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 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).
-
-%TODO: Need to create new standard solutn to standardise the EDTA. Might as well set to heat for 1hr while sorting out Cu? (Use 10.00 cm aliquot)
-
-%TODO: Analysis Points:
-%Explain intention of storing in fridge.
-
-%Losses: centrifuge tube: unable to transfer all of zinc solution out of sample bottles into centrifuge tubes. Insufficent time to centrifuge zeolite with distilled water as well to rinse tubes.
-%After centrifuging solutions were still cloudy so still zeolite suspended. Higher absorbance than true for copper - could have effected zinc as well. Use titrametric method to get more accurate copper reading.
-%Also other byproducts (non-useful) formed - see paper.
-
\section{Results}
\subsection{Copper-Exchanged Zeolite}
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}
\end{equation}
-%TODO: Titre value too small due to ZSM-5 suspended in solution: displaces liquid so actual aliquot size is smaller than appears.
-%TODO: Add notes about titration results: final anomalous reading possibly due human error or water in pipette filler, more solid in aliquot than others since less solution in volumetric flask and solid started to settle on bottom hence aliquot smaller than others.
-%TODO: add note explaining when separate ZnSO4 solution prepared for standardisation of EDTA solution - not a primary analytical standard.
\section{Calculations}
\subsection{Calculation of Maximum Theoretical Number of Ion Exchanges}
\end{align}
\subsection{Calculations for Copper Solution}
-\subsubsection{Determination of Molar Extinction Coefficient}
+\subsubsection{Determination of Molar Extinction Coefficient}\label{sec:cu-percent-exchanged}
Let $V_{\ce{Cu}_\text{std.}}$ be the volume and $[\ce{CuSO4}]_\text{std.}$ be the concentration of the standard \ce{Cu^{2+}} solution.
\begin{align}
n_{\ce{CuSO4}} &= \frac{m_{\ce{CuSO4.5H2O}}}{Mr_{\ce{CuSO4.5H2O}}} \nonumber \\
&= \SI{-18}{\percent}
\end{align*}
-\subsubsection{Error Propagation}
+\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:
\begin{equation}
\end{split}
\end{equation}
-Let $A_{\ce{Cu}_\text{std.}} V_{\ce{Cu}_\text{react.}} - A_{\ce{Cu}_\text{prod.}} V_{\ce{Cu}_\text{prod.}} = S$, thus:
+Let $S = A_{\ce{Cu}_\text{std.}} V_{\ce{Cu}_\text{react.}} - A_{\ce{Cu}_\text{prod.}} V_{\ce{Cu}_\text{prod.}}$, thus:
\begin{align}
\delta S =
[\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 Percentage of \ce{Zn^2+} Exchanged Compared to the Theoretical Maximum}
+\subsubsection{Determination of Percentage of \ce{Zn^2+} Exchanged Compared to the Theoretical Maximum}\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.
\begin{equation}
Let the percentage of \ce{Zn^2+} exchanged be $v_{\ce{Zn}}$ in the following error propagation:
\begin{equation}
-\label{eq:zn-error-propagation}
+\label{eq:zn-error-propagation-1}
\begin{split}
\delta v_{\ce{Zn}} = &v_{\ce{Zn}}
\vast(
%New Line
&+ \left( \frac{\delta Mr_{\ce{ZnSO4.7H2O}}}{Mr_{\ce{ZnSO4.7H2O}}} \right)^2 +
\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 + \dots
+ \left( \frac{\delta V_{\ce{EDTA}_\text{std.}}}{V_{\ce{EDTA}_\text{std.}}} \right)^2 \\
+ %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.}}
+ }
+ {
+ 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.}}
+ } \\
+ %New Line
+ &\frac{
+ V_{\ce{Zn}_\text{std. aliquot}} V_{\ce{Zn}_\text{prod.}} \big)
+ }
+ {
+ V_{\ce{Zn}_\text{std. aliquot}} V_{\ce{Zn}_\text{prod.}}
+ }
+ \Bigg)^2
\vast)^{1/2}
\end{split}
\end{equation}
-%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
+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:
+
+\begin{equation}
+\label{eq:zn-error-propagation}
+\begin{split}
+ \delta v_{\ce{Zn}} = &v_{\ce{Zn}}
+ \Vastt(
+ \left( \frac{\delta Mr_\text{HZSM-5 unit cell}}{Mr_\text{HZSM-5 unit cell}} \right)^2 +
+ \left( \frac{\delta m_{\text{HZSM-5}}}{m_{\text{HZSM-5}}} \right)^2 +
+ \left( \frac{\delta V_{\ce{Zn}_\text{std. orig.}}}{V_{\ce{Zn}_\text{std. orig.}}} \right)^2 +
+ \left( \frac{\delta V_{\ce{Zn}_\text{prod. aliquot}}}{V_{\ce{Zn}_\text{prod. aliquot}}} \right)^2 \\
+ %New Line
+ &+ \left( \frac{\delta Mr_{\ce{ZnSO4.7H2O}}}{Mr_{\ce{ZnSO4.7H2O}}} \right)^2 +
+ \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 \\
+ %New Line
+ &+ \frac{
+ 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
+ }
+ {
+ 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.}}
+ } \\
+ %New Line.
