\documentclass[a4paper]{article}

\usepackage{pgfplots}
\usepackage{siunitx}

\DeclareSIUnit\Molar{\textsc{m}}

\title{Amount of Transmitted Light Relative to the Concentration of a Solution}
\date{22 September 2014}
\author{Tarik Onalan}

\begin{document}
    \maketitle
    \noindent\textbf{Purpose:} Understand how relative concentration of a solution
    in water can affect its transmittance and absorbance. \\\\
    \section{Data}
        \noindent\resizebox{\textwidth}{!}{
        	\Huge
            \begin{tabular}{|l||c|c|c|c|} \hline
                Solution & Dilution Ratio \(\frac{\si\ml\ stock}{\si\ml\ water}\) & Molar Concentration \si{\micro\Molar} & Measured Percent Transmittance & Measured \(\%T\) in Decimal Form \\ \hline\hline
                1. (stock solution) & \(\SI{10}{\ml}/\SI{0}{\ml}\) & \(1.7\cdot10^{1}\)\si{\micro\Molar} & 0.753 & 0.177 \\ \hline
                2. & \(\SI{8}{\ml}/\SI{2}{\ml}\) & \(1.4\cdot10^{1}\)\si{\micro\Molar} & 0.577 & 0.265 \\ \hline
                3. & \(\SI{6}{\ml}/\SI{4}{\ml}\) & \(1.0\cdot10^{1}\)\si{\micro\Molar} & 0.450 & 0.355 \\ \hline
                4. & \(\SI{4}{\ml}/\SI{6}{\ml}\) & \(6.8\cdot10^{0}\)\si{\micro\Molar} & 0.281 & 0.524 \\ \hline
                5. & \(\SI{3}{\ml}/\SI{7}{\ml}\) & \(5.1\cdot10^{0}\)\si{\micro\Molar} & 0.198 & 0.634 \\ \hline
                6. & \(\SI{2}{\ml}/\SI{8}{\ml}\) & \(3.4\cdot10^{0}\)\si{\micro\Molar} & 0.176 & 0.667 \\ \hline
                7. & \(\SI{1}{\ml}/\SI{9}{\ml}\) & \(1.7\cdot10^{0}\)\si{\micro\Molar} & 0.074 & 0.84 \\ \hline
                8. & \(\SI{0}{\ml}/\SI{10}{\ml}\) & \(0.0\cdot10^{0}\)\si{\micro\Molar} & 0.000 & 1.000 \\ \hline\hline
                Glacier Freeze & \(\SI{3.35}{\ml}/\SI{6.65}{\ml}\) & \(5.7\cdot10^{0}\)\si{\micro\Molar} & 0.247 & 0.566 \\ \hline
                Cool Blue & \(\SI{8.82}{\ml}/\SI{1.18}{\ml}\) & \(1.5\cdot10^{1}\)\si{\micro\Molar} & 0.671 & 0.213 \\ \hline
                Berry & \(\SI{20.1}{ml}/\SI{-10.1}{\ml}\) & \(3.4\cdot10^{1}\)\si{\micro\Molar} & 1.476 & 0.03342 \\ \hline
            \end{tabular}
        }\\\\\\
        \begin{tikzpicture}
            \begin{axis}[
                scale=1.25,
                title={Transmittance Relative to Concentration of Brilliant Blue in a Solution},
                xlabel={Molarity [\si{\micro\Molar}]},
                ylabel={Measured Transmittance},
                xmin=0.00, xmax=20.0,
                ymin=0.00, ymax=1.00,
                xtick={17, 14, 10, 6.8, 5.1, 3.4, 1.7, 0.0},
                ytick={0.00, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00},
                legend pos=north west,
                ymajorgrids=true,
                grid style=dashed
            ]
                \addplot coordinates{
                    (17, 0.753)
                    (14, 0.577)
                    (10, 0.450)
                    (6.8, 0.281)
                    (5.1, 0.198)
                    (3.4, 0.176)
                    (1.7, 0.074)
                    (0.0, 0.000)
                };
                \addplot[
                    color=red,
                    domain=0:20,
                    mark=none
                ] {0.0431*x + 0.000953};
                \addlegendentry{Brilliant Blue Transmittance}
                \addlegendentry{\(0.0431\si{\micro\Molar}+0.000953\)}
            \end{axis}
        \end{tikzpicture} \\\\

