From 250c9e747f9e68e611c72ce40f1759fe58d90eb4 Mon Sep 17 00:00:00 2001 From: Sam W Date: Fri, 23 Mar 2018 15:53:00 +0000 Subject: [PATCH] Finished main body of lab report. --- project/project.bcf | 9 +-- project/project.pdf | Bin 333459 -> 336038 bytes project/project.tex | 172 +++++++++++++++++++++++--------------------- 3 files changed, 96 insertions(+), 85 deletions(-) diff --git a/project/project.bcf b/project/project.bcf index 0016cf8..232388c 100644 --- a/project/project.bcf +++ b/project/project.bcf @@ -1958,8 +1958,8 @@ olson81 olson81 olson81 - patent3702886A - zeolite-atlas + zeolite-atlas + patent3702886A ismagilov00 rasouli12 chaudhari02 @@ -2005,8 +2005,9 @@ penzien04 denby-copper-conc tamiyakul15 - pollanen05 - yu12 + yashnik05 + pollanen05 + yu12 diff --git a/project/project.pdf b/project/project.pdf index 027cc639b8cb25e0c013cc692ccabaef583e0f66..684d35d65ba1535b2fe692b354890e7c2e5b3bb8 100644 GIT binary patch delta 108596 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Include? %The pH 10 buffer was used to ensure the EDTA existed in the deprotonated form which is able to complex to metal cations and also to ensure the eriochrome black T indicator exhibits the desired colour change. \begin{table} - \caption{Titration results from standardisation of \ce{EDTA} solution with standard zinc sulphate solution.}\label{tbl:zn-standardisation} + \caption{Titration results from standardisation of the batch A \ce{EDTA} solution with the standard zinc sulphate solution.}\label{tbl:zn-standardisation} \centering \begin{tabular}{|c|c|c|c|} \hline Run & Start Volume / \si{\centi\metre\cubed} & End Volume / \si{\centi\metre\cubed} & Titre Volume / \si{\centi\metre\cubed} \\ \hline 1 & 1.45 & 33.70 & 32.25 \\ + \hline 2 & 2.25 & 34.20 & 31.95 \\ \hline \end{tabular} \end{table} -Due to time constraints the standardisation of the \ce{EDTA} solution was not fully completed, hence the accurate titre volume ($V_{\ce{EDTA}_\text{std.}}$) has been assumed to be the titre volume from the second titre (see table \ref{tbl:zn-standardisation}) in the absence of additional available titrations to confirm this. +Due to time constraints the standardisation of the \ce{EDTA} solution was not fully completed, hence the accurate titre volume ($V_{\ce{EDTA}_\text{std.}}$) has been assumed to be the titre volume from the second run (see table \ref{tbl:zn-standardisation}): \begin{equation}\label{eq:edta-v-standardisation} V_{\ce{EDTA}_{std.}} = \SI{31.95}{\centi\metre\cubed} @@ -208,14 +214,17 @@ Due to time constraints the standardisation of the \ce{EDTA} solution was not fu Run & Start Volume / \si{\centi\metre\cubed} & End Volume / \si{\centi\metre\cubed} & Titre Volume / \si{\centi\metre\cubed} \\ \hline 1 & 2.40 & 29.10 & 26.70 \\ + \hline 2 & 2.90 & 29.55 & 26.65 \\ + \hline 3 & 1.40 & 28.00 & 26.60 \\ + \hline 4 & 11.35 & 37.70 & 26.35 \\ \hline \end{tabular} \end{table} -The average titre volume for the titration with the post ion-exchange solution ($V_{\ce{EDTA}_\text{prod.}}$) was determined from the second and third runs (see table \ref{tbl:zn-analytical-titration}) since the first run was a rough titration and the fourth run can be clearly seen be be anomalous. +The average titre volume for the titration with the post ion exchange solution ($V_{\ce{EDTA}_\text{prod.}}$) was determined from the second and third runs (see table \ref{tbl:zn-analytical-titration}) since the first run was a rough titration and the fourth run can be clearly seen be be anomalous. \begin{equation}\label{eq:edta-v-analytical} V_{\ce{EDTA}_\text{prod.}} = \frac{\SI{26.65}{\centi\metre\cubed} + \SI{26.60}{\centi\metre\cubed}}{2} = \SI{20.63}{\centi\metre\cubed} @@ -224,16 +233,18 @@ The average titre volume for the titration with the post ion-exchange solution ( \section{Calculations} \subsection{Calculation of Maximum Theoretical Number of Ion Exchanges} -The \ce{SiO2}/\ce{Al2O3} ratio in the zeolite used was $23$. In this ratio there are two \ce{Al} atoms per \ce{Si}, so $\ce{Si}/\ce{Al} = \frac{23}{2} = 11.5$. +The \ce{SiO2}/\ce{Al2O3} ratio in the zeolite used was $23$. There are two \ce{Al} atoms in \ce{Al2O3} compared to one \ce{Si} atom in \ce{SiO2}, hence $\ce{Si}/\ce{Al} = \frac{23}{2} = 11.5$. -Using the unit cell general formula (equation \ref{eq:unit-cell}) letting the \ce{Si}/\ce{Al} ratio be $r$ and with $n$ being the number of