syftet med laborationen \u00e4r att ..."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Teori"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\left[\\mathrm{Co\\left(NH_3\\right)_5H_2O}\\right]^{3+} \\;\\xrightarrow[-\\mathrm{H_2O}]{+\\mathrm{NO_2^-}}\\; \\left[\\mathrm{Co\\left(NH_3\\right)_5NO_2}\\right]^{2+} \\rightarrow \\left[\\mathrm{Co\\left(NH_3\\right)_5ONO}\\right]^{2+}$ (mekanism 1)\n",
"\n",
"$\\left[\\mathrm{Co\\left(NH_3\\right)_5H_2O}\\right]^{3+} \\;\\xrightarrow[-\\mathrm{H_2O}]{+\\mathrm{NO_2^-}}\\; \\left[\\mathrm{Co\\left(NH_3\\right)_5ONO}\\right]^{2+} \\rightarrow \\left[\\mathrm{Co\\left(NH_3\\right)_5NO_2}\\right]^{2+}$ (mekanism 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Vi f\u00f6ljer ligandutbytet spektrofotometriskt"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Reaktionsmekanism f\u00f6r ligandutbytet"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$r = -\\frac{d\\left[\\left[\\mathrm{Co(NH_3)_5H_2O}\\right]^{3+}\\right]}{dt} = k_1 \\left[\\left[\\mathrm{Co(NH_3)_5H_2O}\\right]^{3+}\\right] \\left[\\mathrm{HNO_2}\\right] \\left[\\mathrm{NO_2^-}\\right]$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$r = -\\frac{d\\left[\\left[\\mathrm{Co(NH_3)_5H_2O}\\right]^{3+}\\right]}{dt} = k_1^\\prime \\left[\\left[\\mathrm{Co(NH_3)_5H_2O}\\right]^{3+}\\right]$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"D\u00e4r $k_1^\\prime = k_1 \\left[\\mathrm{HNO_2}\\right] \\left[\\mathrm{NO_2^-}\\right]$. \n",
"J\u00e4mvikt inst\u00e4ller sig mellan de tv\u00e5 isomererna. Den observerade hastighetskonstanten \u00e4r av f\u00f6rsta ordningen, $k_2 = k_+ + k_-$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$r = -\\frac{d\\left[\\left[\\mathrm{Co(NH_3)_5H_2O}\\right]^{3+}\\right]}{dt} = k_2 \\left(\\left[\\left[\\mathrm{Co(NH_3)_5H_2O}\\right]^{3+}\\right] - \\left[\\left[\\mathrm{Co(NH_3)_5H_2O}\\right]^{3+}\\right]_\\mathrm{eq}\\right)$$"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Beskrivning av den kinetiska modellen"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\n",
"R \\;\\;\\xrightarrow[]{k_1^\\prime}\\;\\; I \\;\\;\\xrightarrow[]{k_2}\\;\\; P\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\\tag{4}\n",
"[R]_t = [R]_0 \\exp(-k_1^\\prime t)\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\\tag{5}\n",
"[I]_t = \\frac{k_1^\\prime [R]_0}{k_2 - k_1^\\prime} \\left(\\exp(-k_1^\\prime t) - \\exp(-k_2 t)\\right)\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\\tag{6}\n",
"[P]_t = [R]_0 - [R]_t - [I]_t\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\\tag{7}\n",
"\\mathrm{Abs}_\\mathrm{l\u00f6sning} = {\\mathrm{Abs_R}} + {\\mathrm{Abs_I}} + {\\mathrm{Abs_P}} = l\\left([R\\:]\\varepsilon_\\mathrm{R} + [I\\:]\\varepsilon_\\mathrm{I} + [P\\:]\\varepsilon_\\mathrm{P}\\right)\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\\tag{8}\n",
