Chapter 23: Introduction to Analytical Separations

The weak base $\mathbf{B}\left(K_b=1.0\times {10}^{-5}\right)$equilibrates between water (phase 1) and benzene (phase 2)

(a) Define the distribution coefficient, D for this system.

(b) Explain the difference between D and K the partition coefficient.

(c) Calculate D at $\mathbf{pH}\mathbf{}\mathbf{8}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{if}\mathbf{}\mathbf{k}\mathbf{=}\mathbf{50}\mathbf{.}\mathbf{0}$

(d) Will D be greater or less at $\mathbf{pH}\mathbf{10}\mathbf{}\mathbf{than}\mathbf{}\mathbf{at}\mathbf{}\mathbf{pH}\mathbf{8}$? Explain why.

Consider the extraction of ${\mathbf{M}}^{\mathbf{nt}}$from aqueous solution into organic solution by reaction with protonated ligand HL : $\mathbf{D}\mathbf{=}{\mathbf{M}}^{\mathbf{n}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{nHL}\mathbf{\left(}\mathbf{org}\mathbf{\right)}\mathbf{\square }\mathbf{}{\mathbf{ML}}_{\mathbf{n}}\mathbf{\left(}\mathbf{org}\mathbf{\right)}\mathbf{+}{\mathbf{nH}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}{\mathbf{K}}_{\mathbf{extraction}}\mathbf{=}\frac{{\left[{\mathrm{ML}}_n\right]}_{\mathbf{org}}\mathbf{}{\left[H^{+}\right]}_{\mathbf{aq}}^{\mathbf{n}}}{{\left[M^{n+}\right]}_{\mathbf{aq}\mathbf{}}{\left[\mathrm{HL}\right]}_{\mathbf{org}}^{\mathbf{n}}}$.Rewrite Equation 23 - 13 in terms of role="math" localid="1654863844402" ${\mathbf{K}}_{\mathbf{e}\mathbf{x}\mathbf{t}\mathbf{r}\mathbf{a}\mathbf{c}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}}$and express ${\mathbf{K}}_{\mathbf{extraction}}$in terms of the constants in Equation 23 - 13 . Give a physical reason why each constant increases or decreases ${\mathbf{K}}_{\mathbf{extraction}}$

Butanoic acid has a partition coefficient of 3.0 (favouring benzene) when distributed between water and benzene. Find the formal concentration of butanoic acid in each phase when 100mL of 0.10M aqueous butanoic acid is extracted with 25mL of benzene (a) at pH 4.00 and (b) at pH 10.00.

For a given value of ${\left[\mathrm{HL}\right]}_{\mathbf{org}}$in Equation 23-13, over what pH range (how many pH units) will D change from if n = 2?

23-14 For the extraction of ${\mathbf{Cu}}^{\mathbf{2}\mathbf{+}}$by dithizone ${\mathbf{CCI}}_{\mathbf{4}\mathbf{}}\mathbf{,}{\mathbf{K}}_{\mathbf{L}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}\mathbf{,}{\mathbf{K}}_{\mathbf{M}}\mathbf{=}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}\mathbf{,}}{\mathbf{K}}_{\mathbf{a}}\mathbf{=}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{,}\mathbf{b}\mathbf{=}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{22}}\mathbf{,}\mathbf{}\mathbf{n}\mathbf{=}\mathbf{2}$

(a) Calculate the distribution coefficient for extraction of 0.1mM ${\mathbf{Cu}}^{\mathbf{2}\mathbf{+}}$

into ${\mathbf{CCI}}_{\mathbf{4}}$by 0.1mM dithizone at and at pH = 1 and at pH = 4 .

(b) If 100mL of 0.1mM aqueous ${\mathbf{Cu}}^{\mathbf{2}\mathbf{+}}$are extracted once with 10mL

of 0.1mM dithizone atpH = 1 , what fraction of ${\mathbf{Cu}}^{\mathbf{2}\mathbf{+}}$remains in the aqueous phase?