aluminium atoms per unit cell: -\begin{gather*} - r = \frac{\text{Number of \ce{Si} per unit cell}}{\text{Number of \ce{Al} per unit cell}} = \frac{96 - n}{n} \\ - n r + n = 96 \\ - \therefore n = \frac{96}{r + 1} -\end{gather*} +Using the unit cell general formula (equation \ref{eq:unit-cell}) and letting the \ce{Si}/\ce{Al} ratio be $r$ and $n$ be the number of aluminium atoms per unit cell: + +\begin{align*} + r &= \frac{\text{Number of \ce{Si} per unit cell}}{\text{Number of \ce{Al} per unit cell}} \\ + \therefore r &= \frac{96 - n}{n} \\ + n r + n &= 96 \\ + \therefore n &= \frac{96}{r + 1} +\end{align*} -Hence for $r = 11.5$ there are $n = \frac{96}{11.5 + 1} = 7.68$ \ce{Al} per unit cell. Letting $q$ be the cation charge and $x$ be the number of water molecules for unit cell: +Hence for $r = 11.5$ there are $n = \frac{96}{11.5 + 1} = 7.68$ \ce{Al} per unit cell. Letting $q$ be the cation charge and $x$ be the number of water molecules for unit cell thus gives: \begin{align*} Mr_{\text{unit cell}} = \frac{7.68}{q} Mr_{\text{cation}} &+ (11.5(26.982)+ (96-7.68)(28.085) + 192(15.999) \\ @@ -249,14 +260,14 @@ Thus for HZSM-5 where the cation is \ce{H+} and $x \approx 25$~\autocite{donder0 \end{split} \end{equation} -Let: $q$ be the cation charge; $n_{\text{max. cation}}$ be the theoretical maximum amount of cation which can be exchanged and $n_{\text{cation}}$, $m_{\text{cation}}$ and $Mr_{\text{cation}}$ be the actual amount, mass and $Mr$ of the cation exchanged respectively. +Let: $q$ be the cation charge; $n_{\text{max. cation}}$ be the theoretical maximum amount of cation which can be exchanged and $n_{\text{cation}}$, $m_{\text{cation}}$ and $Mr_{\text{cation}}$ respectively be the actual amount, mass and $Mr$ of the cation exchanged. \begin{align} n_{\text{HZSM-5 unit cell}} &= \frac{m_{\text{HZSM-5}}}{Mr_{\text{HZSM-5 unit cell}}} \nonumber \\ n_{\text{max. cation}} &= \frac{7.68}{q} n_{\text{HZSM-5 unit cell}} \nonumber \\ &= \frac{7.68}{q} \frac{m_{\text{HZSM-5}}}{Mr_{\text{HZSM-5 unit cell}}} \nonumber \\ % - \si{\percent} \text{ Exchanged} &= \frac{n_{\text{cation}}}{n_{\text{max. cation}}} \times \SI{100}{\percent} \nonumber \\ + \si{\percent} \text{ Exchange Level} &= \frac{n_{\text{cation}}}{n_{\text{max. cation}}} \times \SI{100}{\percent} \nonumber \\ \label{eq:cation-percent-exchanged} &= \frac{q Mr_{\text{HZSM-5 unit cell}} n_{\text{cation}}}{7.68 m_{\text{HZSM-5}}} \times \SI{100}{\percent} \end{align} @@ -296,18 +307,18 @@ Hence using equations \ref{eq:[cuso4]-std} and \ref{eq:beer-lambert-epsilon}: % &= \frac{0.484 \times \SI{50.00e-3}{\deci\metre\cubed} \times \SI{249.677}{\gram\per\mole}}{\SI{1.0}{\centi\metre} \times \SI{0.5014}{\gram}} = \SI{12.05}{\deci\metre\cubed\per\mole\per\centi\metre} %\end{align} -\subsubsection{Determination of \ce{Cu^2+} Ion-Exchange Level} +\subsubsection{Determination of \ce{Cu^2+} Ion Exchange Level} By rearranging the Beer-Lambert Law (equation \ref{eq:beer-lambert}) for concentration: \begin{equation} \label{eq:beer-lambert-c} c = \frac{A}{\epsilon l} \end{equation} -Letting $[\ce{CuSO4}]_\text{prod.}$ be the concentration, $n_{\ce{Cu}_\text{prod.}}$ be the amount of \ce{Cu^{2+}} ions and $V_{\ce{Cu}_\text{prod.}}$ be the volume of the solution after the ion-exchange reaction while using equation \ref{eq:beer-lambert-c}: +Letting $[\ce{CuSO4}]_\text{prod.}$ be the concentration, $n_{\ce{Cu}_\text{prod.}}$ be the amount of \ce{Cu^{2+}} ions and $V_{\ce{Cu}_\text{prod.}}$ be the volume of the solution after the ion exchange process while using equation \ref{eq:beer-lambert-c}: \begin{align} [\ce{CuSO4}]_\text{prod.} &= \frac{A_{\ce{Cu}_\text{prod.}}}{\epsilon_{\text{\ce{CuSO4}}} l} \nonumber \\ - n_{\ce{Cu}_\text{prod.}} &= [\ce{CuSO4}]_\text{prod.} V_{\ce{Cu}_\text{prod.}} \nonumber \\ + \text{So: } n_{\ce{Cu}_\text{prod.}} &= [\ce{CuSO4}]_\text{prod.} V_{\ce{Cu}_\text{prod.}} \nonumber \\ \label{eq:n_cu-prod} &= \frac{A_{\ce{Cu}_\text{prod.}} V_{\ce{Cu}_\text{prod.}}}{\epsilon_{\text{\ce{CuSO4}}} l} \end{align} @@ -318,7 +329,7 @@ Substituting equation \ref{eq:molar-extinction} into \ref{eq:n_cu-prod}: n_{\ce{Cu}_\text{prod.}} = \frac{A_{\ce{Cu}_\text{prod.}} V_{\ce{Cu}_\text{prod.}} m_{\ce{CuSO4.5H2O}}}{A_{\ce{Cu}_\text{std.}} V_{\ce{Cu}_\text{std.}} Mr_{\ce{CuSO4.5H2O}}} \end{equation} -Using equations \ref{eq:[cuso4]-std} and \ref{eq:n_cu-prod-final} to determine the amount of copper which was exchanged into the zeolite ($n_{\ce{Cu}_\text{ex.