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Setup. +\documentclass{article} +\usepackage{graphicx} %Allows import of images. +%\usepackage{float} +\usepackage{floatrow} %Align tables and figures side-by-side. +\usepackage[extreme,mathspacing=normal,leading=normal]{savetrees} %Reduce whitespace. +\usepackage{siunitx} %SI Units formatting. +%\usepackage{vhistory} %Revision History. +\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[autostyle]{csquotes} +\usepackage{array} %Table centering. +\usepackage[british]{babel} %British localisation. +\usepackage[backend=biber,citestyle=verbose-note]{biblatex} %Bibliography. + +\numberwithin{equation}{section} %Number equations based on their section. +\bibliography{../bibliographies/reference,specific} %Use Bibliography of reference books. +\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. + +%Document Headings. +\begin{document} +\title{A Redox Titration to Determine the Ethanol Content of Wine (8A/RTE)} +\author{Sam White Lab Partner: Mihkel Raidal} +\date{05/12/2017} +%\date{\vhCurrentDate\\\vhCurrentVersion} +\maketitle + +{\centering Reported percentage of alcohol by volume (\si{\percent} ABV): \SI{13}{\percent} + +} +% +\section{Titration Results and Calculation of \si{\percent} ABV of Wine} +A \SI{7.7910}{\gram} of \ce{(NH4)2Fe(SO4)2.6H2O} was dissolved in \SI{60}{\centi\metre\cubed} of \ce{H2SO4} and made up to \SI{200.00}{\centi\metre\cubed} with deionised water in a volumetric flask. Each \ce{(NH4)2Fe(SO4)2.6H2O} molecule liberates one \ce{Fe^{2+}} ion in solution, thus their concentrations in the solution are equal. The molar mass of \ce{(NH4)2Fe(SO4)2.6H2O} is \SI{392.139}{\gram\per\mole}.\footcite[Physical Constants of Inorganic Compounds, 4-46]{crc-handbook} +% +\begin{displaymath} + \text{Moles of \ce{Fe^{2+}} in \SI{200.00}{\centi\metre\cubed} standard solution} = \frac{\SI{7.7910}{\gram}}{\SI{392.139}{\gram\per\mole}} = \SI{0.019868}{\mole} +\end{displaymath} +Hence: +\begin{align} \label{[fe2+]} + \text{Concentration of \ce{Fe^{2+}} in standard solution} = \frac{\SI{0.019868}{\mole}}{\SI{200.00}{\centi\metre\cubed} \times (\frac{\SI{1}{\deci\metre}}{\SI{10}{\centi\metre}})^3} = \frac{\SI{0.019869}{\mole}}{\SI{200.00e-3}{\deci\metre\cubed}} = \SI{0.099340}{\mole\per\deci\metre\cubed} +\end{align} +% +%\section{Titration between \ce{K2Cr2O7} and \ce{(NH4)2Fe(SO4)2.6H2O}} +The reaction which occurred in both titrations was: +\begin{equation} \label{eq:cr2o72--fe2+} + \ce{Cr2O7^{2-} + 14H+ + 6Fe^{2+} -> 6Fe^{3+} + 2Cr^{3+} + 7H2O} +\end{equation} +With sodium diphenylamine-4-sulphonate used as the indicator (colour change from green (due to \ce{Cr^{3+}}) to purple at the end point). +% +\begin{table}[h] + \caption{Results of titration between \ce{K2Cr2O7} and standard solution of \ce{(NH4)2Fe(SO4)2.6H2O}} + \centering + \begin{tabular}{|c|c|c|c|} + \hline + Run & Start Volume / \si{\centi\metre\cubed} & End Volume / \si{\centi\metre\cubed} & Titre / \si{\centi\metre\cubed} \\ + \hline + 1 & 2.40 & 18.30 & 15.90 \\ + \hline + 2 & 2.20 & 18.80 & 16.60 \\ + \hline + 3 & 2.25 & 18.85 & 16.60 \\ + \hline + \end{tabular} +\end{table} +% +\begin{gather*} + \text{Average titre} = \frac{\SI{16.60}{\centi\metre\cubed} + \SI{16.60}{\centi\metre\cubed}}{2} = \SI{16.60}{\centi\metre\cubed} \\ + \text{Using~\ref{[fe2+]}, moles of \ce{Fe^{2+}} in \SI{20.00}{\centi\metre\cubed} aliquot} = \SI{0.099340}{\mole\per\deci\metre\cubed} \times \SI{20.00}{\centi\metre\cubed} \times \frac{\SI{1}{\deci\metre\cubed}}{\SI{1000}{\centi\metre\cubed}} = \SI{1.987e-3}{\mole} +\end{gather*} +% +From chemical equation~\ref{eq:cr2o72--fe2+} there is a 6:1 molar ratio between the \ce{Fe^{2+}} and \ce{Cr2O7^{2-}}. +\begin{equation} \label{[cr2o72-]} + \text{Concentration of \ce{Cr2O7^{2-}}} = \frac{\frac{1}{6} \times \SI{1.987e-3}{\mole}}{\SI{16.60}{\centi\metre\cubed} \times \frac{\SI{1}{\deci\metre\cubed}}{\SI{1000}{\centi\metre\cubed}}} = \frac{\SI{3.311e-4}{\mole}}{\SI{16.60e-3}{\deci\metre\cubed}} = \SI{0.01995}{\mole\per\deci\metre\cubed} +\end{equation} +% +%\section{Titration between Product Mixture and \ce{(NH4)2Fe(SO4)2.6H2O}} +During the reflux the ethanol from the sample of wine was oxidised by the \ce{Cr2O7^{2-}} ions to acetic acid as shown in this equation: +\begin{equation} \label{eq:ethanol-cr2o72-} + \ce{3CH3CH2OH + 2Cr2O7^{2-} + 16H+ -> 3CH3COOH + 4Cr^{3+} + 11H2O} +\end{equation} +During this the solution changed colour from orange (due to the \ce{Cr2O7^{2-}}) to dark green (due to the liberation of \ce{Cr^{3+}}). A back titration was then performed with the standard solution of \ce{Fe^{2+}} ions. The volumes used for this were half of those stated in the method since when the stated volumes were used the initial titre was very large and a maximum of two more titrations would have possible before the reaction mixture was exhausted. This would have been problematic if these two titres were not concordant since the completion of additional titrations would have been impossible. +% +\begin{table}[h] + \centering + \caption{Results of titration between \ce{K2Cr2O7} in product mixture and standard solution of \ce{(NH4)2Fe(SO4)2.6H2O}} + \begin{tabular}{|c|c|c|c|} + \hline + Run & Start Volume / \si{\centi\metre\cubed} & End Volume / \si{\centi\metre\cubed} & Titre / \si{\centi\metre\cubed} \\ + \hline + 1 & 2.20 & 18.40 & 16.20 \\ + \hline + 2 & 18.90 & 39.75 & 16.35 \\ + \hline + 3 & 3.10 & 19.50 & 16.40 \\ + \hline + \end{tabular} +\end{table} +% +\begin{gather*} + \text{Average titre} = \frac{\SI{16.35}{\centi\metre\cubed}+\SI{16.40}{\centi\metre\cubed}}{2} = \SI{16.38}{\centi\metre\cubed} \\ + \text{Using~\ref{[fe2+]}, moles of \ce{Fe^{2+}} in \SI{5.00}{\centi\metre\cubed} aliquot} = \SI{0.099340}{\mole\per\deci\metre\cubed} \times \SI{5.00}{\centi\metre\cubed} \times \frac{\SI{1}{\deci\metre\cubed}}{\SI{1000}{\centi\metre\cubed}} = \SI{4.97e-4}{\mole} +\end{gather*} +% +From chemical equation~\ref{eq:cr2o72--fe2+} there is a 6:1 molar ratio between \ce{Fe^{2+}} and \ce{Cr2O7^{2-}}. +\begin{align*} + \text{Concentration of \ce{Cr2O7^{2-}} in product mixture} &= \frac{\frac{1}{6} \times \SI{4.97e-4}{\mole}}{\SI{16.38}{\centi\metre\cubed}} = \SI{5.05e-6}{\mole\per\centi\metre\cubed} \\ + \therefore\text{Moles of \ce{Cr2O7^{2-}} in \SI{126}{\centi\metre\cubed} product mixture} &= \SI{5.05e-6}{\mole\per\centi\metre\cubed} \times \SI{126}{\centi\metre\cubed} = \SI{6.37e-4}{\mole} +\end{align*} +% +%\section{Calculation of \si{\percent} ABV of the Wine} +Initially \SI{100.00}{\centi\metre\cubed} of \ce{Cr2O7^{2-}} of concentration \SI{0.01995}{\mole\per\deci\metre\cubed} (from~\ref{[cr2o72-]}) was in the reactant mixture. +\begin{align*} + \text{Initial moles of \ce{Cr2O7^{2-}}} &= \SI{100.00}{\centi\metre\cubed} \times \frac{\SI{1}{\deci\metre\cubed}}{\SI{1000}{\centi\metre\cubed}} \times \SI{0.01995}{\mole\per\deci\metre\cubed} = \SI{1.995e-3}{\mole} \\ + \therefore\text{Moles of \ce{Cr2O7^{2-}} which reacted} &= \SI{1.995e-3}{\mole} - \SI{6.37e-4}{\mole} = \SI{1.36e-3}{\mole} +\end{align*} +% +From chemical equation~\ref{eq:ethanol-cr2o72-} molar ratio between \ce{Cr2O7^{2-}} and ethanol is 2:3. The molar mass of ethanol is \SI{46.068}{\gram\per\mole}.\footcite[Physical Constants of Organic Compounds, 3-246]{crc-handbook} +\begin{align*} + \text{Moles of ethanol in \SI{1.00}{\centi\metre\cubed} sample} &= \frac{\SI{1.36e-3}{\mole}}{2} \times 3 = \SI{2.04e-3}{\mole} \\ + \therefore\text{Mass of ethanol in \SI{1.00}{\centi\metre\cubed}} &= \SI{2.04e-3}{\mole} \times \SI{46.068}{\gram\per\mole} = \SI{0.0938}{\gram} +\end{align*} +The density of ethanol is \SI{0.7893}{\gram\per\centi\metre\cubed}.$^2$ %Quick and dirty way to make footer smaller. +%\footcite[Physical Constants of Organic Compounds, 3-246]{crc-handbook} +\begin{displaymath} + \text{\si{\percent} ABV of wine} = \frac{\SI{0.0938}{\gram}}{\SI{0.7893}{\gram\per\centi\metre\cubed}}\times \frac{\SI{100}{\percent}}{\SI{1.00}{\centi\metre\cubed}} = \SI{11.9}{\percent} +% \text{Volume of ethanol in \SI{1.00}{\centi\metre\cubed}} &= \frac{\SI{0.0938}{\gram}}{\SI{0.7893}{\gram\per\centi\metre\cubed}} = \SI{0.119}{\centi\metre\cubed} \\ +% \text{Hence, \si{\percent} ABV of wine} &= \frac{\SI{0.119}{\centi\metre\cubed}}{\SI{1.00}{\centi\metre\cubed}} \times \SI{100}{\percent} = \SI{11.9}{\percent} +\end{displaymath} +% +\section{Error Propagation} +\begin{align*} + \delta\ce{[Fe^{2+}]} &= \pm\SI{0.099340}{\mole\per\deci\metre\cubed} \sqrt{\left(\frac{\pm\SI{0.00005}{\gram}\times2}{\SI{7.7910}{\gram}}\right)^2 + \left(\frac{\pm\SI{0.001}{\gram\per\mole}}{\SI{392.139}{\gram\per\mole}}\right)^2 + \left(\frac{\pm\SI{0.15}{\centi\metre\cubed}}{\SI{200.00}{\centi\metre\cubed}}\right)^2} = \pm\SI{0.00007}{\mol\per\deci\metre\cubed} \\ +% + \delta\ce{[Cr2O7^{2-}]} &= \pm\SI{0.01995}{\mole\per\deci\metre\cubed} \sqrt{\left(\frac{\pm\SI{0.00007}{\mole\per\deci\metre\cubed}}{\SI{0.099340}{\mole\per\deci\metre\cubed}}\right)^2 + \left(\frac{\pm\SI{0.06}{\centi\metre\cubed}}{\SI{20.00}{\centi\metre\cubed}}\right)^2 + \left(\frac{\pm\SI{0.1}{\centi\metre\cubed}\times 2}{\SI{16.60}{\centi\metre\cubed}}\right)^2} = \pm\SI{0.0002}{\mole\per\deci\metre\cubed} \\ + % + \delta V_{reaction \text{ } mixture} &= \pm\sqrt{\left(\pm\SI{0.015}{\centi\metre\cubed}\right)^2 + \left(\pm\SI{0.15}{\centi\metre\cubed}\right)^2 + \left(\pm\SI{0.06}{\centi\metre\cubed}\right)^2} = \pm\SI{0.2}{\centi\metre\cubed} \\ +% + \delta n_{initial \text{ } \ce{Cr2O7^{2-}}} &= \pm\SI{1.995e-3}{\mole} \sqrt{\left(\frac{\pm\SI{0.15}{\centi\metre\cubed}}{\SI{100.00}{\centi\metre\cubed}}\right)^2 + \left(\frac{\pm\SI{0.0002}{\mole\per\deci\metre\cubed}}{\SI{0.01995}{\mole\per\deci\metre\cubed}}\right)^2} = \pm\SI{0.02e-3}{\mole} \\ +% + \delta n_{final \text{ } \ce{Cr2O7^{2-}}} &= \pm\SI{6.37e-4}{\mole} \sqrt{\left(\frac{\pm\SI{0.00007}{\mole\per\deci\metre\cubed}}{\SI{0.099340}{\mole\per\deci\metre\cubed}}\right)^2 + \left(\frac{\pm\SI{0.03}{\centi\metre\cubed}}{\SI{5.00}{\centi\metre\cubed}}\right)^2 + \left(\frac{\pm\SI{0.1}{\centi\metre\cubed}\times2}{\SI{16.38}{\centi\metre\cubed}}\right)^2 + \left(\frac{\pm\SI{0.2}{\centi\metre\cubed}}{\SI{126}{\centi\metre\cubed}}\right)^2} \\ + &= \pm\SI{0.09e-4}{\mole} \\ +% + \delta n_{ethanol} &= \sqrt{\left(\pm\SI{0.02e-3}{\mole}\right)^2 + \left(\pm\SI{0.09e-4}{\mole}\right)^2} = \pm\SI{0.03e-3}{\mole} \\ +% + \delta \si{\percent} \text{ } ABV &= \pm\SI{11.9}{\percent} \sqrt{\left(\frac{\pm\SI{0.03e-3}{\mole}}{\SI{2.04e-3}{\mole}}\right)^2 + \left(\frac{\pm\SI{0.0001}{\gram\per\centi\metre\cubed}}{\SI{0.7893}{\gram\per\centi\metre\cubed}}\right)^2 + \left(\frac{\pm\SI{0.001}{\gram\per\mole}}{\SI{46.068}{\gram\per\mole}}\right)^2} = \pm\SI{0.2}{\percent} +\end{align*} +Hence the \si{\percent} ABV of ethanol of the wine was found to be $11.9 \pm 0.2 \si{\percent}$. +% +\section{Analysis of Results} +The reported \si{\percent} ABV value of the wine is greater than that determined by experiment, however the reported \si{\percent} ABV value of wine is required to be accurate within $\pm\SI{1}{\percent}$\footcite[Annex XII]{eur-32011R1169-en}, hence there is a slight overlap between the possible error in the reported value and that of the determined value from \SIrange{12.0}{12.1}{\percent}. Despite this systematic errors are likely to have influenced the \si{\percent} ABV determined since this is at the extreme end of the uncertainty in the reported value, hence it is unlikely that the true \si{\percent} ABV value lies within this range. + +A possible error is that the ethanol might not have been fully oxidised to acetic acid hence reducing the amount of \ce{Cr2O7^{2-}} reacted and thus the \si{\percent} ABV value determined. To minimise this the reaction mixture could be refluxed for a longer (e.g. 2 hours). There may have also been a loss of ethanol and ethanal vapour while the reactants were being transferred into the round bottomed flask. To minimise this the flask could have been cooled in an ice bath during this process, hence reducing losses due to evaporation. There was also uncertainty about the end point for the second titration since the indicator colour change was not very distinct. To reduce this an alternative indicator such as 1,10-phenanthroline ferrous sulphate solution which would have more distinct colour change from blue-green to brown at the end point.\footcite[pp.~3]{senior-chem} +% +\end{document} diff --git a/8a/specific.bib b/8a/specific.bib new file mode 100644 index 0000000..5c30bb6 --- /dev/null +++ b/8a/specific.bib @@ -0,0 +1,14 @@ +@online{eur-32011R1169-en, + title = {Regulation (EU) No 1169/2011 of the European Parliament and of the Council of 25 October 2011}, + author = {Official Journal of the European Union}, + date = {2011-11-22}, + url = {http://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELEX:30211R1169}, + urldate = {2017-12-08} +} + +@online{senior-chem, + title = {Estimation of Alcohol Content in Wine by Dichromate Oxidation followed by Redox Titration}, + author = {Sirromet Wines Pty Ltd}, + url = {http://seniorchem.com/4. Alcohol-Content-bu-Dichromate-Oxidation-and-Redox-Titration.pdf}, + urldate = {2017-12-09} +} -- 2.25.1