HOW DO I PRECONCENTRATE CR(VI) FROM A LEACHATE USING COPRECIPITATION?

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285



hydronium ion is removed by reaction with the hydroxide ion or other base, the

equilibrium adjusts to produce more CrO 2− . Let us assume that we have an aqueous

4

solution containing Cr(VI) as either chromate or dichromate and CrCl3. The addition

of a source of the Pb2+ ion, such as lead(II) sulfate, will precipitate Cr(VI) as the

insoluble PbCrO4 while leaving Cr(III) in the supernatant as Cr3+. Thus, a speciation

of chromium via coprecipitation can be realized. Hence,

CrO 2 −aq )

4(



2+



Pb → PbCrO 4(s )





The PbCrO4 precipitate is washed clean of occluded Cr3+ and chemically reduced

by the addition of hydrogen peroxide and nitric acid according to

PbCrO 4(s )



2+

HNO3 , H2O2 → Cr(3+ ) + Pb (aq )



aq



If it is expected that the concentration is within the range of 1 to 10 mg/L Cr,

the dissolved Cr(III) can now be analyzed after adjustment to a precise volume of

either FlAA or ICP-AES. If it is expected that the concentration is within the range

of 5 to 100 µg/L Cr, the Cr(III) could be injected into the GFAA. A procedure for

the possible speciation of chromium that might be found in the environment between

Cr(III) and Cr(VI), along with the appropriate sample prep, is found in EPA Method

7195 from the SW-846 series.

Chromium(VI) can be quantitated without coprecipitation by forming a metal

chelate. Method 7196A provides a procedure to prepare the diphenyl carbazone

complex with Cr(VI) in an aqueous matrix. The method is not sensitive in that it is

useful for a range of concentrations between 0.5 and 50 mg/L Cr. A more sensitive

colorimetric method converts Cr(VI) to Cr(VI) chelate with ammonium pyrrolidine

dithiocarbamate (APDC), followed by LLE into methyl isobutyl ketone (MIBK).

The molecular structure for APDC is as follows:



N

S2−



S

NH4+



The APDC forms chelates with some two dozen metal ions.141 The extent of

formation of the metal chelate is determined by the magnitude of the formation

constant β. The efficiency of LLE as defined by a metal chelate’s percent recovery

depends on the distribution ratio, D, of the metal chelate in the two-phase LLE. We

use the fundamental definition of D to develop a useful relationship for metal chelate

LLE.

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93. TO WHAT EXTENT CAN A GIVEN METAL CHELATE

BE RECOVERED BY LLE?

Recall the definition of a distribution ratio for a specific chemical species as defined

by Equation (3.9). If a chelate itself is a weak acid, secondary equilibrium plays a

dominant role. We start by writing down a definition for the distribution ratio that

accounts for all chemical species involving a metal ion M:



D=



∑ C (organic)

∑ C (aqueous)

M



M



This generalization can be reduced to

D=



[ML n ]organic

[ML n ]aqueous + [M n + ]aqueous



(3.49)



This definition assumes that the only metal-containing species are the neutral

chelate, MLn, and the free metal ion, Mn+. This assumption simplifies the mathematics. Other chemical species that might contain the metal are not in appreciable

enough concentrations to be considered. The degree to which a metal remains as

the uncomplexed metal ion, Mn+, is given by αM, whereby αM is the fraction of all

of the metal-containing species in the aqueous phase that is in the Mn+ form:142

αM =



[M n + ]organic

[ML n ]aqueous + [M n + ]aqueous



(3.50)



Equation (3.50) is solved for the term {[MLn] + [Mn+]} and then substituted into

Equation (3.49) to give the following relationship:

D=



[ML n ]organic

[M n + ]



αM



(3.51)



Equation (3.51) states that the degree to which a given metal chelate, MLn,

partitions into the organic phase depends on the ratio of the concentration of extracted

MLn to the concentration of free metal ion, and on the degree to which metal ion

remains uncomplexed in the aqueous phase. Equation (3.51) is quite complex, and

as it stands, this equation is not too useful in being able to predict the extraction

efficiency. Figure 3.28 is a diagrammatic representation of what happens when a

metal ion, Mn+, forms a metal chelate with a weak acid-chelating reagent, HL. The

metal chelate is formed where one metal ion complexes to n singly charged anionic

ligands, L, to form the metal chelate, MLn. The several equilibria shown set the



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287



MLn

HL



H + + L−



HL



MLn



Mn+ + nL−



FIGURE 3.28 Various equilibria for the distribution of a metal chelate between two immiscible phases where the chelate itself is a weak acid.



stage for secondary equilibrium effects in which the concentrations of HL and MLn,

both present in the organic phase, can be changed from a consideration of the effect

of pH in the aqueous phase. We now proceed to discuss and derive a much more

useful relationship that, once derived, enables some predictions to be made about

the LLE extraction efficiency of metal chelates.