}}$) letting $V_{\ce{Cu}_\text{react.}}$ be the volume of the standard solution added to the HZSM-5. +The amount of \ce{Cu^2+} exchanged ($n_{\ce{Cu}_\text{ex.}}$) can hence be determined using equations \ref{eq:[cuso4]-std} and \ref{eq:n_cu-prod-final} where $V_{\ce{Cu}_\text{react.}}$ is the volume of the standard copper solution added to the HZSM-5. \begin{align} n_{\ce{Cu}_\text{ex.}} &= [\ce{CuSO4}]V_{\ce{Cu}_\text{react.}} - n_{\ce{Cu}_\text{prod.}} \nonumber\\ @@ -328,10 +339,13 @@ Using equations \ref{eq:[cuso4]-std} and \ref{eq:n_cu-prod-final} to determine t &= \frac{m_{\ce{CuSO4.5H2O}} \left(A_{\ce{Cu}_\text{std.}} V_{\ce{Cu}_\text{react.}} - A_{\ce{Cu}_\text{prod.}} V_{\ce{Cu}_\text{prod.}} \right)}{A_{\ce{Cu}_\text{std.}} V_{\ce{Cu}_\text{std.}} Mr_{\ce{CuSO4.5H2O}}} \end{align} -Substituting equation \ref{eq:cu-exchanged} into equation \ref{eq:cation-percent-exchanged} and setting $q = 2$ hence gives: +Substituting equation \ref{eq:cu-exchanged} into equation \ref{eq:cation-percent-exchanged} as $n_\text{cation}$ and setting $q = 2$ hence gives: \begin{equation} \label{eq:cu-percent-exchanged} - \si{\percent} \text{ \ce{Cu^{2+}} Exchanged} = \frac{2 Mr_{\text{HZSM-5 unit cell}} m_{\ce{CuSO4.5H2O}} \left(A_{\ce{Cu}_\text{std.}} V_{\ce{Cu}_\text{react.}} - A_{\ce{Cu}_\text{prod.}} V_{\ce{Cu}_\text{prod.}} \right)}{7.68 m_{\text{HZSM-5}} A_{\ce{Cu}_\text{std.}} V_{\ce{Cu}_\text{std.}} Mr_{\ce{CuSO4.5H2O}}} \times \SI{100}{\percent} +\begin{split} + \si{\percent} \text{ \ce{Cu^{2+}} Exchanged} &= \frac{2 Mr_{\text{HZSM-5 unit cell}} m_{\ce{CuSO4.5H2O}} \left(A_{\ce{Cu}_\text{std.}} V_{\ce{Cu}_\text{react.}} - A_{\ce{Cu}_\text{prod.}} V_{\ce{Cu}_\text{prod.}} \right)}{7.68 m_{\text{HZSM-5}} A_{\ce{Cu}_\text{std.}} V_{\ce{Cu}_\text{std.}} Mr_{\ce{CuSO4.5H2O}}} \\ + &\phantom{=} \times \SI{100}{\percent} +\end{split} \end{equation} Using \ref{eq:cu-percent-exchanged} with: @@ -357,7 +371,7 @@ Using \ref{eq:cu-percent-exchanged} with: \end{align*} \subsubsection{Error Propagation} \label{sec:cu-error-propagation} -Let the percentage of \ce{Cu^2+} exchanged be $v_{\ce{Cu}}$ in the error propagation below: +Let the percentage exchange level of \ce{Cu^2+} be $v_{\ce{Cu}}$ in the error propagation below: \begin{equation} \label{eq:cu-error-propagation-initial} @@ -468,43 +482,43 @@ Hence substituting equation \ref{eq:delta-s} into \ref{eq:cu-error-propagation-i \end{split} \end{equation} -Substituting values into equation \ref{eq:cu-error-propagation} thus yields: +Substituting values into equation \ref{eq:cu-error-propagation} yields: \begin{displaymath} \delta v_{\ce{Cu}} = \pm \SI{3}{\percent} \end{displaymath} -So the percentage of \ce{Cu^2+} exchanged is \SI{-37 \pm 3}{\percent}. +So the percentage exchange level of \ce{Cu^2+} is \SI{-37 \pm 3}{\percent}. \subsection{Calculations for Zinc Solution} \subsubsection{Determination of EDTA Solution (Batch A) Concentration} -Letting $V_{\ce{Zn}_\text{std.}}$ be the volume, $[\ce{ZnSO4}]_\text{std.}$ be the concentration and $m_{\ce{ZnSO4.7H2O}_\text{std}.}$ be the mass of \ce{ZnSO4.7H2O} used for the preparation of the \ce{ZnSO4} standard solution used to standardise the \ce{EDTA} solution. +Let: $V_{\ce{Zn}_\text{std.}}$ be the volume, $[\ce{ZnSO4}]_\text{std.}$ be the concentration and $m_{\ce{ZnSO4.7H2O}_\text{std}.}$ be the mass of \ce{ZnSO4.7H2O} used for the preparation of the \ce{ZnSO4} standard solution used to standardise the \ce{EDTA} solution. Thus: \begin{equation}\label{eq:[znso4]-std} [\ce{ZnSO4}]_\text{std.} = \frac{m_{\ce{ZnSO4.7H2O}_\text{std}.}}{Mr_{\ce{ZnSO4.7H2O}} V_{\ce{Zn}_\text{std.}}} \end{equation} -From equation \ref{eq:edta-zn-reaction} there is a 1:1 stoichiometric ratio between the \ce{Zn^2+} and \ce{EDTA^4-} ions hence letting $[\ce{EDTA^4-}]$ be the concentration of the \ce{EDTA} solution $n_{\ce{Zn}_\text{std. analyte}}$ be the amount and $V_{\ce{Zn}_\text{std. aliquot}}$ be the volume of \ce{Zn^2+} ions in the analyte. +From equation \ref{eq:edta-zn-reaction} there is a 1:1 stoichiometric ratio between the \ce{Zn^2+} and \ce{EDTA^4-} ions. Letting $[\ce{EDTA^4-}]$ be the concentration of the \ce{EDTA} solution, $n_{\ce{Zn}_\text{std. analyte}}$ be the amount and $V_{\ce{Zn}_\text{std. aliquot}}$ be the volume of \ce{Zn^2+} ions in the analyte hence gives: \begin{equation}\label{eq:[edta]-1} [\ce{EDTA^4-}] = \frac{n_{\ce{Zn}_\text{std. analyte}}}{V_{\ce{EDTA}_\text{std.