91影视

Beer's law states that through the sample and the concentration of the absorbing species, the absorbance is proportional to the path length.

$\mathbf{A}\mathbf{=}\mathbf{蔚产颁}$

A is the absorbance,$\mathbf{蔚}$ is the molar absorptivity,b is the length of light path, C is the concentration.

Hence, the spreadsheet is,

Calculatevalues using Beer鈥檚 Law,

$系=\frac{A}{b鈰�[s\tan dard]}$

Thus, Column can be calculated by using the formula,

$\mathrm{A}={\mathrm{系}}_{\mathrm{x}}鈰�\mathrm{b}鈰�[\mathrm{X}{]}_{\mathrm{guess}}+{\mathrm{系}}_{\mathrm{y}}鈰�\mathrm{b}鈰�[\mathrm{Y}{]}_{\mathrm{Guess}}$

Hence, in cell D10 and D11 we know the values.

Take the concentration is 0.001 M for each compound.

Thus, we calculated column G and H column.

Calculate the sum in column H8.

Use the solver to calculate the concentration of unknown and highlight the cell.

Select data tab$鈫�$ Solver and enter H8 in Set Objective.

Select the min button and in by Changing Variables enter D10 and D11.

Thus, solving method should be GRG nonlinear.

Hence, set Constraint Precision to a small number such as 1E-12.

Click solve, the values appears in the cell D10 and D11.

Therefore, the values of$\left[{\mathrm{In}}^{-}\right]\mathrm{and}\left[\mathrm{HIn}\right]$ are $\left[{\mathrm{In}}^{-}\right]=3.28.{10}^{-6}\mathrm{M},\left[\mathrm{HIn}\right]=6.91.{10}^{-6}\mathrm{M}$.

Consider the Henderson-Hassel Balch equation,

$\mathrm{pH}={\mathrm{pK}}_{\mathrm{a}}+\log \left(\frac{\left[{\mathrm{I}}^{-}\right]}{\left[\mathrm{HIn}\right]}\right)$

$\mathrm{pH}=7.10+\log \left(\frac{7.10+\log 3.28鈰�{10}^{-6}}{6.91鈰�{10}^{-6}}\right)$

pH = 6.78

Calculate the concentration of${\mathrm{In}}^{-}$ by using the formula,

$[\ln ]=\frac{{\displaystyle \left|\begin{array}{lc}{\mathrm{A}}_{\mathrm{mixture}}& {\stackrel{藱}{\mathrm{o}}}_{\mathrm{HIn}}鈰�\mathrm{b}\\ {\mathrm{A}}_{\mathrm{mixture}}& {\stackrel{藱}{\mathrm{o}}}_{\mathrm{HIn}\text{'}}鈰�\mathrm{b}\end{array}\right|}}{\left|\begin{array}{l}{\stackrel{藱}{\mathrm{l}}}_{\mathrm{In}{}^{鈭�}}鈰�\mathrm{b}鈥呪赌呪赌呪赌�{\stackrel{藱}{\mathrm{H}}}_{\mathrm{HIn}}鈰�\mathrm{b}\\ {\stackrel{藱}{\mathrm{o}}}_{\mathrm{In}{}^{鈭�}}鈰�\mathrm{b}鈥呪赌呪赌呪赌�{\stackrel{藱}{\mathrm{o}}}_{{\mathrm{Hln}}^{\mathrm{鈥�}}}鈰�\mathrm{b}\end{array}\right|}$

Use the values from the mention spreadsheet,

$$\begin{gathered} \left[{\ln }^{鈭�}\right]=\frac{\left|\begin{array}{cc}0.265& 34400\\ 0.272& 500\end{array}\right|}{\left|\begin{array}{cc}7600& 34400\\ 81100& 500\end{array}\right|} \\ \left[{\ln }^{鈭�}\right]=\frac{(0.265鈰�500)鈭�(34400鈰�0.272)}{(7600鈰�500)鈭�(34400鈰�81100)} \\ \left[{\ln }^{鈭�}\right]=3.31鈰�{10}^{鈭�6}\mathrm{M} \end{gathered}$$

Find the concentration of HIn,

$[\mathrm{Hln}]=\frac{\left|\begin{array}{cc}{\stackrel{藱}{\mathrm{o}}}_{{\mathrm{In}}^{鈭�}}鈰�\mathrm{b}& {\mathrm{A}}_{\mathrm{mixture}}\\ {\widehat{\mathrm{o}}}_{\mathrm{l}}{\ln }^{鈭�}鈰�\mathrm{b}& {\mathrm{A}}_{\mathrm{mixture}}\end{array}\right|}{\left|\begin{array}{cc}{\stackrel{藱}{\mathrm{o}}}_{{\mathrm{In}}^{鈭�}}鈰�\mathrm{b}& {\stackrel{藱}{\mathrm{o}}}_{\mathrm{HIn}}鈰�\mathrm{b}\\ {\widehat{\mathrm{o}}}^{\mathrm{鈥�}}{\ln }^{鈭�}鈰�\mathrm{b}& {\stackrel{藱}{\mathrm{o}}}_{{\mathrm{HIn}}^{\mathrm{鈥�}}}鈰�\mathrm{b}\end{array}\right|}$

Use the values from spreadsheet,

$\mathrm{Hln}]=\frac{\left|\begin{array}{cc}7600& 0.265\\ 81100& 0.272\end{array}\right|}{\left|\begin{array}{cc}7600& 34400\\ 81100& 500\end{array}\right|}$

$$\begin{gathered} [\mathrm{H}\ln ]=\frac{(7600鈰�0.272)-(81100鈰�0.265)}{(7600鈰�500)-(34400鈰�81100)} \\ \left[\mathrm{Hln}\right]=6.97鈰�{10}^{-6}\mathrm{M} \end{gathered}$$

Therefore, the answer (a) is probably more accurate.