From: Sam W Date: Fri, 30 Nov 2018 23:51:34 +0000 (+0000) Subject: Started work on Experiment 4B laboratory report. X-Git-Url: https://git.dalvak.com/public/?a=commitdiff_plain;h=6991dfe08676ee950e4a23932eedab6982064ea6;p=chemistry%2Funiversity-chemistry-lab-reports.git Started work on Experiment 4B laboratory report. --- diff --git a/year2/4b/4b.bcf b/year2/4b/4b.bcf new file mode 100644 index 0000000..8633058 --- /dev/null +++ b/year2/4b/4b.bcf @@ -0,0 +1,2003 @@ + + + + + + output_encoding + utf8 + + + input_encoding + utf8 + + + debug + 0 + + + mincrossrefs + 2 + + + minxrefs + 2 + + + sortcase + 1 + + + sortupper + 1 + + + + + + + alphaothers + + + + + labelalpha + 0 + + + labelnamespec + shortauthor + author + shorteditor + editor + translator + + + labeltitle + 0 + + + labeltitlespec + shorttitle + title + maintitle + + + labeltitleyear + 0 + + + labeldateparts + 0 + + + labeldatespec + date + year + eventdate + origdate + urldate + nodate + + + julian + 0 + + + gregorianstart + 1582-10-15 + + + maxalphanames + 3 + + + maxbibnames + 999 + + + maxcitenames + 2 + + + maxitems + 3 + + + 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+%Load useful packages. +\usepackage[a4paper,margin=2.3cm]{geometry} %Set page size to A4. +\usepackage{graphicx} %Allow import of images. +\usepackage{floatrow} %Positioning of table & figure captions. +\usepackage{siunitx} %SI Units formatting. +\usepackage[version=4]{mhchem} %Chemical Equations. +\usepackage{amsmath} %Mathematical alignments. +\usepackage{amssymb} %Mathematical symbols e.g. therefore. +\usepackage[parfill]{parskip} %Blank lines between paragraphs. +\usepackage{array} %Table centring. +\usepackage[autostyle]{csquotes} %Recommended for babel. +\usepackage[british]{babel} %British localisation. +\usepackage[backend=biber,style=chem-rsc]{biblatex} %Bibliography. +\usepackage[extreme,mathspacing=normal,leading=normal]{savetrees} %Reduce whitespace. +\usepackage{multirow} %Use fields over multiple rows in tables. + +%Configure settings. +\numberwithin{equation}{subsection} %Number equations based on their section +\bibliography{../../bibliographies/reference,../../bibliographies/coretextbooks,../../bibliographies/additionaltextbooks,specific} %Use Bibliography of reference books. +\bibliography{specific} +\floatsetup[table]{style = plaintop} %Put captions on top of tables. +\floatsetup[figure]{style = plain} %Ensure figure captions are below figures. +\sisetup{range-phrase = --,range-units = single} %Use - for ranges and only have a single unit shown after. +\sisetup{separate-uncertainty = true,multi-part-units=single} %Use \pm for uncertainties. +\setlength{\parindent}{0cm} % Don't indent paragraphs. + +%Document Headings. +\begin{document} +\title{Experiment 4B: The rotational-vibrational spectrum of \ce{HCl}} +\author{Sam White (Author) and Emma Winful (Laboratory Partner)} +\date{30/11/2018} +\maketitle + +\begin{abstract} + Experiment abstract. +\end{abstract} + +\section{Results and Analysis} +\begin{table}[h] + \caption{Rotational absorbances for the fundamental transition.