}}} = \frac{[\ce{ZnSO4}]_\text{std.} V_{\ce{Zn}_\text{std. aliquot}}}{V_{\ce{EDTA}_\text{std.}}} \end{equation} -Thus substituting equation \ref{eq:[znso4]-std} into equation \ref{eq:[edta]-1} gives: +Substituting equation \ref{eq:[znso4]-std} into equation \ref{eq:[edta]-1} gives: \begin{equation}\label{eq:[edta]-final} [\ce{EDTA^4-}] = \frac{m_{\ce{ZnSO4.7H2O}_\text{std}.} V_{\ce{Zn}_\text{std. aliquot}}}{Mr_{\ce{ZnSO4.7H2O}} V_{\ce{Zn}_\text{std.}} V_{\ce{EDTA}_\text{std.}}} \end{equation} \subsubsection{Determination of \ce{Zn^2+} Ion Exchange Level}\label{sec:zn-percent-exchanged} -Let $[\ce{ZnSO4}]_\text{std. orig.}$ be the concentration of, $m_{\ce{ZnSO4.7H2O}_\text{orig.}}$ be the mass of zinc sulphate used and $V_{\ce{Zn}_\text{std. orig.}}$ be the volume of the standard zinc sulphate solution created for the ion exchange process. +For the standard \ce{ZnSO4} solution added to the HZSM-5 let $m_{\ce{ZnSO4.7H2O}_\text{orig.}}$ be the mass of \ce{ZnSO4.7H2O} used and let $V_{\ce{Zn}_\text{std. orig.}}$ and $[\ce{ZnSO4}]_\text{std. orig.}$ be the volume and concentration of the solution respectively. \begin{equation} \label{eq:[znso4]-std-orig} [\ce{ZnSO4}]_\text{std. orig.} = \frac{m_{\ce{ZnSO4.7H2O}_\text{orig.}}}{Mr_{\ce{ZnSO4.7H2O}} V_{\ce{Zn}_\text{std. orig.}}} \end{equation} -Using equation \ref{eq:[znso4]-std-orig} with $V_{\ce{Zn}_\text{orig.}}$ as the volume of the stanadard solution used in the ion-exchange process. +Using equation \ref{eq:[znso4]-std-orig} with $V_{\ce{Zn}_\text{orig.}}$ as the volume of the standard solution used in the ion-exchange process: \begin{align} n_{\ce{Zn}_\text{orig.}} &= [\ce{ZnSO4}]_\text{std. orig.} V_{\ce{Zn}_\text{orig.}} \nonumber \\ @@ -512,15 +526,15 @@ Using equation \ref{eq:[znso4]-std-orig} with $V_{\ce{Zn}_\text{orig.}}$ as the &= \frac{m_{\ce{ZnSO4.7H2O}_\text{orig.}} V_{\ce{Zn}_\text{orig.}}}{Mr_{\ce{ZnSO4.7H2O}} V_{\ce{Zn}_\text{std. orig.}}} \end{align} -Using equation \ref{eq:[edta]-final} the amount of zinc remaining in solution after the ion-exchange ($n_{\ce{Zn}_\text{prod.}}$) can be calculated with $V_{\ce{Zn}_\text{prod.}}$ being the volume of this resultant solution and $V_{\ce{Zn}_\text{prod. aliquot}}$ being the volume of the aliquot titrated. +The amount of zinc remaining in solution after the ion exchange ($n_{\ce{Zn}_\text{prod.}}$) can be calculated using equation \ref{eq:[edta]-final} with $V_{\ce{Zn}_\text{prod.}}$ being the volume the solution after the reaction and $V_{\ce{Zn}_\text{prod. aliquot}}$ being the volume of the aliquot titrated. By equation \ref{eq:edta-zn-reaction} the stoichiometric ratio for the reaction between the \ce{Zn^2+} and \ce{EDTA^4-} in the titration is 1:1, so: \begin{align} - n_{\ce{Zn}_\text{prod.}} &= \frac{V_{\ce{EDTA}_\text{prod.}} [\ce{EDTA^4-}] V_{\ce{Zn}_\text{prod.}}}{V_{\ce{Zn}_\text{prod. aliquot}}} \nonumber \\ + n_{\ce{Zn}_\text{prod.}} &= \frac{V_{\ce{EDTA}_\text{prod.}} [\ce{EDTA^4-}]}{V_{\ce{Zn}_\text{prod. aliquot}}} \times V_{\ce{Zn}_\text{prod.}} \nonumber \\ \label{eq:zn-amount-product} &= \frac{V_{\ce{EDTA}_\text{prod.}} m_{\ce{ZnSO4.7H2O}_\text{std.}} V_{\ce{Zn}_\text{std. aliquot}} V_{\ce{Zn}_\text{prod.}}}{V_{\ce{Zn}_\text{prod. aliquot}} Mr_{\ce{ZnSO4.7H2O}} V_{\ce{Zn}_\text{std.}} V_{\ce{EDTA}_\text{std.}}} \end{align} -Using equations \ref{eq:zn-amount-orig} and \ref{eq:zn-amount-product} to calculate the amount of \ce{Zn^2+} ions exchanged with the HZSM-5 ($n_{\ce{Zn}_\text{ex.}}$): +Using equations \ref{eq:zn-amount-orig} and \ref{eq:zn-amount-product} to calculate the amount of \ce{Zn^2+} ions exchanged with the HZSM-5 ($n_{\ce{Zn}_\text{ex.}}$) gives: \begin{align} n_{\ce{Zn}_\text{ex.}} &= n_{\ce{Zn}_\text{orig.}} - n_{\ce{Zn}_\text{prod.}} \nonumber \\ @@ -532,7 +546,7 @@ Using equations \ref{eq:zn-amount-orig} and \ref{eq:zn-amount-product} to calcul \end{split} \end{align} -Hence substituting equation \ref{eq:zn-amount-exchanged} into \ref{eq:cation-percent-exchanged} and setting $q=2$ gives: +Hence substituting equation \ref{eq:zn-amount-exchanged} into \ref{eq:cation-percent-exchanged} for $n_\text{cation}$ and setting $q=2$ gives: \begin{equation}\label{eq:zn-percent-exchanged} \begin{split} @@ -585,24 +599,24 @@ Let the percentage of \ce{Zn^2+} exchanged be $v_{\ce{Zn}}$ in the following err %New Line &+ \Bigg( \frac{ - \delta \big( V_{\ce{Zn}_\text{prod. aliquot}} V_{\ce{Zn}_\text{std.