%Document Headings.
\begin{document}
-\title{Investigation on the Effect of the Cation Counterion used on the Ion Exchange Efficiency with HZSM-5}
+\title{Effect of the Copper and Zinc Cations on the Ion Exchange Level Obtained for the Aqueous Phase Ion Exchange Process with the ZSM-5 Zeolite}
\author{Sam White}
\date{06/03/2018}
%\date{\vhCurrentDate\\\vhCurrentVersion}
\maketitle
\begin{abstract}
-In this project the efficiency of the ion exchange process of HZSM-5 with copper and zinc cations was investigated. The method utilised was found to be ineffective at the completion of this aim and no meaningful conclusions could be drawn from the data collected.
+ An investigation into how the ion exchange level for ZSM-5 differs when using copper and zinc cations in an aqueous phase ion exchange process was attempted. The spectrophotometric method utilised for the measurement of the exchange level for the copper cations was found to be ineffective at producing meaningful results within the timescale of the investigation, hence precluding the comparison of the exchange levels for the different metal cations.
\end{abstract}
\section{Aim}
-This project aimed to investigate how the efficiency of the ion exchange process is effected by the cation being exchanged. Specifically a comparison between the copper and zinc cation exchange processes of an HZSM-5 zeolite was attempted.
+This project aimed to compare how the ion exchange level for a HZSM-5 zeolite differs for the aqueous phase ion exchange process with copper and zinc cations.
\section{Introduction}
-Zeolites are crystalline, microporous solids used for a large number of purposes such as for catalytic cracking, air purification, water softening and desiccants.~\autocite{hardsoftwater,petrov12} This project was completed using the ZSM-5 (Zeolite Socony Mobil-5)\autocite{zhang15} zeolite which has important uses in the petrochemical industry such as for the conversion of methanol to gasoline, dewaxing of distillates, separation of organic products (such as separating para-xylene from its isomers), the interconversion of hydrocarbons.\autocite{olson81,rasouli12,sarkany99}
+Zeolites are crystalline, microporous solids used for a large number of uses such as for catalytic cracking, air purification, water softening and as desiccants.~\autocite{hardsoftwater,petrov12} This project was completed using the ZSM-5 (Zeolite Socony Mobil-5)\autocite{zhang15} zeolite which is used within the petrochemical industry for the conversion of methanol to gasoline, dewaxing of distillates, separation of organic products (such as separating para-xylene from its isomers) and the interconversion of hydrocarbons.\autocite{olson81,rasouli12,sarkany99}
\subsection{Structure}
-Each zeolite is comprised of a finite or infinite number of unique unit cells each of which is made from a constant, integral number of the same type of secondary building unit (SBU) with each vertex in the SBU being a tetrahedron of either \ce{[SiO4]} or \ce{[AlO4]^{-}} (which are themselves the primary building units).\autocite{zeolite-atlas,petrov12,ic-zeolite-structure,han09,danaher17} Each aluminium tetrahedron in a SBU introduces a negative charge -- since aluminium has a 3+ oxidation state compared the 4+ oxidation state of silicon -- which is balanced by the presence of cationic counterions.\autocite{gomez16,petrov12,han09,danaher17} The ZSM-5 zeolite used is a pentasil\autocite{danaher17,olson81} zeolite (constructed of eight five-membered rings) with an SBU containing twelve \ce{AO4} tetrahedra which form a pair of five-one units\autocite{zeolite-atlas,olson81,wu79} as shown in figure \ref{fig:zsm-5-sbu} (A-O-A bridges are shown as straight lines to increase the clarity of the images and since the A-O-A bond angle is around $\text{\SIrange{140}{150}{\degree}} \approx \SI{180}{\degree}$ for silicas and aluminosilicates and the A atoms are represented by the vertices).\autocite{zeolite-atlas}
