91Ó°ÊÓ

For the extraction of $100\mathrm{mL}\mathrm{of}{\mathrm{M}}^{+2}\mathrm{by}2\mathrm{mL}\mathrm{of}1×{10}^{-5}\mathrm{M}\mathrm{dithizone}\mathrm{in}{\mathrm{CHCl}}_3$as

${\mathrm{K}}_{\mathrm{L}}=1.1×{10}^4$.

$K_M=7×{10}^4$,

$\mathrm{Ka}=3×{10}^{-5}$,

$\mathrm{β}=5×{10}^{18}$

n=2,

The expression for the fraction between the concentration of${\mathrm{ML}}_2$ in organic and aqueous phase

$\mathrm{D}=\frac{{\left[{\mathrm{ML}}_2\right]}_{\mathrm{org}}}{{\left[{\mathrm{ML}}_2\right]}_{\mathrm{aq}}}=\frac{{\mathrm{c}}_{\mathrm{org}}×{\mathrm{v}}_{\mathrm{org}}}{{\mathrm{c}}_{\mathrm{aq}}×{\mathrm{V}}_{\mathrm{aq}}}$

Expression for${\mathrm{c}}_{\mathrm{org}}$ by rearranging the equation is

${\mathrm{c}}_{\mathrm{org}}=\mathrm{D}×\frac{{\mathrm{c}}_{\mathrm{aq}}×{\mathrm{V}}_{\mathrm{aq}}}{{\mathrm{V}}_{\mathrm{org}}}$

Expression for the percentage of the extracted metal ion

role="math" localid="1664883296728" $$\begin{gathered} \mathrm{Extracted}\%=\frac{100×{\mathrm{c}}_{\mathrm{org}}}{{\mathrm{c}}_{\mathrm{org}}+{\mathrm{c}}_{\mathrm{aq}}} \\ \mathrm{Extracted}\%=\frac{100×\mathrm{D}×{\displaystyle \frac{{\mathrm{c}}_{\mathrm{aq}}×{\mathrm{v}}_{\mathrm{aq}}}{{\mathrm{v}}_{\mathrm{org}}}}}{\mathrm{D}×{\displaystyle \frac{{\mathrm{c}}_{\mathrm{aq}}×{\mathrm{v}}_{\mathrm{aq}}}{{\mathrm{v}}_{\mathrm{org}}}}+{\mathrm{c}}_{\mathrm{aq}}} \end{gathered}$$

To eliminate these values in the equation is

$\mathrm{Extracted}\%=\frac{100×\mathrm{D}×{\displaystyle \frac{{\mathrm{v}}_{\mathrm{aq}}}{{\mathrm{v}}_{\mathrm{org}}}}}{\mathrm{D}×{\displaystyle \frac{{\mathrm{c}}_{\mathrm{aq}}}{{\mathrm{v}}_{\mathrm{org}}}}+1}$

Spreadsheet of percentage of metal ion extracted over the pH range

Column B calculation

$\left[{\mathrm{H}}^{+}\right]={10}^{-\mathrm{pH}}$

Column C calculation

$\mathrm{D}=\frac{{\mathrm{K}}_{\mathrm{M}}{\mathrm{β°­}}_{\mathrm{a}}^{\mathrm{n}}{\left[\mathrm{HL}\right]}_{\mathrm{org}}^{\mathrm{n}}}{{\mathrm{K}}_{\mathrm{L}}^{\mathrm{n}}{\left[{\mathrm{H}}^{+}\right]}_{\mathrm{aq}}^{\mathrm{n}}}$

Column D calculation

$\mathrm{Extracted}\%=\frac{100×\mathrm{D}×{\displaystyle \frac{{\mathrm{v}}_{\mathrm{aq}}}{{\mathrm{v}}_{\mathrm{org}}}}}{\mathrm{D}×{\displaystyle \frac{{\mathrm{v}}_{\mathrm{aq}}}{{\mathrm{v}}_{\mathrm{org}}}}+1}$

By using these values for column, A and column D values in the graph as shown below.