}} V_{\ce{EDTA}_\text{std.}} m_{\ce{ZnSO4.7H2O}_\text{orig.}} V_{\ce{Zn}_\text{orig.}} - V_{\ce{Zn}_\text{std. orig.}} V_{\ce{EDTA}_\text{prod.}} m_{\ce{ZnSO4.7H2O}_\text{std.}} + \delta \big( V_{\ce{Zn}_\text{prod. aliquot}} V_{\ce{Zn}_\text{std.}} V_{\ce{EDTA}_\text{std.}} m_{\ce{ZnSO4.7H2O}_\text{orig.}} V_{\ce{Zn}_\text{orig.}} - V_{\ce{Zn}_\text{std. orig.}} V_{\ce{EDTA}_\text{prod.}} } { - V_{\ce{Zn}_\text{prod. aliquot}} V_{\ce{Zn}_\text{std.}} V_{\ce{EDTA}_\text{std.}} m_{\ce{ZnSO4.7H2O}_\text{orig.}} V_{\ce{Zn}_\text{orig.}} - V_{\ce{Zn}_\text{std. orig.}} V_{\ce{EDTA}_\text{prod.}} m_{\ce{ZnSO4.7H2O}_\text{std.}} + V_{\ce{Zn}_\text{prod. aliquot}} V_{\ce{Zn}_\text{std.}} V_{\ce{EDTA}_\text{std.}} m_{\ce{ZnSO4.7H2O}_\text{orig.}} V_{\ce{Zn}_\text{orig.}} - V_{\ce{Zn}_\text{std. orig.}} V_{\ce{EDTA}_\text{prod.}} } \\ %New Line &\frac{ - V_{\ce{Zn}_\text{std. aliquot}} V_{\ce{Zn}_\text{prod.}} \big) + m_{\ce{ZnSO4.7H2O}_\text{std.}} V_{\ce{Zn}_\text{std. aliquot}} V_{\ce{Zn}_\text{prod.}} \big) } { - V_{\ce{Zn}_\text{std. aliquot}} V_{\ce{Zn}_\text{prod.}} + m_{\ce{ZnSO4.7H2O}_\text{std.}} V_{\ce{Zn}_\text{std. aliquot}} V_{\ce{Zn}_\text{prod.}} } \Bigg)^2 \vast)^{1/2} \end{split} \end{equation} -Using the same method demonstrated in section \ref{sec:cu-error-propagation} in equation \ref{eq:delta-s} to expand equation \ref{eq:zn-error-propagation-1} hence gives: +Using the same process demonstrated in section \ref{sec:cu-error-propagation} used for equation \ref{eq:delta-s} to expand the subtraction within equation \ref{eq:zn-error-propagation-1} hence gives equation \ref{eq:zn-error-propagation} below: \begin{equation} \label{eq:zn-error-propagation} @@ -622,34 +636,34 @@ Using the same method demonstrated in section \ref{sec:cu-error-propagation} in V_{\ce{Zn}_\text{prod. aliquot}}^2 V_{\ce{Zn}_\text{std.}}^2 V_{\ce{EDTA}_\text{std.}}^2 m_{\ce{ZnSO4.7H2O}_\text{orig.}}^2 V_{\ce{Zn}_\text{orig.}}^2 \vast( \left( \frac{\delta V_{\ce{Zn}_\text{prod. aliquot}}}{V_{\ce{Zn}_\text{prod. aliquot}}} \right)^2 - + \left( \frac{\delta V_{\ce{Zn}_\text{std.}}}{V_{\ce{Zn}_\text{std.}}} \right)^2 } { - \big( V_{\ce{Zn}_\text{prod. aliquot}} V_{\ce{Zn}_\text{std.}} V_{\ce{EDTA}_\text{std.}} m_{\ce{ZnSO4.7H2O}_\text{orig.}} V_{\ce{Zn}_\text{orig.}} - V_{\ce{Zn}_\text{std. orig.}} V_{\ce{EDTA}_\text{prod.}} m_{\ce{ZnSO4.7H2O}_\text{std.}} + \big( V_{\ce{Zn}_\text{prod. aliquot}} V_{\ce{Zn}_\text{std.}} V_{\ce{EDTA}_\text{std.}} m_{\ce{ZnSO4.7H2O}_\text{orig.}} V_{\ce{Zn}_\text{orig.}} - V_{\ce{Zn}_\text{std. orig.}} V_{\ce{EDTA}_\text{prod.}} } \\ %New Line. &\frac{ + + \left( \frac{\delta V_{\ce{Zn}_\text{std.}}}{V_{\ce{Zn}_\text{std.}}} \right)^2 + \left( \frac{\delta V_{\ce{EDTA}_\text{std.}}}{V_{\ce{EDTA}_\text{std.}}} \right)^2 + \left( \frac{\delta m_{\ce{ZnSO4.7H2O}_\text{orig.}}}{m_{\ce{ZnSO4.7H2O}_\text{orig.}}} \right)^2 + \left( \frac{\delta V_{\ce{Zn}_\text{orig.}}}{V_{\ce{Zn}_\text{orig.}}} \right)^2 \vast) - + V_{\ce{Zn}_\text{std. orig.}}^2 V_{\ce{EDTA}_\text{prod.}}^2 m_{\ce{ZnSO4.7H2O}_\text{std.}}^2 + + V_{\ce{Zn}_\text{std. orig.}}^2 } { - V_{\ce{Zn}_\text{std. aliquot}} V_{\ce{Zn}_\text{prod.}} \big)^2 \hfill + m_{\ce{ZnSO4.7H2O}_\text{std.}} V_{\ce{Zn}_\text{std. aliquot}} V_{\ce{Zn}_\text{prod.}} \big)^2 \hfill } \\ %New Line. &\frac{ - V_{\ce{Zn}_\text{std. aliquot}}^2 V_{\ce{Zn}_\text{prod.}}^2 + V_{\ce{EDTA}_\text{prod.}}^2 m_{\ce{ZnSO4.7H2O}_\text{std.}}^2 V_{\ce{Zn}_\text{std. aliquot}}^2 V_{\ce{Zn}_\text{prod.}}^2 \vast( \left( \frac{\delta V_{\ce{Zn}_\text{std. orig.}}}{V_{\ce{Zn}_\text{std. orig.}}} \right)^2 + \left( \frac{\delta V_{\ce{EDTA}_\text{prod.}}}{V_{\ce{EDTA}_\text{prod.}}} \right)^2 - + \left( \frac{\delta m_{\ce{ZnSO4.7H2O}_\text{std.}}}{m_{\ce{ZnSO4.7H2O}_\text{std.}}} \right)^2 - + \left( \frac{\delta V_{\ce{Zn}_\text{std. aliquot}}}{V_{\ce{Zn}_\text{std. aliquot}}} \right)^2 } {} \\ %New Line &\frac{ + + \left( \frac{\delta m_{\ce{ZnSO4.7H2O}_\text{std.}}}{m_{\ce{ZnSO4.7H2O}_\text{std.}}} \right)^2 + + \left( \frac{\delta V_{\ce{Zn}_\text{std. aliquot}}}{V_{\ce{Zn}_\text{std. aliquot}}} \right)^2 + \left( \frac{\delta V_{\ce{Zn}_\text{prod.}}}{V_{\ce{Zn}_\text{prod.