94. HOW DO YOU DERIVE A MORE USEFUL

RELATIONSHIP FOR METAL CHELATES?

We derive a more useful relationship for the LLE of metal chelates by considering

the well-known secondary ionic equilibria described in Figure 3.28. Let us start by

assuming that the chelating reagent to be used to complex with our metal ion or

environmental interest is, in general, a weak acid. This monoprotic (our assumption)

weak acid can ionize only in the aqueous phase and does so according to



HL (aq )



+

−



→

← H + L





The extent of this dissociation is governed by its acid dissociation constant, Ka,

and is defined in the case of a monoprotic weak acid, HL, as follows:



Ka =



[H + ][L− ]

[HL ]



The neutral chelate can also partition into the organic phase according to

HL



HL (aq )



© 2006 by Taylor & Francis Group, LLC



K D → HL (organic )



←





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The extent to which HL partitions into the organic phase is governed by its

HL

partition coefficient, K D , and is defined as

HL

KD =



[HL ]organic

[HL ]aqueous



(3.52)



Chelating reagents that are amphiprotic, such as 8-hydroxyquinoline, HOx, have

a more limited pH range within which the distribution ratio for HOx approxiHL

mates K D .

Free metal ions, Mn+, and the conjugate base to the weak acid chelate, L–, that

are present in the aqueous phase will form the metal chelate by reaction of n ligands

coordinating around a central metal ion. The extent of complexation is governed by

the formation complex, β, according to

M n + + nL−



β→ ML n



←





The formation constant of the metal chelate in aqueous solution is defined as

β=



[ML n ]aqueous

n+



n

[M ]aqueous [L− ]aqueous



(3.53)



The partition coefficient for the neutral metal chelate, MLn, where a relatively

nonpolar and water-immiscible solvent is added to an aqueous solution containing

the dissolved metal chelate, is given as follows:

ML

KD n =



[ML n ]organic

[ML n ]aqueous



(3.54)



The acid dissociation constant expression, the formation constant expression,

and the two expressions for the partition coefficients can be substituted into the

defining equation for D ([Equation (3.49)], rearranged, and simplified.



95. CAN WE DERIVE A WORKING EXPRESSION

FOR THE DISTRIBUTION RATIO?

Yes, we can, and we utilize all of the above equations to do so. This is an instructive

exercise that can be found in a number of analytical chemistry texts that introduce

the topic of metal chelate extraction. Usually the derivation itself is not included

and only the final equation is given and interpreted. In the derivation that follows,

we find that we do not need to add any more simplifying assumptions to those

already given to reach the final working equations.



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289



Let us consider eliminating the concentration of free metal ion by solving

Equation (3.53) for [Mn+] and substituting this expression into Equation (3.50). This

gives

D=



ML

K D N [ML n ]

αM

[ML n ]β[L− ]n



The concentration of metal chelate in the aqueous phase cancels, and we obtain

the following expression for D:

ML

D = K D n β[ L− ]n α M



This equation can be further simplified by eliminating the ligand concentration

term by solving the equation for Ka given earlier for [L–] and substituting this

expression. We get

n



D=K



ML n

D



 K [HL ] 

β  a +  αM

 [H ] 



Rearranging this equation gives

D=



ML

n

K D n βK a

n

[HL ]aqueous α M

+ n

[H ]



This equation can be further simplified by eliminating the concentration of the

undissociated weak acid chelate in the aqueous phase by substituting for [HL]aqueous

using Equation (3.52). Upon rearrangement, we have the final working relationship

for the distribution ratio of the metal chelate MLn when the chelate itself is a

monoprotic weak acid HL:

D=



ML

n

n

K D n βK a [HL ]organic

HL

( K D ) n [H + ]n



αM



(3.55)



Equation (3.55) is the generalized relationship. This relationship was developed

earlier for a specific metal chelate, as was shown in Equation (3.18). Equation (3.55)

shows that the magnitude of the distribution ratio depends on the magnitude of the

four equilibrium constants. These constants depend on the particular metal chelate.

The distribution ratio can be varied by changing either the concentration of chelate

in the organic phase or the pH of the aqueous phase. The number of ligands that

bond to the central metal ion, n, is also an important parameter. As shown earlier

[Equation (3.16)], once we know D we can calculate E if we know or can measure

the phase ratio for LLE. Knowing E enables us to determine the percent recovery

and hence to quantitatively estimate the extraction efficiency. Because 100 × E equals

the percent recovery for a given metal chelate, a plot of the percent recovery of a

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Trace Environmental Quantitative Analysis, Second Edition



% Extracted



290



50%



1.9



4.7

7.4

pH



8.5



FIGURE 3.29 Plot of the percent extracted vs. the pH for four metal dithizones.



given metal chelate vs. pH reveals a sigmoid-shaped curve. The inflection point in

the curve yields the pH1/2 for the specific metal. This is the pH at which 50% of a

metal is extracted.