+ &\frac{
+ + \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. aliquot}} V_{\ce{Zn}_\text{prod.}} \hfill
+ } \\
+ %New Line.
+ &\frac{
+ 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 V_{\ce{Zn}_\text{prod.}}}{V_{\ce{Zn}_\text{prod.}}} \right)^2
+ \vast)
+ }
+ {}
+ \Vastt)^{1/2}
+\end{split}
+\end{equation}
+%TODO: Substitute uncertainties into equation.
+Substituting values into equation \ref{eq:zn-error-propagation} gives:
+
+\begin{displaymath}
+ \delta v_{\ce{Zn}} = \pm \SI{0.00}{\percent}
+\end{displaymath}
+
+Hence the percentage of \ce{Zn^2+} exchanged is \SI{66 \pm 0.00}{\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
%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 about centrifugation used for zeolite separation due to recommendation by Russell: nano-sized zeolite particles clog filter paper and prevent efficient filtration of solution.
+%TODO: Titre value too small due to ZSM-5 suspended in solution: displaces liquid so actual aliquot size is smaller than appears.
+%TODO: Add notes about titration results: final anomalous reading possibly due human error or water in pipette filler, more solid in aliquot than others since less solution in volumetric flask and solid started to settle on bottom hence aliquot smaller than others.
+%TODO: add note explaining when separate ZnSO4 solution prepared for standardisation of EDTA solution - not a primary analytical standard.
+%TODO: Analysis Points:
+%Explain intention of storing in fridge.
+%Losses: centrifuge tube: unable to transfer all of zinc solution out of sample bottles into centrifuge tubes. Insufficient time to centrifuge zeolite with distilled water as well to rinse tubes.
+%After centrifuging solutions were still cloudy so still zeolite suspended. Higher absorbance than true for copper - could have effected zinc as well. Use titrimetric method to get more accurate copper reading.
+%Also other byproducts (non-useful) formed - see paper.
+
+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.
+
+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. This was not completed due to time constraints.
+
+\subsection{Copper Exchanged ZSM-5}
+As seen in section \ref{sec:cu-percent-exchanged} the percentage of copper calculated to have been exchanged with the HZSM-5 was negative. This can be explained by the fact that the solution placed in the spectrophotometer still contained some suspended zeolite (seen by how the solution was slightly cloudy after the centrifugation), hence this increased the absorbance value of the sample over the true value and thus resulting in the negative yield calculated. To reduce the effect of any zeolite remaining suspended in the solution a titrimetric method to calculate the copper ion concentration would have been better such as titrating against an \ce{EDTA} solution using Fast Sulphon F as the indicator.~\autocite{denby-copper-conc} This is also a better method since it allows a more direct comparison between the copper and zinc ion exchange processes since very similar methods are used to determine the cation concentrations which may partially compensate for unforeseen 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 0.0}{\percent}. This value is much higher than expected since S.A. Yasnik et al. calculated an exchange efficiency of \SI{48}{\percent} for \ce{CuSO4} ZSM-17 following contact for 48 hours at room temperature.\autocite{yashnik05}
+
+The zeolite suspended in the zinc solution resulted in the aliquot volume being less than expected since the suspended zeolite displaced some of the solution when the aliquot volume was being measured, hence making it too small. This may explain the anomalous final titre volume (run 4) obtained (see 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.
+
+Further centrifugations could have been completed to reduce the amount of suspended zeolite from the solutions. Centrifugation was used instead of filtration to separate the zeolite since small nano-scale particles ZSM-5 often block the filter paper during filtrations hence resulting in a very slow filtration.~\autocite{russell}
+
+%Bibliography.
\printbibliography
\section{Supplementary Information}
projects / chemistry / university-chemistry-lab-reports.git / commitdiff