}}} \right)^2 \vast) } @@ -664,38 +678,34 @@ Substituting values into equation \ref{eq:zn-error-propagation} gives: \delta v_{\ce{Zn}} = \pm \SI{3}{\percent} \end{displaymath} -Hence the percentage of \ce{Zn^2+} exchanged is \SI{66 \pm 3}{\percent}. +Hence the percentage ion exchange level of \ce{Zn^2+} is \SI{66 \pm 3}{\percent}. -\section{Analysis} -%Over 100% exchange is possible e.g. due to formation of oxide species phyllosilicate outside zeolite e.t.c. influence on cobalt salt precursers on cobalt speciation and catalytic properties of H-ZSM-5 modified ... mhamdi +\section{Discussion} %TODO: Compared molar extinction coefficient value to literature value. - %TODO: Note the acidity of some metal ions formed other substances in solution. %TODO: add note explaining when separate ZnSO4 solution prepared for standardisation of EDTA solution - not a primary analytical standard. -%TODO: Analysis Points: -%Also other byproducts (non-useful) formed - see paper. \subsection{General} -Between laboratory sessions the solutions were stored in a fridge in an attempt to reduce the rate of ion exchange since some of the ZSM-5 had already been separated out of the copper solution. This is not likely to have been very effective since the temperature of the fridge is still fairly high and the samples were left for a long period of time (one week), hence both samples are likely to have reached new equilibriums during this time thus effecting the results collected. It would have been better if the initial centrifugation of the copper solution was not completed since then both mixtures would have been exposed to the same conditions, hence allowing direct comparison of the ion exchange results. +Between laboratory sessions the solutions were stored in a fridge in an attempt to reduce the rate of ion exchange since some of the ZSM-5 had already been separated out of the copper solution. This is not likely to have been very effective since the temperature of the fridge is still fairly high and the samples were left for a long period of time (one week), hence both samples are likely to have reached new equilibriums during this time thus effecting the results collected. It would have been better if the initial centrifugation of the copper solution was not completed since then both mixtures would have been exposed to the same conditions, hence still allowing direct comparison of the ion exchange results. -Losses in the non-exchanged ions are likely to have occurred for both solutions during the centrifugation process since some metal ions will have remained within the precipitate and in the tube when the supernatant fluid was collected. To reduce this loss distilled water could be added to the centrifuge tube and additional centrifugations performed, hence washing the tubes. This was not completed due to time constraints. +Losses of the non-exchanged ions occurred for both solutions during the centrifugation process since some metal ions will have remained within the precipitate and in the centrifuge tube when the supernatant fluid was collected. To reduce this loss distilled water could be added to the centrifuge tube and additional centrifugation performed, hence washing the tube. This was not completed due to time limitations. -Both the copper and zinc solutions were cloudy following the centrifugation indicating that some ZSM-5 remained suspended in the solutions. Further centrifugations wold have reduced the amount of suspended zeolite from the solutions and hence the errors resultant from this (see below). Centrifugation was chosen instead of filtration to separate the zeolite since the nano-size particles of ZSM-5 can block the filter paper during filtrations hence resulting in very long filtration times.~\autocite{russell} +Both the copper and zinc solutions were cloudy following the centrifugation indicating that some ZSM-5 remained suspended in the solutions. Further centrifugation would have reduced the amount of suspended zeolite from the solutions and hence the errors resultant from this (see sections \ref{sec:cu-discussion} and \ref{sec:zn-discussion}). Centrifugation was chosen instead of filtration to separate the zeolite since the nano-size particles of ZSM-5 can block the filter paper during filtrations hence resulting in very long filtration times.