} + \label{tbl:fundamental-results} + \centering + \begin{tabular}{|c|c|c|c|c|c|} + \hline + & $J$ & $R(J)$ / \si{\per\centi\meter} & $P(J)$ / \si{\per\centi\meter} & $R(J) - P(J)$ / + \si{\per\centi\meter} & $R(J - 1) - P(J + 1)$ / \si{\per\centi\meter} \\ + \hline + \multirow{13}{*}{\ce{H^{35}Cl}} & 0 & 2906.4 & & & \\ + \cline{2-6} + & 1 & 2926.03 & 2865.24 & 60.79 & 62.64 \\ + \cline{2-6} + & 2 & 2945.05 & 2843.76 & 101.29 & 104.33 \\ + \cline{2-6} + & 3 & 2963.42 & 2821.70 & 141.72 & 145.98 \\ + \cline{2-6} + & 4 & 2981.14 & 2799.07 & 182.07 & 187.53 \\ + \cline{2-6} + & 5 & 2998.19 & 2775.89 & 222.30 & 228.97 \\ + \cline{2-6} + & 6 & 3014.57 & 2752.17 & 262.40 & 270.26 \\ + \cline{2-6} + & 7 & 3030.27 & 2727.93 & 302.34 & 311.4 \\ + \cline{2-6} + & 8 & 3045.28 & 2703.17 & 342.11 & 352.37 \\ + \cline{2-6} + & 9 & 3059.52 & 2677.90 & 381.62 & 393.13 \\ + \cline{2-6} + & 10 & 3073.10 & 2652.15 & 420.95 & 433.62 \\ + \cline{2-6} + & 11 & 3085.88 & 2625.90 & 459.98 & 473.88 \\ + \cline{2-6} + & 12 & & 2599.22 & & \\ + \hline + \multirow{13}{*}{\ce{H^{37}Cl}} & 0 & 2904.29 & & & \\ + \cline{2-6} + & 1 & 2923.91 & 2863.20 & 60.71 & 62.53 \\ + \cline{2-6} + & 2 & 2942.90 & 2841.76 & 101.14 & 104.19 \\ + \cline{2-6} + & 3 & 2961.24 & 2819.72 & 141.52 & 145.76 \\ + \cline{2-6} + & 4 & 2978.93 & 2797.14 & 181.79 & 187.25 \\ + \cline{2-6} + & 5 & 2995.96 & 2773.99 & 221.97 & 228.62 \\ + \cline{2-6} + & 6 & 3012.32 & 2750.31 & 262.01 & 269.86 \\ + \cline{2-6} + & 7 & 3027.98 & 2726.10 & 301.88 & 310.95 \\ + \cline{2-6} + & 8 & 3042.97 & 2701.37 & 341.60 & 351.84 \\ + \cline{2-6} + & 9 & 3057.22 & 2676.14 & 381.08 & 392.57 \\ + \cline{2-6} + & 10 & 3070.73 & 2650.40 & 420.33 & 432.99 \\ + \cline{2-6} + & 11 & 3083.51 & 2624.23 & 459.28 & 473.20 \\ + \cline{2-6} + & 12 & & 2597.53 & & \\ + \cline{2-6} + \hline + \end{tabular} +\end{table} + +\begin{table}[h] + \caption{Rotational absorbances for the overtone transition.} + \label{tbl:overtone-results} + \centering + \begin{tabular}{|c|c|c|c|c|c|} + \hline + & $J$ & $R(J)$ / \si{\per\centi\meter} & $P(J)$ / \si{\per\centi\meter} & $R(J) - P(J)$ / + \si{\per\centi\meter} & $R(J - 1) - P(J + 1)$ / \si{\per\centi\meter} \\ + \hline + \multirow{9}{*}{\ce{H^{35}Cl}} & 0 & 5688.16 & & & \\ + \cline{2-6} + & 1 & 5706.59 & 5647.71 & 58.88 & 62.66 \\ + \cline{2-6} + & 2 & 5723.78 & 5625.50 & 98.28 & 104.35 \\ + \cline{2-6} + & 3 & 5739.75 & 5602.24 & 137.51 & 145.98 \\ + \cline{2-6} + & 4 & 5754.53 & 5577.80 & 176.73 & 187.53 \\ + \cline{2-6} + & 5 & 5767.89 & 5552.22 & 215.67 & 229.05 \\ + \cline{2-6} + & 6 & 5780.07 & 5525.48 & 254.59 & 270.26 \\ + \cline{2-6} + & 7 & 5790.92 & 5497.63 & 293.29 & 