"\\mathrm{Abs}_t = l[R\\:]_0\\left(\\varepsilon_P + \\left(\\varepsilon_R + \\frac{\\varepsilon_I k_1^\\prime - \\varepsilon_P k_2}{k_2 - k_1^\\prime} \\right)\\exp(-k_1^\\prime t) + \\frac{k_1^\\prime(\\varepsilon_P - \\varepsilon_I)}{k_2 - k_1^\\prime}\\exp(-k_2 t)\\right)\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\\tag{9}\n",
"\\mathrm{Abs}_t = \\mathrm{Abs} _\\infty + \\Delta\\mathrm{Abs}_1\\exp(-k_1^\\prime t) + \\Delta\\mathrm{Abs}_2\\exp(-k_2 t)\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\\tag{10}\n",
"\\mathrm{Abs}_t = \\mathrm{Abs} _\\infty + \\Delta\\mathrm{Abs}_1\\exp(-t/\\tau_1) + \\Delta\\mathrm{Abs}_2\\exp(-t/\\tau_2), \\quad\\quad k_1^\\prime = \\left(\\tau_1\\right)^{-1}, \\quad k_2 = \\left(\\tau_2\\right)^{-1}\n",
"\\end{equation}"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Svar till f\u00f6rstuderingsfr\u00e5gor"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Del 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Best\u00e4m v\u00e5gl\u00e4ngden vid absorptionsmaxima f\u00f6r de tre koboltkomplexen (aqua, nitro, nitrito).\n",
" Vilken f\u00e4rg har ljus med motsvarande v\u00e5gl\u00e4ngd?\n",
" Vilken f\u00e4rg har l\u00f6sningar som absorberar vid respektive v\u00e5gl\u00e4ngd?\n",
"\n",
"2. Skissa absorbansen, `Abs`, vid 510 nm mot tiden, `t`, f\u00f6r de tv\u00e5 f\u00f6reslagna reaktionsmekanismerna.\n",
"\n",
"3. Vilken eller vilka av f\u00f6ljande v\u00e5gl\u00e4ngder kan anv\u00e4ndas f\u00f6r att urskilja mellan de tv\u00e5 f\u00f6reslagna reaktionsmekanismerna?\n",
" - 415 nm, \n",
" - 450 nm, \n",
" - 482 nm, \n",
" - 495 nm, \n",
" - 510 nm.\n",
"\n",
"4. Antag att mekanism 1 \u00e4r korrekt. Vilken eller vilka av de ovanst\u00e5ende v\u00e5gl\u00e4ngderna skulle vara bra f\u00f6r att anv\u00e4nda f\u00f6r att best\u00e4mma hastighetskonstanten f\u00f6r\n",
" - reaktion 1?\n",
" - reaktion 2?\n",
" - reaktion 1 och reaktion 2?\n",
"\n",
"5. G\u00e5r det att anv\u00e4nda resonemanget fr\u00e5n fr\u00e5ga 4 (ovan) om vi ist\u00e4llet antar att mekanism 2 \u00e4r korrekt? Vilka skillnader kan f\u00f6rutses?"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Del 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"6. Vilka \u00e4r de \u00f6nskv\u00e4rda reaktionsf\u00f6rh\u00e5llandena f\u00f6r att ligandutbytesreaktionen ska bli en pseudo-f\u00f6rsta ordningens reaktion?\n",
"\n",
"7. N\u00e4mn tv\u00e5 parametrar som \u00e4r viktiga att kontrollera under ett kinetikexperiment."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Utf\u00f6rande"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Utrustning och kemikalier"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Spektrofotometer (fabrikat, modell), termostat (fabrikat, modell), pH-meter, etc. \n",
"Co-l\u00f6sningar (koncentrationer, och dylikt)."