+Zeolites are comprised of a finite or infinite number of unique unit cells each of which is made from a constant, integral number of the same type of secondary building unit (SBU) with each vertex in the SBU being a tetrahedron of either \ce{[SiO4]} or \ce{[AlO4]^{-}} (which are themselves known as the primary building units and are henceforth generically referred to as \ce{XO4} tetrahedra).\autocite{zeolite-atlas,petrov12,ic-zeolite-structure,han09,danaher17} Each aluminium tetrahedron in the SBU introduces a negative charge -- since aluminium has a 3+ oxidation state whereas silicon has a 4+ oxidation state -- which is balanced by the presence of cationic counterions.\autocite{gomez16,petrov12,han09,danaher17}
+
+The ZSM-5 zeolite used is a pentasil\autocite{danaher17,olson81} zeolite (constructed of eight five-membered rings) with an SBU containing twelve \ce{XO4} tetrahedra which form a pair of five-one units\autocite{zeolite-atlas,olson81,wu79} as shown in figure \ref{fig:zsm-5-sbu} where the vertices represent the \ce{X} atoms and the X-O-X bridges are shown as straight lines for clarity which is a reasonable approximation since the X-O-X bond angle is around $\text{\SIrange{140}{150}{\degree}} \approx \SI{180}{\degree}$ for silicas and aluminosilicates.\autocite{zeolite-atlas}
\begin{figure}[H]
\centering
\caption{Secondary building unit for ZSM-5 zeolite.\autocite{olson81}}\label{fig:zsm-5-sbu}
\end{figure}
-These SBUs then form long chains (figure \ref{fig:zsm-5-chain}) which then themselves interconnect to form layers hence giving a unit cell containing eight SBUs figure \ref{fig:zsm-5-layer}.\autocite{olson81} In \ref{fig:zsm-5-layer} one of the chains (shown in figure \ref{fig:zsm-5-chain}) is highlighted to demonstrate how the chains interconnect to form layers.
+These SBUs then form long chains (depicted in figure \ref{fig:zsm-5-chain}) which themselves interconnect to form layers hence giving a unit cell containing eight SBUs shown at the centre of figure \ref{fig:zsm-5-layer}.\autocite{olson81} In figure \ref{fig:zsm-5-layer} one of the chains (shown in figure \ref{fig:zsm-5-chain}) is highlighted to demonstrate how the chains interconnect to form layers.
\begin{figure}[H]
\begin{floatrow}
\end{floatrow}
\end{figure}
-Since there are eight SBUs of twelve tetrahedra per unit cell there are $8 \times 12 = 96$ \ce{A} atoms and there are two oxygen atoms per individual \ce{A} atom in the cell\autocite{patent3702886A} so per unit cell there are $2 \times 96 = 192$ oxygen atoms. \autocite{zeolite-atlas} This gives the unit cell formula given in \ref{eq:unit-cell} where \ce{X} is a cation with a charge of $q$, hence $\frac{1}{q}$ of these cations are required per negative charge.\autocite{ismagilov00}
+As there are eight SBUs of twelve tetrahedra per unit cell in ZSM-5 there are $8 \times 12 = 96$ \ce{X} atoms per cell hence there are $2 \times 96 = 192$ oxygen atoms per cell\autocite{zeolite-atlas} since there are two oxygen atoms per individual \ce{X} atom.\autocite{patent3702886A} This gives the unit cell formula given in \ref{eq:unit-cell} where \ce{M} is a cation with a charge of $q$, so $\frac{1}{q}$ of these cations are required per negative charge and hence aluminium atom.\autocite{ismagilov00}
\begin{equation}\label{eq:unit-cell}
- \ce{X_{\frac{n}{q}} Al_n Si_{96-n}O_{192}.x H2O}
+ \ce{M_{\frac{n}{q}} Al_n Si_{96-n}O_{192}.x H2O}
\end{equation}
-\subsection{Ion-Exchange}