311.52 \\ + \cline{2-6} + & 8 & & 5468.55 & & \\ + \hline + \multirow{9}{*}{\ce{H^{37}Cl}} & 0 & 5684.12 & & & \\ + \cline{2-6} + & 1 & 5703.13 & 5643.60 & 59.53 & 62.58 \\ + \cline{2-6} + & 2 & 5719.67 & 5621.54 & 98.13 & 104.80 \\ + \cline{2-6} + & 3 & 5735.61 & 5598.33 & 137.28 & 145.76 \\ + \cline{2-6} + & 4 & 5750.30 & 5573.91 & 176.39 & 197.19 \\ + \cline{2-6} + & 5 & 5763.27 & 5548.42 & 214.85 & 228.64 \\ + \cline{2-6} + & 6 & 5775.12 & 5521.66 & 253.46 & 269.43 \\ + \cline{2-6} + & 7 & 5786.65 & 5493.84 & 292.81 & 310.49 \\ + \cline{2-6} + & 8 & 5464.63 & & & \\ + \hline + \end{tabular} +\end{table} + +The values of $\tilde{B_0}$, $\tilde{B_1}$ and $\tilde{B_2}$ were calculated +accounting for the centrifugal distortion of the molecules by using equations +\ref{eq:comb-diff-upper} and \ref{eq:comb-diff-lower}. + +\begin{align} + R(J) - P(J) &= (4\tilde{B_1} - 6\tilde{D_1})(J + \frac{1}{2}) - + 8\tilde{D_1} (J + \frac{1}{2})^3 \nonumber \\ + % + \label{eq:comb-diff-upper} + \frac{R(J) - P(J)}{J + \frac{1}{2}} &= -8\tilde{D_1} (J + \frac{1}{2})^2 + 4\tilde{B_1} - 6\tilde{D_1} +\end{align} + +A similar rearrangement for the transitions with a common excited vibrational +state yields equation \ref{eq:comb-diff-lower}. + +\begin{equation}\label{eq:comb-diff-lower} + \frac{R(J - 1) - P(J + 1)}{J + \frac{1}{2}} = -8\tilde{D_0} (J + \frac{1}{2})^2 + + 4\tilde{B_0} - 6\tilde{D_0} +\end{equation} + +Graphs of $\frac{R(J) - P(J)}{J + \frac{1}{2}}$ and respectively $\frac{R(J - 1) +- P(J + 1)}{J + \frac{1}{2}}$ were plotted against $(J + \frac{1}{2})^2$ and +linear regressions were performed in order to determine the values for +the centrifugal distortion coefficients, $\tilde{D_{\nu}}$, shown in table +\ref{tbl:centrifugal-distortion-const} and hence the rotational constants, +$\tilde{B_{\nu}}$ shown in table \ref{tbl:rot-const-bond-lengths}. + +The bond lengths were calculated from the $\tilde{B_{\nu}}$ values using equation \ref{eq:bond-length}. + +\begin{equation}\label{eq:bond-length} + r_{\nu} = \sqrt{4 \pi c \hbar \mu \tilde{B_{\nu}}} +\end{equation} + +\begin{table}[h] + \caption{Rotational constants and bond lengths.} + \label{tbl:rot-const-bond-lengths} + \centering + \begin{tabular}{|c|c|c|c|} + \hline + & $\nu$ & $\tilde{B_{\nu}}$ / \si{\per\centi\metre} & $r_{\nu}$ / \si{\pico\meter} \\ + \hline + \multirow{3}{*}{\ce{^{35}Cl}} & 0 & & \\ + \cline{2-4} + & 1 & & \\ + \cline{2-4} + & 2 & & \\ + \hline + \multirow{3}{*}{\ce{^{37}Cl}} & 0 & & \\ + \cline{2-4} + & 1 & & \\ + \cline{2-4} + & 2 & & \\ + \hline + \end{tabular} +\end{table} + +The error propagation shown in equation \ref{eq:b-err-prop} was completed to estimate the uncertainty in the +values of $\tilde{B_{\nu}}$ where $\alpha_B$, $\alpha_D$, $\alpha_m$ are the uncertainties in +$\tilde{B_{\nu}}$, $\tilde{D_{\nu}}$ and the gradient found in the linear +regression