Figure 3.29 is a plot of the percent extracted against the solution pH for four

metals, Cu(II), Sn(II), Pb(II), and Zn(II), as their respective dithizones. The exact

values for each metal’s pH1/2 are as follows:

Metal Dithizone



pH1/2



Cu(II)

Sn(II)

Pb(II)

Zn(II)



1.9

4.7

7.4

8.5



It should become clear that pH is a powerful secondary equilibrium effect that

can be used to selectively extract a particular metal from a sample that may contain

more than one metal.

Day and Underwood143 have shown that if the logarithm is taken on both sides

of Equation (3.55), we obtain a more useful form. Let us first rewrite Equation (3.55)

combining the various equilibrium constants as follows:

D=



n

K ex [HL ]organic

n

[H + ]aqueous



(3.56)



where Kex is substituted for all of the equilibrium constants in Equation (3.55). Upon

taking the logarithm of both sides of Equation (3.56), we obtain

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291



(HL)organic is larger

(HL)organic is smaller



Log D



0



pH



FIGURE 3.30 Plot of the logarithm of the distribution ratio vs. pH.



log D = log K ex + n log[HL ] − n log[H + ]

This equation can be rewritten in terms of pH as follows:

log D = log K ex + n log[HL ] + npH

A plot of log D vs. pH should in theory be a straight line whose slope is n and

whose intercept on the log D axis (i.e., when pH = 0) is {log Kex + n log [HL]}.

Figure 3.30 shows such a plot in general terms. Note that the two lines drawn

correspond to two different values for [HL]organic. These straight lines eventually

curve and plateau as the pH of the aqueous phase becomes very high. In this case,

the [H+] becomes so low that abundant L– is made available, which in turn drives

the formation of the metal chelate equilibrium to the right. As more aqueous metal

chelate becomes available, the partitioning of the metal chelate shifts in favor of the

organic metal chelate. Hence, in the absence of any hydroxide, the value for D

approaches the value for the molecular partition coefficient for the metal chelate,

ML

K D n . Metal hydroxide precipitation at a high pH competes for the free metal ion,

Mn+, a factor not taken into account during the development of Equation (3.55).



96. ARE THERE OTHER WAYS TO PRECONCENTRATE

METAL IONS FROM ENVIRONMENTAL SAMPLES?

Yes, there are, and these are in essence SPE type methods. Both cation and anion

exchange resins have been used to preconcentrate inorganic metal cations while

removing anionic interferents. A large body of work has been related to the formation

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of the polychloro-anionic complex such as FeCl– and its isolation using anion

4

exchange resins.

Chelating resins, styrene–divinyl benzene copolymer, containing iminodiacetrate

functional groups have been successfully used to preconcentrate transition metal

ions from solutions of high salt concentrations. Selective neutral metal chelates have

been found to be isolated and recovered using C18 chemically bonded silica gel.144

We now digress to some of the author’s findings in this area.



97. CAN WE ISOLATE AND RECOVER A NEUTRAL

METAL CHELATE FROM AN ENVIRONMENTAL

SAMPLE USING BONDED SILICAS?

Neutral metal chelates should behave no differently with respect to the adsorption/partitioning of the species from water to an octadecyl-bonded silica than neutral

organics, as discussed earlier. This author has developed mathematical equations for

the reaction of cadmium ion, Cd2+, with 8-hydroxyquinoline (HOx), also referred

to as oxine, to form a series of complexes. If it is assumed that only the neutral 1:2

complex, CdOx2, will partition into the bonded sorbent, equations can be derived

that relate the distribution ratio to measurable quantitities. We now proceed through

this derivation and start with a consideration of the secondary equilibria involved.

We first need to consider a more expanded concept, enlarging upon that shown for

metal chelate LLE (refer back to Figure 3.23). The schematic in Figure 3.31 depicts

the bonded silica–aqueous interface, in which only the neutral 1:2 engages in the

primary equilibrium, that of partitioning onto or into the monolayer of wetted C18

ligates.



C18 surface



Aqueous

phase

CdOx2 (aq)

CdOx +



CdOx2

(sorbed)



Cd2+ + 2 Ox −



Ox − + H +



HOx

H+

H2Ox +



FIGURE 3.31 Various equilibria for the distribution of cadmium oxinate between an aqueous

phase and the C18 sorbent surface.