~\autocite{russell} -While monomeric species such as \ce{Cu^2+} and \ce{Zn^2+} are likely to be the predominant species present in the ZSM-5 zeolite after the ion exchange process other species such as (\ce{[ZnOH]+} which subsequently form \ce{[ZnOZn]^2+} dimeric bridges upon drying) and \ce{[Cu2(OH)2]^2+} may alternatively be formed.\autocite{almutairi11,schreier05,mhamdi09} The formation of these species allows a 1:1 exchange between the hydrogen and the metal cations thus enabling an ion exchange level greater than that calculated,~\autocite{almutairi11,schreier05} however the exchange of the monomeric species is the preferred thermodynamic product and the other species only form at isolated \ce{Al} centres when using aqueous phase ion exchange as the preparation technique.~\autocite{aleksandrov10,penzien04} It is thus unlikely that a large amount of the dimeric species was present in the products created. +While monomeric species such as \ce{Cu^2+} and \ce{Zn^2+} are likely to be the predominant species present in the ZSM-5 zeolite after the ion exchange process other species such as (\ce{[ZnOH]+} which subsequently form \ce{[ZnOZn]^2+} dimeric bridges upon drying) and \ce{[Cu2(OH)2]^2+} may alternatively be formed.\autocite{almutairi11,schreier05,mhamdi09} The formation of these species allows a 1:1 exchange between the hydrogen and the metal cations thus allowing the possibility of an ion exchange level greater than the maximum calculated,~\autocite{almutairi11,schreier05} however the exchange of the monomeric species is thermodynamically preferred and the alternative species only form at isolated \ce{Al} centres when using aqueous phase ion exchange as the preparation technique.~\autocite{aleksandrov10,penzien04} It is thus unlikely that a large amount of the dimeric species was present in the products created, thus they can be assumed to have no effect on the ion exchange level obtained. -\subsection{Copper Exchanged ZSM-5} -As seen in section \ref{sec:cu-percent-exchanged} the calculated exchange level for the \ce{Cu^2+} ions with the HZSM-5 was negative. This can be explained by the presence of the suspended ZSM-5 in solution whichincreased the absorbance value of the sample over the true value thus resulting in the negative yield calculated. To reduce the effect of this suspended zeolite a titrimetric method for calculating the copper ion concentration could have been used for example using \ce{EDTA} solution as the titrant and Fast Sulphon F as the indicator.~\autocite{denby-copper-conc} This would also allow a better comparison between the copper and zinc ion exchange processes since the similar methods could compensate for common systematic errors. +\subsection{Copper Exchanged ZSM-5}\label{sec:cu-discussion} +As seen in section \ref{sec:cu-percent-exchanged} the calculated exchange level for the \ce{Cu^2+} ions with the HZSM-5 was negative. This can be explained by the presence of the suspended ZSM-5 in solution which increased the absorbance value of the sample thus resulting in the negative yield calculated. To reduce the effect of this suspended zeolite a titrimetric method for calculating the copper ion concentration could have been used for example using \ce{EDTA} solution as the titrant and Fast Sulphon F as the indicator.~\autocite{denby-copper-conc} This would also allow a better comparison between the copper and zinc ion exchange processes since the similar methods could compensate for common systematic errors. -\subsection{Zinc Exchanged ZSM-5} -From section \ref{sec:zn-percent-exchanged} the percentage of zinc calculated to have been exchanged with the ZSM-5 zeolite was \SI{66 \pm 3}{\percent}. Tamiyakul et al. completed an ion exchange between HZSM-5 with an \ce{SiO2}/\ce{AlO3} ratio of 30 and \ce{Zn(NO3)2} at \SI{70}{\celsius} for 12 hours and obtained an ion exchange level of $\frac{0.64}{1.5} \times \SI{100}{\percent} = \SI{43}{\percent}$.\autocite{tamiyakul15} The exchange level calculated in this project is expected to be slightly greater than that reported by Tamiyakul et al. due to the lower \ce{SiO2}/\ce{AlO3} ratio of ZSM-5 used, however the $\SI{66}{\percent} - \SI{43}{\percent} = \SI{23}{\percent}$ difference in ion exchange levels is fairly large and at least art of the difference is likely to be due to the systematic errors discussed (see below): all of which result in an ion exchange value which is too great. +\subsection{Zinc Exchanged ZSM-5}\label{sec:zn-discussion} +From section \ref{sec:zn-percent-exchanged} the percentage of zinc calculated to have been exchanged with the ZSM-5 zeolite was \SI{66 \pm 3}{\percent}. Tamiyakul et al.