-These \ce{X^{$q$+}} cations can be exchanged with other ions in a process called ion-exchange. Changing the counterion of the ZSM-5 zeolite can alter the acidity, hydrophobicity, reaction selectivity and other properties of the zeolite.\autocite{rasouli12,chaudhari02,han09}
+\subsection{Ion Exchange}
+These \ce{M^{$q$+}} cations can be exchanged with other ions in a process called ion exchange. Changing the counterion of the ZSM-5 zeolite can alter the acidity, hydrophobicity, reaction selectivity and other properties of the zeolite.~\autocite{rasouli12,chaudhari02,han09}
-The copper exchanged form of ZSM-5 is known to be one of the best forms of ZSM-5 for the selective catalytic reduction of \ce{NO} by \ce{C2-C4} hydrocarbons.\autocite{sato91,yashnik05,ismagilov00} This is an important use case since large amounts of \ce{NO} are produced in vehicle and industrial boiler emissions and \ce{NO} is known to cause air pollution and acid rain.\autocite{iwamoto91}
+The copper exchanged form of ZSM-5 is known to be one of the best forms of ZSM-5 for the selective catalytic reduction of \ce{NO} by \ce{C2-C4} hydrocarbons.~\autocite{sato91,yashnik05,ismagilov00} This is an important use case since large amounts of \ce{NO} are produced in vehicle and industrial boiler emissions and \ce{NO} is known to cause air pollution and acid rain.~\autocite{iwamoto91}
-Similarly the zinc exchanged form of ZSM-5 is currently subject to much research since it has been found to be effective at selectively converting methanol to use aromatic species such as benzene, toluene and xylene (important for the manufacture of polyester fibers, dyes, pesticides and medicines) as an alternative method to petroleum processing.\autocite{niu14,wang16} Specifically ZnZSM-5 has -- so far -- been the best choice of cation for this purpose since it is cheap, non-toxic and highly effective at the aforementioned aromatization process.\autocite{sun18}
+Similarly the zinc exchanged form of ZSM-5 is currently subject to much research since it has been found to be effective at selectively converting methanol to use aromatic species such as benzene, toluene and xylene (important for the manufacture of polyester fibers, dyes, pesticides and medicines) as an alternative method to petroleum processing.~\autocite{niu14,wang16} Specifically ZnZSM-5 has -- so far -- been the best choice of cation for this purpose since it is cheap, non-toxic and highly effective at the aforementioned aromatization process.~\autocite{sun18}
-A ZSM-5 zeolite with a \ce{SiO2}/\ce{AlO3} ratio of 23 was used since this maximised the number of sites which were available for ion-exchange due to the higher aluminium content. In addition this increased the efficiency of the ion-exchange process since zeolites with a high Si/Al ratio are hydrophobic\autocite{chen76,han09,olson99} hence the cation solution does not spontaneously enter the zeolite nanopores so ion-exchange happens only at sites close to the pore entrance.\autocite{han09,olson99} This will thus reduce the percentage uncertainties in the values recorded.
+A ZSM-5 zeolite with a low \ce{SiO2}/\ce{AlO3} ratio of 23 was used in this investigation since this maximised the number of sites which were available for ion exchange due to the higher aluminium content. In addition zeolites with a high \ce{SiO2}/\ce{AlO3} ratio are hydrophobic\autocite{chen76,han09,olson99} hence in aqueous phase ion exchange the cation solution does not spontaneously enter the zeolite nanopores so ion exchange happens only at sites close to the pore entrance.\autocite{han09,olson99} This maximisation of the ion exchange is important since it should accentuate any differences between the ion exchange level with the different cations and make them easier to detect.