        \begin{tikzpicture}
            \begin{axis}[
               	scale=1.25,
                title={Transmittance Relative to Concentration of Brilliant Blue in Gatorade},
                xlabel={Molarity [\si{\micro\Molar}]},
                ylabel={Measured Transmittance},
                xmin=0.00, xmax=35.0,
                ymin=0.00, ymax=1.50,
                xtick={34, 15, 5.7},
                ytick={0.00, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 1.10, 1.20, 1.30, 1.40, 1.50},
                legend pos=north west,
                ymajorgrids=true,
                grid style=dashed
            ]
                \addplot coordinates {
                    (17, 0.753)
                    (14, 0.577)
                    (10, 0.450)
                    (6.8, 0.281)
                    (5.1, 0.198)
                    (3.4, 0.176)
                    (1.7, 0.074)
                    (0.0, 0.000)
                };
                \addplot[
                    color=green,
                    domain=0:35,
                    mark=square*,
                    only marks
                ] coordinates {
                    (5.7, 0.247)
                    (15, 0.671)
                    (34, 1.476)
                };
                \addplot[
                    color=red,
                    domain=0:35,
                    mark=none
                ] {0.0431*x + 0.000953};
                \addlegendentry{Brilliant Blue Transmittance}
                \addlegendentry{Gatorade Transmittance}
                \addlegendentry{\(0.0431\si{\micro\Molar}+0.000953\)}
            \end{axis}
        \end{tikzpicture} \\\\

        Note the Gatorade is in order (from left to right):
        \begin{itemize}
            \item Glacier Freeze
            \item Cool Blue
            \item Berry
        \end{itemize}

    \section{Calculations}
        \begin{itemize}
            \item Molar Concentration for First Dilution \((M_{1}V_{1} = M_{2}V_{2})\): \\
            \[(1.7\cdot10^{1}\si{\micro\Molar})\cdot\SI{8}{\ml} = (x\si{\micro\Molar})\cdot\SI{10}{\ml}\]
            \[x = \frac{(1.7\cdot10^{1}\si{\micro\Molar})\cdot\SI{8}{\ml}}{\SI{10}{\ml}} = 1.4\cdot10^{1}\si{\micro\Molar}\]
            \item Percent Transmittance for Stock Solution \((\%T = 10^{-A})\) \\
            \[(\%T) = 10^{-0.753} = 0.177\to17.7\%\]
        \end{itemize}

    \section{Questions}
        \begin{enumerate}
            \item Suppose a solution was too concentrated for an accurate reading
            with the spectrophotometer. The concentrated solution was diluted
            by placing \SI{1.00}{\ml} of the concentrated solution into
            \SI{4.00}{\ml} of water. The solution was then placed in the
            spectrophotometer, an absorbance was obtained, and after a few
            calculations the molar concentration was calculated to be
            \(3.5\cdot10^{-6}\si\Molar\). What was the concentration of the
            original stock solution before dilution? \\\\
            \[(\si\Molar) = \frac{(3.5\cdot10^{-6}\si\Molar)\cdot\SI{5.00}{\ml}}{\SI{1.00}{\ml}} = 1.8\cdot10^{-5}\si\Molar\]
            \item If a \SI{0.10}{\Molar} solution of a colored substance has a
            maximum absorbance at \SI{500}{\nm} and an absorbance of 0.26
            at this wavelength, what will be the measured absorbance of a
            \SI{0.20}{\Molar} solution at \SI{500}{\nm}? \\\\
            \[(A) = \frac{\SI{0.20}{\Molar}}{\SI{0.10}{\Molar}}\cdot0.26 = 0.52\]
            \item The spectrophotometer really measures the percent of light
            that is transmitted through the solution. The instrument then converts
            \(\%T\) (transmittance) into absorbance by using the equation you
            determined in the prelab section. If the absorbance of a sample is
            0.85, what is the percent light transmitted through the colored
            sample at this collected wavelength?
            \[(A) = -\log{(T)}\]
            \[(T) = 10^{-(A)}\to10^{-0.85} = 0.14\to14\%\]
        \end{enumerate}
\end{document}