\@ completed an ion exchange between HZSM-5 with an \ce{SiO2}/\ce{AlO3} ratio of 30 and \ce{Zn(NO3)2} at \SI{70}{\celsius} for 12 hours and obtained an ion exchange level of $\frac{\SI{0.64}{\percent}}{\SI{1.5}{\percent}} \times \SI{100}{\percent} = \SI{43}{\percent}$.\autocite{tamiyakul15} The \ce{SiO2}/\ce{AlO3} ratio of the HZSM-5 used by Tamiyakul et al.\@ is larger than that used in this project, hence a higher ion exchange level is expected, however Yashnik et al.\@ only obtained a \SI{22}{\percent} higher ion exchange level with \ce{CuSO4} while using HZSM-5 with an \ce{SiO2}/\ce{AlO3} ratio of 17 compared to when HZSM-5 with a ratio of 30 was used.~\autocite{yashnik05} The difference in the \ce{SiO2}/\ce{AlO3} ratio of the HZSM-5 between this project and the HZSM-5 used by Tamiyakul et al.\@ is almost half of the difference between the samples compared by Yashnik et al.\@ while the difference in ion exchange level is slightly greater (\SI{23}{\percent}), thus suggesting that the ion exchange level obtained is too high. -The zeolite suspended in the zinc solution resulted in the aliquot volume being too small since the suspended zeolite displaced some of the solution when the aliquot volume was being measured. This thus reduced the titre volume recorded which can be seen to have inflated the ion exchange level calculated (by inspection of equation \ref{eq:zn-percent-exchanged}. +This can be explained by the losses in the centrifugation described earlier and also since the post-ion exchange solution contained suspended zeolite hence the aliquot volume in the titration was too small since the suspended zeolite displaced some of the solution when the volume was being measured. This thus reduced the titre volume recorded which can be seen to have inflated the ion exchange level calculated (by inspection of equation \ref{eq:zn-percent-exchanged}). -This may partially explain the anomalous final titre volume obtained in the titration (see run 4 in table \ref{tbl:zn-analytical-titration}) since some of the solid zeolite may have settled in the bottom of the volumetric flask, hence for this final titration the pipette contained a greater number of suspended zeolite particles thus reducing the analyte volume and resulting in the anomalously small titre volume. +This may also partially explain the anomalous final titre volume obtained in the titration (see run 4 in table \ref{tbl:zn-analytical-titration}) since some of the solid zeolite may have settled in the bottom of the volumetric flask, hence for this final titration the pipette contained a greater number of suspended zeolite particles thus further reducing the analyte volume and resulting in the anomalously small titre volume. \subsection{Uncertainties} -The percentage uncertainty in both of the obtained results is fairly high at \SI{3}{\percent}, although the actual error is greater than this due to the systematic errors discussed. This could be reduced by instead using Diffuse Reflectance Fourier Transform Infrared Spectroscopy (DRIFT-IR)\autocite{pollanen05} on the ZSM-5 samples and obtaining the ion exchange level through comparing the integration of the \SIrange{3570}{3630}{\per\centi\metre} peak between the ion exchanged ZSM-5 samples and the original HZSM-5 sample~\autocite{yu12} instead of using a titrimetric method on the solutions used, thus reducing the number quantities involved in the calculations and hence reducing the number of errors introduced. +The percentage uncertainty in both of the obtained results is quite high at \SI{3}{\percent}, although the actual error is greater than this due to the systematic errors discussed. This could be reduced by instead using Diffuse Reflectance Fourier Transform Infrared Spectroscopy (DRIFT-IR)\autocite{pollanen05} on the ZSM-5 samples and obtaining the ion exchange level through comparing the integration of the \SIrange{3570}{3630}{\per\centi\metre} peak between the ion exchanged ZSM-5 samples and the original HZSM-5 sample.~\autocite{yu12} This would result in a smaller error compared to the titrimetric method since the number of measurements required for the calculation is much less hence reducing the number of errors introduced. %Bibliography. \printbibliography -- 2.25.1