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Beredning av reaktionsl\u00f6sningar"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. **Tillredde reaktionsl\u00f6sningar** \n",
" L\u00f6sning av $\\mathrm{Co}$-komplex vatten. \n",
" L\u00f6sning av $\\mathrm{NaNO_2}$ i vatten, med tillsats av stark syra.\n",
"\n",
"2. **Startade upp termostaten**\n",
"\n",
"3. **Tillverkade l\u00f6sning f\u00f6r m\u00e4tning av \"slutproduktens\" absorbans**\n",
"\n",
"4. **F\u00f6rv\u00e4rmde l\u00f6sningarna (temperatur?)**\n",
"\n",
"5. **Kalibrerade spektrofotometerns baslinje med avjonat vatten**\n",
"\n",
"6. **Kinetikstudier vid $510~\\mathrm{nm}$ och $45^{\\circ}\\mathrm{C}$**\n",
"\n",
"7. **Best\u00e4mde $[\\mathrm{HNO_2}]$ och $[\\mathrm{NO_2^-}]$**\n",
"\n",
"8. **M\u00e4tte absorbans f\u00f6r startmaterialet**\n",
"\n",
"9. **M\u00e4tte absorbans f\u00f6r \"slutprodukten\"**\n",
"\n",
"\n"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Resultat"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Vi b\u00f6rjar med att plotta den uppm\u00e4tta absorbanskurvan. F\u00f6r att kunna g\u00f6ra det beh\u00f6ver vi *importera* den funktion som vi vill anv\u00e4nda f\u00f6r plottning (vi anv\u00e4nder `matplotlib`). Detta g\u00e4ller f\u00f6r resten av dokumentet."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt\n",
"# \u00d6ka bredden p\u00e5 text-output till 140 kolumner\n",
"numpy.set_printoptions(linewidth = 140)\n",
"# G\u00f6r plottar lite st\u00f6rre \u00e4n annars\n",
"figsize(14, 8.75)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 150
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nedan plottar vi v\u00e5r experimentellt uppm\u00e4tta absorbanskurva, Abs mot tid i sekunder. \n",
"Det \u00e4r tydligt att isomeriseringsreaktionen f\u00f6ljer reaktionsmekanism 2 (Abs \u00f6kar f\u00f6rst, sjunker sedan)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"filnamn = \"data-Lindgren-Holm.csv\"\n",
"# perhaps we could use scipy.loadtxt() instead? More pedagogical if it avoids the \"unpack\" parameter\n",
"# from scipy import loadtxt\n",
"# loadtxt(\"TEK0006.CSV\", delimiter=\",\", usecols=(0,1)) # load cols number 0 and 1\n",
"x_data, y_data = numpy.loadtxt(filnamn, delimiter=\",\", unpack=True)\n",
"plt.plot(x_data, y_data)\n",
"plt.xlabel(\"Tid/sekunder\")\n",
"plt.ylabel(\"Abs\")\n",
"plt.title(filnamn)\n",
"plt.yscale(\"linear\")\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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JknQksZF+wU2bNlG9evWsjxMSEkhJSTns48eMGUPXrl0B+PTTTylVqhQdO3Yk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\nnz6drVu3snXrVqZPn06nTp0SVn9ZsXsZGMCECRNiyzK6dev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}
],
"prompt_number": 151
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"H\u00e4r har vi vissa saker som f\u00f6rmodligen b\u00f6r l\u00f6sas: \n",
"\n",
"1. Hur tar vi enklast bort outliers i data?"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Analys av kinetikdata -- anpassning av kinetiksp\u00e5r"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Vi importerar tv\u00e5 funktioner som vi kommer att anv\u00e4nda f\u00f6r kurvanpassningen (`curve_fit`) och f\u00f6r annan ber\u00e4kning (`chdtrc`)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# fit with arbitrary function\n",
"# fr\u00e5n modulen scipy.optimize importerar vi funktionen curve_fit, som optimiserar anpassningen baserat p\u00e5 non-linear least squares\n",
"from scipy.optimize import curve_fit\n",
"# n\u00e5got obskyr funktion, k\u00e4lla http://docs.scipy.org/doc/scipy/reference/generated/scipy.special.chdtrc.html\n",