\section{Experimental}\label{sec:experimental}
-Standard solutions of \ce{Cu^{2+}} and \ce{Zn^{2+}} (\SI{50.00}{\centi\metre\cubed}) were made using \ce{CuSO4.5H2O} and \ce{ZnSO4.7H2O} with concentration \SI{2.008e-3}{\mole\per\deci\metre\cubed} and \SI{2.02e-3}{\mole\per\deci\metre\cubed} respectively. The absorbance of the standard copper sulphate solution was taken at \SI{806}{\nano\metre} (\num{0.484}) then \SI{20.00}{\centi\metre\cubed} of the standard solutions were added to \SI{0.4810}{\gram} (for the copper solution) and \SI{0.5274}{\gram} (for the zinc solution) of HZSM-5 zeolite with an \ce{SiO2}/\ce{AlO3} ratio of 23 -- forming an opaque white suspension -- before heating both solutions (with stirring) at \SI{70}{\celsius} for one hour. Centrifugation was completed on part of the resultant copper mixture, however time constraints prevented the completion of this process. The two mixtures were thus stored in a fridge for one week until the following laboratory session.
+Standard solutions of \ce{Cu^{2+}} and \ce{Zn^{2+}} (\SI{50.00}{\centi\metre\cubed}) were made using \ce{CuSO4.5H2O} and \ce{ZnSO4.7H2O} with concentrations of \SI{2.008e-3}{\mole\per\deci\metre\cubed} and \SI{2.02e-3}{\mole\per\deci\metre\cubed} respectively. The absorbance of the standard copper sulphate solution was taken at \SI{806}{\nano\metre} (\num{0.484}) then \SI{20.00}{\centi\metre\cubed} of the solutions was added to \SI{0.4810}{\gram} (for the copper solution) and \SI{0.5274}{\gram} (for the zinc solution) of HZSM-5 zeolite with an \ce{SiO2}/\ce{AlO3} ratio of 23 (forming an opaque white suspension) prior to heating both solutions with stirring at \SI{70}{\celsius} for one hour. Centrifugation was completed on part of the resultant copper mixture, however time constraints prevented the completion of this process. The two mixtures were then stored in a fridge for one week until the following laboratory session.
-After one week the zeolite had settled in the bottom of the solutions. The clear solution was decanted and the remainder was centrifuged for 30 minutes before the supernatant was reintroduced to the initially decanted solution producing a slightly cloudy copper solution and a moderately cloudy zinc solution. The solutions were made up to \SI{100.00}{\centi\metre\cubed} before the absorbance of the copper solution at \SI{806}{\nano\metre} was determined (\num{0.110}) and \SI{20.00}{\centi\metre\cubed} aliquots of the zinc solution was titrated against a standard ethylenediaminetetraacetate (EDTA) solution (batch A: \SI{0.4993}{\mole\per\deci\metre\cubed}) with \SI{2}{\centi\metre\cubed} of a pH 10 buffer solution and eriochrome black T as the indicator (colour change from red to light blue).
+After one week the zeolite had sedimented so clear solution was collected and the remainder was centrifuged for 30 minutes before the supernatant was reintroduced to rest of the solution producing a slightly cloudy copper and a moderately cloudy zinc solution. The solutions were made up to \SI{100.00}{\centi\metre\cubed} before the absorbance of the copper solution at \SI{806}{\nano\metre} was determined (\num{0.110}) and \SI{20.00}{\centi\metre\cubed} aliquots of the zinc solution in a pH 10 buffer solution (\SI{2}{\centi\metre\cubed}) were titrated against a standard ethylenediaminetetraacetate (EDTA) solution (batch A: \SI{0.4993}{\mole\per\deci\metre\cubed}) with an eriochrome black T indicator (colour change from red to light blue).