respectively. + +\begin{equation}\label{eq:b-err-prop} + \alpha_B = \tilde{B_{\nu}} \sqrt{\left( \frac{\alpha_m}{m} \right)^2 + \left( + \frac{\alpha_D}{\tilde{D_{\nu}}} \right)^2} +\end{equation} + +Furthermore the calculus-based approximation\autocite{hughes-hase-uncertainties} was utilised to give the estimation in the uncertainty for $r_{\nu}$ +($\alpha_r$) given in equation \ref{eq:r-err-prop} since the $\alpha_B$ values are small. + +\begin{equation}\label{eq:r-err-prop} + \alpha_r = \sqrt{\frac{\pi c \hbar \mu}{\tilde{B_{\nu}}}} \alpha_B +\end{equation} + +The values for the harmonic constant $\tilde{\nu_e}$ and the dimensionless anharmonicity constant $x_e$ in equation +\ref{eq:vib-energy} (which gives the expected vibrational energy levels if the rotational spectrum is +ignored) can be determined by + +\begin{equation}\label{eq:vib-energy} + \tilde{E_{\nu}} = \tilde{\nu_e} \left( \nu + \frac{1}{2} \right) - + \tilde{\nu_e} x_e \left( \nu + \frac{1}{2} \right)^2 +\end{equation} + +%TODO: Total energy equation, determination of \nu_e x_e, calculation of values, determination of k with error +%propagation and table. + +\section{Discussion} +Two methods able to be used to determine the value of $\tilde{B_0}$: using +either the absorption data from the fundamental or the overtone transition. Much +larger signal:noise ratio for overtone due to lower probability of transition, +hence greater uncertainty in this value. + + +\printbibliography + +\section{Supplementary Information} + +\begin{table}[h] + \caption{Centrifugal distortion coefficients.} + \label{tbl:centrifugal-distortion-const} + \centering + \begin{tabular}{|c|c|c|} + \hline + & $\nu$ & $\tilde{D_{\nu}}$ / \num{e-4} \si{\per\centi\metre}\\ + \hline + \multirow{3}{*}{\ce{^{35}Cl}} & 0 & \num{-5.25(4)} and \num{-5.4(3)} \\ + \cline{2-3} + & 1 & \num{-5.11(2)} \\ + \cline{2-3} + & 2 & \num{-4.3(8)} \\ + \hline + \multirow{3}{*}{\ce{^{37}Cl}} & 0 & \num{-5.20(3)} and \num{-9(2)} \\ + \cline{2-3} + & 1 & \num{-5.13(1)} \\ + \cline{2-3} + & 2 & \num{-11(4)}\\ + \hline + \end{tabular} +\end{table} +\end{document} +%Note: gq means : reformat the text included in the motion +% vim:tw=80 diff --git a/year2/4b/specific.bib b/year2/4b/specific.bib new file mode 100644 index 0000000..ec46ffc --- /dev/null +++ b/year2/4b/specific.bib @@ -0,0 +1,17 @@ +@online{berkeley-pigments, + title = {Photosynthetic Pigments}, + author = {Brain R. Speer}, + date = {1997-07-09}, + url = {http://www.ucmp.berkeley.edu/glossary/gloss3/pigments.html}, + urldate = {2018-11-06} +} + +@article{chlorophyll-uv-vis, + title = {Chlorophylls and Carotenoids: Measurement and Characterization by UV-VIS Spectroscopy}, + author = {Hartmut K. Lichtenthaler and Claus Buschmann}, + year = {2001}, + journal = {Current Protocols in Food Analytical Chemistry}, + volume = {1}, + issue = {1}, + pages = {F4.3.1--F4.3.8} +}