"from scipy.special import chdtrc\n",
"# uncertainties f\u00f6r att enklare utf\u00f6ra ber\u00e4kningar med os\u00e4kerheter\n",
"from uncertainties import unumpy"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 152
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"De fyra f\u00f6ljande rutorna med kod \u00e4r viktiga, och b\u00f6r skrivas f\u00f6r hand av studenten."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Definiera den kinetiska modellen\n",
"def kinetic_model(t, abs0, abs1, abs2, tau1, tau2):\n",
" return abs0 + abs1 * exp(-t/tau1) + abs2 * exp(-t/tau2)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 153
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Namngivning i str\u00e4ngen p_names av rent kosmetiska sk\u00e4l (anv\u00e4nds senare...)\n",
"p_names = (\"abs0\", \"abs1\", \"abs2\", \"tau1\", \"tau2\")\n",
"# Initialv\u00e4rden f\u00f6r parametrarna till v\u00e5r kinetiska modell (gissningar)\n",
"p_guess = (2.0E-1, # abs0 = p_guess[0]\n",
" -5.0E-2, # abs1 = p_guess[1]\n",
" 2.0E-1, # abs2 = p_guess[2]\n",
" 250, # tau1 = p_guess[3]\n",
" 900) # tau2 = p_guess[4]\n",
"# Ber\u00e4kna absorbansv\u00e4rden baserat p\u00e5 initialv\u00e4rdena ovan (f\u00f6r senare j\u00e4mf\u00f6relse med anpassade parametrar)\n",
"y_initial = kinetic_model(x_data, *p_guess)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 154
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Anv\u00e4nd den kinetiska modellen f\u00f6r att anpassa parametrarna\n",
"# popt: anpassade parametrar, pcov: deras kovariansmatris (statistik)\n",
"popt, pcov = curve_fit(kinetic_model,\n",
" x_data,\n",
" y_data,\n",
" p0 = p_guess,\n",
" maxfev = int(1E2))\n",
"# maxfev is the maximum number of iterations tried; you\n",
"# can try increasing this value if the fit fails."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 155
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Stoppa in de anpassade parametrarna i den kinetiska modellen och ber\u00e4kna anpassad absorbans-kurva\n",
"y_fit = kinetic_model(x_data, *popt)\n",
"# Ber\u00e4kna residualer (skillnad mellan experimentell absorbans och anpassad absorbans-kurva)\n",
"y_residual = y_data - y_fit\n",
"# Calculate degrees of freedom of fit\n",
"DoF = len(x_data) - len(p_guess)\n",
"# Calculate Chi-Squared\n",
"chisq = sum((y_residual)**2)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 156
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Resterande rutor med kod i denna sektion (\"Analys av kinetikdata\") kan med f\u00f6rdel kopieras och klistras in verbatim, ingen anledning att knappa in rad-f\u00f6r-rad."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_exp, = plt.plot(x_data, y_data, \"k:\", linewidth = 2, label = \"Experimental\")\n",
"plot_init, = plt.plot(x_data, y_initial, \"c-\", linewidth = 2, label = \"Initial fit\")\n",
"plot_final, = plt.plot(x_data, y_fit, \"r--\", linewidth = 2, label = \"Optimized fit\")\n",
"# Skapa en legend\n",
"legend(loc = 1, ncol = 1)\n",
"# Skapa titel och ben\u00e4mning p\u00e5 axlarna\n",
"plt.title(\"Comparing experimental data, initial fit, and optimized fit\")\n",
"plt.xlabel(\"Time/seconds\")\n",
"plt.ylabel(\"Abs\")\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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f1gYAVVVVmDdvHgwGA44cOYLvv/8eQ4cOhYWFBcLDw/H6668j95/H6Fy8eLHe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\nQmCC\n"
}
],
"prompt_number": 157
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Show residual: difference between data and optimized fit\n",