\section{Results}
Substance & Mass / \si{\gram} \\
\hline
\ce{CuSO4.5H2O} & 0.5014 \\
+ \hline
HZSM-5 & 0.4810 \\
\hline
\end{tabular}
\end{table}
\begin{table}[h]
- \caption{Spectrophotometric results.}\label{tbl:cu-absorbance}
+ \caption{Spectrophotometric results for the copper sulphate solutions.}\label{tbl:cu-absorbance}
\centering
\begin{tabular}{|c|c|}
\hline
Substance & Absorbance \\
\hline
Standard Solution & 0.484 \\
+ \hline
Post-Reaction Solution & 0.110 \\
\hline
\end{tabular}
\end{table}
-The uncertainty in the absorbance values recorded by the spectrophotometer can be modelled using the following equation:~\autocite{galban07}
+The uncertainty in these absorbance values can be modelled using the following equation:~\autocite{galban07}
\begin{equation}\label{eq:spectrophotometer-uncertainty}
\delta Abs = Abs \sqrt{ \left( \frac{0.434}{Abs} k_2 \sqrt{1 + 10^{Abs}} \right)^2
Where $k_2$ is a measure of the expected precision of the instrument itself for a specific solution and $k_3$ is a measure of the uncertainty introduced by replacing the cuvette.
-Using the values of $k_2=\num{4.5e-4}$ and $k_3=\num{27e-4}$ recorded by Galb\'{a}n et al.~\autocite{galban07} for the PerkinElmer Lambda 5 spectrophotometer with the ferroin solution since these values produce the largest overall uncertainty, hence giving the most generous reasonable estimate in the uncertainty of the absorbances recorded. Using these values with the absorbances in table \ref{tbl:cu-absorbance} and letting $A_{\ce{Cu}_\text{std.}}$ be the absorbance of the standard \ce{CuSO4} solution and $A_{\ce{Cu}_\text{prod.}}$ be the absorbance of the post-reaction solution:
+Values of $k_2=\num{4.5e-4}$ and $k_3=\num{27e-4}$ were used (recorded by Galb\'{a}n et al.\@ for the PerkinElmer Lambda 5 spectrophotometer with ferroin solution)~\autocite{galban07} since they produce the largest overall uncertainty of values recorded by Galb\'{a}n et al.\@, hence giving the most generous estimate in the uncertainty of the absorbances recorded. Letting $A_{\ce{Cu}_\text{std.}}$ be the absorbance of the standard \ce{CuSO4} solution and $A_{\ce{Cu}_\text{prod.}}$ be the absorbance of the post-reaction solution thus gives:
\begin{align}
\delta A_{\ce{Cu}_\text{std.}} &= 0.484 \sqrt{ \left( \frac{0.434}{0.484} \times \num{4.5e-4} \sqrt{1 + 10^{0.484}} \right)^2
\subsection{Zinc-Exchanged Zeolite}
\begin{table}[h]
- \caption{Masses used in preparation of the \ce{ZnSO4} standard solution utilised in the standardisation of the \ce{EDTA} solution.}\label{tbl:zn-std-masses}
+ \caption{Mass used in preparation of the \ce{ZnSO4} standard solution utilised in the standardisation of the \ce{EDTA} solution.}\label{tbl:zn-std-masses}
\centering
\begin{tabular}{|c|c|}
\hline
Substance & Mass / \si{\gram} \\
\hline
\ce{ZnSO4.7H2O} & 0.6331 \\
+ \hline
HZSM-5 & 0.5274 \\
\hline
\end{tabular}
\end{table}
-The reaction which occurred during the titrations between the \ce{EDTA^4-} and \ce{Zn^2+} ions in given in equation \ref{eq:edta-zn-reaction}.
+The reaction which occurred during the titrations between the \ce{EDTA^4-} and \ce{Zn^2+} ions in given in equation \ref{eq:edta-zn-reaction}:
\begin{equation}\label{eq:edta-zn-reaction}
\ce{Zn^2+ (aq) + EDTA^4- (aq) -> ZnEDTA^2-(aq)}
\end{equation}
-%TODO: Reference.
+%TODO: Reference. 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}
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}
\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) \\
\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}
% &= \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}
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\\
&= \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:
\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}
\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 \\
&= \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 \\
\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}
%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}
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)
}
\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
projects / chemistry / university-chemistry-lab-reports.git / commitdiff