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293



The extent to which the free cadmium ion complexes with the oxinate ion to

form the 1:1 cation is governed by



Cd 2 + + Ox −



+

β1 → CdOx



←





The extent to which the cadmium ion complexes with two oxinate anions to

form the 1:2 complex is governed by



Cd 2 + + 2 Ox −



β2 → CdOx 2



←





Oxine, itself being amphiprotic, can exist as either the neutral, weak acid or a

protonated species. A molecular structure for oxine is as follows:



N

O

H



The hydroxyl group behaves as a weak acid, whereas the aromatic nitrogen can

accept a proton and behave as a weak base. The degree to which oxine is protonated,

H2Ox+, remains neutral, HOx, or dissociates to H+, and oxinate, Ox–, is governed

by the pH of the aqueous phase.

For the protonated species, we can write an equilibrium for the acid dissociation:



H 2 Ox +



+

K a 1 H + HOx

→

←





The extent of dissociation of this weak acid is governed by the first acid dissociation constant, Ka1.

For the neutral weak acid, it too dissociates in aqueous media according to



HOx



+

−

K a 2 → H Ox



←





The extent to which the neutral form of oxine dissociates is governed by the

magnitude of the second acid dissociation constant, Ka2.



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If Cd2+ and oxine are present in the aqueous phase, these four ionic equilibria

would be present to the extent determined by their formation constants. Which

complex predominates — 1:1 or 1:2? We need to define what we mean by a formation

constant for metal complexes, and these definitions we take from well-established

chemical concepts. The formation constant for the 1:1 complex is defined as



β1 =



[CdOx + ]

[Cd 2 + ][Ox − ]



(3.57)



Likewise, the equilibrium expression for the formation of the 1:2 complex is

given by

β2 =



[CdOx 2 ]

[Cd 2 + ][Ox − ]2



(3.58)



The acid dissociation constants for the amphiprotic oxine are

K a1 =



[H + ][HOx ]

[H 2 Ox + ]



(3.59)



K a2 =



[H + ][Ox - ]

[HOx ]



(3.60)



Because our discussion centers around trace Cd analysis, let us consider the

fraction of all forms of this metal existing as the free, uncomplexed ion δ0, where

this fraction is defined as

δ0 =



[Cd 2 + ]

CM



(3.61)



Likewise, the fraction of cadmium complexed 1:1 is given by

δ1 =



[CdOx + ]

CM



(3.62)



Furthermore, the fraction of cadmium complexed 1:2 is given by

δ2 =



[CdOx 2 ]

CM



(3.63)



We also need to distinguish between the concentration of oxine in the aqueous

phase, [HOx], and the total concentration of oxine, CHOx. This total oxine concentration results from the actual addition of a given amount of the substance to water,

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295



with adjustment of a final solution volume. With all of these definitions in mind, we

can now proceed to substitute and manipulate using simple algebra to help us arrive

at more useful relationships than those given by just the definitions.

We start by considering the fraction of cadmium complexed as the 1:2 complex.

Solving Equation (3.58) for [CdOx2] yields

[CdOx 2 ] = β2 [Cd 2 + ][Ox ]2



(3.64)



Equation (3.57) can also be solved for the concentration of the 1:1 complex:

[CdOx + ] = β1 Cd 2 +  Ox − 









(3.65)



Substituting Equation (3.64) into Equation (3.57) gives

δ2 =

=



β2 [Cd 2 + ][Ox ]2

[Cd 2 + ] + [CdOx + ] + [CdOx 2 ]

x

β2 [Ox − ]2

=

2+

1 + [CdOx ][Cd ] + [CdOx 2 ][Cd 2 = ]



Upon substituting Equations (3.64) and (3.65) into the denominator in the above

expression, we get the following simplified result:

δ2 =



β2 [Ox − ]2

1 + β1[Ox − ] + β2 [Ox ]2



(3.66)



Equation (3.66) is important, but this equation is not the ultimate objective of

this derivation. Equation 3.66 states that the fraction of all cadmium can be found

in the aqueous phase from knowledge of only the two formation constants and the

free oxinate ion concentration. It is difficult analytically to measure this free [Ox–].

There is a solution to this dilemma. Let us consider how the chelate, oxine, is

distributed in the aqueous phase. We start by writing a mass balance expression for

the total concentration of oxine, CHOx, as follows:

CHOx =  H 2Ox +  +  HOx  +  Ox − 

 





 

We have thus accounted for all forms that the chelate can take. Equations (3.59)

and (3.60) can be solved for the undissociated forms and substituted into the mass

balance expression to yield

[H + ][HOx ] [H + ][Ox ][Ox − ]

+

+ [Ox − ]

K a1

K a2

© 2006 by Taylor & Francis Group, LLC