"plt.plot(x_data, y_residual, \"r-\")\n",
"plt.title(\"Residual\")\n",
"# Draw horizontal line at 0\n",
"plt.axhline(y = 0)\n",
"# Label axes\n",
"plt.xlabel(\"Time/seconds\")\n",
"plt.ylabel(\"Abs\")\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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nP7GGm3/mGWDBAu/Hm80RlVsIMwfmKCyUpo3HHw8MHgwcPmw1R7z2WoYwop7K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\nSUVORK5CYII=\n"
}
],
"prompt_number": 158
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Antal datapunkter =\", len(x_data)\n",
"print \"Antal parametrar =\", len(p_guess)\n",
"print \"Degrees of freedom =\", DoF"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Antal datapunkter = 1601\n",
"Antal parametrar = 5\n",
"Degrees of freedom = 1596\n"
]
}
],
"prompt_number": 159
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Kovariansmatris : \\n\", pcov, \"\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Kovariansmatris : \n",
"[[ 6.10020726e-09 -4.71160660e-08 4.24484128e-08 1.13179885e-04 -2.72915619e-04]\n",
" [ -4.71160660e-08 4.31034079e-07 -3.98674727e-07 -1.09888474e-03 2.34604279e-03]\n",
" [ 4.24484128e-08 -3.98674727e-07 3.72520016e-07 1.04321100e-03 -2.15564451e-03]\n",
" [ 1.13179885e-04 -1.09888474e-03 1.04321100e-03 3.04216653e+00 -5.87442427e+00]\n",
" [ -2.72915619e-04 2.34604279e-03 -2.15564451e-03 -5.87442427e+00 1.31057966e+01]] \n",
"\n"
]
}
],
"prompt_number": 160
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"# G\u00f6m undan i en funktion?\n",
"print \"Correlation Matrix :\"\n",
"for i,row in enumerate(pcov):\n",
" for j in range(len(popt)) :\n",
" print \"%10f\"%(pcov[i, j]/sqrt(pcov[i, i]*pcov[j, j])), # note: comma at end of print statement suppresses new line\n",
" print # required for proper formatting of matrix"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Correlation Matrix :\n",
" 1.000000 -0.918842 0.890460 0.830817 -0.965216\n",
" -0.918842 1.000000 -0.994920 -0.959632 0.987071\n",
" 0.890460 -0.994920 1.000000 0.979954 -0.975597\n",
" 0.830817 -0.959632 0.979954 1.000000 -0.930341\n",
" -0.965216 0.987071 -0.975597 -0.930341 1.000000\n"
]
}
],
"prompt_number": 161
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Estimated parameters with uncertainties (initial guess in parentheses)\"\n",
"poptwerr = range(len(popt))\n",
"for i in range(len(popt)):\n",
" # Here (inside the for-loop) we should build up a unumpy array (arrary with uncertainty values) for each parameter\n",
" poptwerr[i] = unumpy.uarray([popt[i], pcov[i,i]**0.5*max(1, sqrt(chisq/DoF))])\n",
" print (\" %s = %10.5f +/- %10.8f (%9.5f)\" %(p_names[i], unumpy.nominal_values(poptwerr[i]), unumpy.std_devs(poptwerr[i]), p_guess[i]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Estimated parameters with uncertainties (initial guess in parentheses)\n",
" abs0 = 0.15877 +/- 0.00007810 ( 0.20000)\n",
" abs1 = -0.10565 +/- 0.00065653 ( -0.05000)\n",
" abs2 = 0.22035 +/- 0.00061034 ( 0.20000)\n",
" tau1 = 408.55501 +/- 1.74418076 (250.00000)\n",
" tau2 = 1358.81341 +/- 3.62019289 (900.00000)\n"
]
}
],
"prompt_number": 162
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"Curve fit converged with:\"\n",
"print \" ChiSq = %1.5E\" %(chisq)\n",
"print \" DoF = %4g\" %(DoF)\n",
"print \" ChiSq/DoF = %1.5E\" %(chisq/DoF)\n",
"print \" CDF = %4.2f%%\" %(100*chdtrc(DoF,chisq))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Curve fit converged with:\n",
" ChiSq = 1.29030E-04\n",
" DoF = 1596\n",
" ChiSq/DoF = 8.08461E-08\n",
" CDF = 100.00%\n"
]
}
],
"prompt_number": 163