Consider the extraction of $\mathbf{100}\mathbf{mL}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{M}}^{\mathbf{+}\mathbf{2}}\mathbf{}\mathbf{}\mathbf{by}\mathbf{}\mathbf{2}\mathbf{mL}\mathbf{}\mathbf{of}\mathbf{}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{}\mathbf{}\mathbf{M}\mathbf{}\mathbf{dithizone}\mathbf{}\mathbf{in}\mathbf{}{\mathbf{CHCl}}_{\mathbf{3}}$for which ${\mathbf{K}}_{\mathbf{L}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}\mathbf{,}{\mathbf{K}}_{\mathbf{M}}\mathbf{=}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{24}}\mathbf{,}\mathbf{Ka}\mathbf{=}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{,}\mathbf{\beta }\mathbf{=}\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{18}}\mathbf{,}\mathbf{n}\mathbf{=}\mathbf{2}$(a) Derive an expression for the fraction of metal ion extracted into the organic phase, in terms of the distribution coefficient and volumes of the two phases. (b) Prepare a graph of the percentage of metal ion extracted over the pH range 0 to 5.

The theoretical limit for extracting solute Sfrom ${\mathbf{Phase}}_{\mathbf{}\mathbf{1}}$$\mathbf{(}\mathbf{volume}\mathbf{}{\mathbf{V}}_{\mathbf{1}}\mathbf{)}\mathbf{}$into phase2 $\mathbf{(}\mathbf{volume}\mathbf{}{\mathbf{V}}_{\mathbf{2}\mathbf{}}\mathbf{)}\mathbf{}$is attained by dividing ${\mathbf{V}}_{\mathbf{2}}$into an infinite number of infinitesimally small portions and conducting an infinite number of extractions. With a partition coefficient, $\mathbf{K}\mathbf{=}{\mathbf{\left[}\mathbf{S}\mathbf{\right]}}_{\mathbf{2}}\mathbf{}\mathbf{/}{\mathbf{\left[}\mathbf{S}\mathbf{\right]}}_{\mathbf{1}}$the limiting fraction of solute remaining in phase $\mathbf{1}\mathbf{}\mathit{i}{\mathit{s}}^{\mathbf{2}\mathbf{q}}\mathit{l}\mathit{i}\mathit{m}\mathit{i}\mathit{t}\mathbf{}\mathbf{=}\mathbf{e}\mathbf{-}\mathbf{(}{\mathbf{V}}_{\mathbf{2}}\mathbf{/}{\mathbf{V}}_{\mathbf{1}}\mathbf{)}\mathbf{K}\mathbf{}\mathbf{(}{\mathbf{V}}_{\mathbf{1}}\mathbf{=}{\mathbf{V}}_{\mathbf{2}}\mathbf{=}\mathbf{50}\mathbf{mL}\mathbf{}\mathbf{and}\mathbf{}\mathbf{K}\mathbf{=}\mathbf{2}\mathbf{)}$. Let volume ${\mathbf{V}}_{\mathbf{2}}$be divided intoequal portions to conduct extractions. Find the fraction of S extracted into phase 2 for n = 1,2, and 10extractions. How many portions are required to attain 95%of the theoretical limit?

The partition coefficient for a solute in chromatography is $\mathbf{K}\mathbf{=}{\mathbf{c}}_{\mathbf{s}}\mathbf{/}{\mathbf{c}}_{\mathbf{m}}$, where ${\mathbf{c}}_{\mathbf{s}}$is the concentration in the stationary phase and ${\mathbf{c}}_{\mathbf{m}}$is the concentration in the mobile phase. The larger the partition coefficient, the longer it takes a solute to be eluted. Explain why.

(a) Write the meaning of the retention factor,k, in terms of time spent by solute in each phase. (b) Write an expression in terms of kfor the fraction of time spent by a solute molecule in the mobile phase. (c) The retention ratio in chromatography is defined as $\mathbf{R}\mathbf{=}\frac{\mathbf{time}\mathbf{}\mathbf{for}\mathbf{}\mathbf{solvent}}{\mathbf{time}\mathbf{}\mathbf{for}\mathbf{}\mathbf{solute}\mathbf{}\mathbf{to}\mathbf{}\mathbf{pass}\mathbf{}\mathbf{through}\mathbf{}\mathbf{column}}\mathbf{=}\frac{{\mathbf{t}}_{\mathbf{m}}}{{\mathbf{t}}_{\mathbf{r}}}$Show that is related to the retention factor by the equation $\mathbf{R}\mathbf{=}\mathbf{1}\mathbf{/}\mathbf{k}\mathbf{+}\mathbf{1}$

23-1.If you are extracting a substance from water into ether, is it more effective to do one extraction with of ether or three extractions with ?