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Next step:** calculate $k$ and $K$, preferably without losing uncertainties \n",
"Perhaps we should use the `uncertainties` package!"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k1prim = 1 / poptwerr[3]\n",
"k2 = 1 / poptwerr[4]\n",
"print \"k1prim =\", k1prim, \"ENHET?\"\n",
"print \"k2 =\", k2, \"ENHET?\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"k1prim = 0.00244765079648+/-1.04493772085e-05 ENHET?\n",
"k2 = 0.00073593621875+/-1.96070413922e-06 ENHET?\n"
]
}
],
"prompt_number": 164
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Ta 5 ml av $\\mathrm{HNO_2}/\\mathrm{NaNO_2}$-l\u00f6sningen och sp\u00e4d ut det med 5 ml avjonat vatten (s\u00e5 att koncentrationen blir samma som under kinetikm\u00e4tningen). M\u00e4t pH p\u00e5 l\u00f6sningen. \n",
"Fr\u00e5n k\u00e4nd koncentration av $\\mathrm{NaNO_2}$, k\u00e4nt pH och $p\\mathrm{K_a}$-v\u00e4rde f\u00f6r $\\mathrm{HNO_2}$ (se SI-data) kan ni sedan r\u00e4kna ut $[\\mathrm{HNO_2}]$ och $[\\mathrm{NO_2^-}]$. \n",
"Vi saknar v\u00e4rden f\u00f6r $[\\mathrm{NaNO_2}]$, $[\\mathrm{HNO_2}]$ och $[\\mathrm{NO_2^-}]$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"conc_NaNO2 = 0.5 # mol/L\n",
"conc_HNO2 = 0.0125 # mol/L\n",
"conc_NO2m = 0.5 # mol/L\n",
"k1 = k1prim / (conc_HNO2 * conc_NO2m)\n",
"print \"k1 =\", k1 # H\u00c4R BEH\u00d6VS KORREKTA V\u00c4RDEN\n",
"print \"k2 =\", k2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"k1 = 0.391624127437+/-0.00167190035336\n",
"k2 = 0.00073593621875+/-1.96070413922e-06\n"
]
}
],
"prompt_number": 165
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Conc Co is known (each lab group should calculate from weighed mass)\n",
"conc_Co = 1 # H\u00c4R BEH\u00d6VS L\u00c4MPLIGT V\u00c4RDE\n",
"# Abs / (conc * length)\n",
"# Abs read from plot at 510 nm, conc in M, length in dm\n",
"epsilon510_ONO = 0.35 / (6.7E-3 * 0.1)\n",
"epsilon510_NO2 = 0.15 / (6.7E-3 * 0.1)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 166
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\n",
"A_\\infty = \\varepsilon_\\mathrm{ONO^-} \\cdot [\\mathrm{ONO^-}] \\cdot l + \\varepsilon_\\mathrm{NO_2^-} \\cdot [\\mathrm{NO_2^-}] \\cdot l\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\n",
"[\\mathrm{Co^{3+}}] = [\\mathrm{ONO^-}] + [\\mathrm{NO_2^-}] \\quad\\Leftrightarrow\\quad [\\mathrm{ONO^-}] = [\\mathrm{Co^{3+}}] - [\\mathrm{NO_2^-}]\n",
"\\end{equation}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{equation}\n",
"[\\mathrm{NO_2^-}] = \\frac{A_\\infty - \\varepsilon_\\mathrm{ONO^-} \\cdot [\\mathrm{Co^{3+}}] \\cdot l}{\\varepsilon_\\mathrm{NO_2^-} \\cdot l - \\varepsilon_\\mathrm{ONO^-} \\cdot l}\n",
"\\end{equation}"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Slutsats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Anpassningen ..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Check this out* \n",
"http://nbviewer.ipython.org/ \n",
"Could be nice in combination with http://gist.github.com/ \n",
"(Let students add ipynb file contents to gist.github.com"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Referenser"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. http://dawes.wordpress.com/2011/01/02/scientific-python/\n",
"2. http://packages.python.org/uncertainties/numpy_guide.html \n",
"3. http://web.uvic.ca/~jalexndr/192UncertRules.pdf \n",
"4. http://spiff.rit.edu/classes/phys273/uncert/uncert.html"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 166
}
],
"metadata": {}
}
]
}
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