^{1}

^{1}

An idea on interfacial equilibrium-potential differences (
) which are generated for the extraction of univalent metal picrate (MPic) and divalent ones (MPic
_{2}) by crown ethers (L) into high-polar diluents was improved. These potentials were clarified with some experimental extraction-data reported before on the M = Ag(I), Ca(II), Sr(II) and Ba(II) extraction with 18-crown-6 ether (18C6) and benzo-18C6 into 1,2-dichloroethane (DCE) and nitrobenzene (NB). Consequently, it was demonstrated that the
values from the extraction-experimentally obtained log
K
_{D,Pic} ones are in agreement with or close to those calculated from charge balance equations in many cases, where the symbol,
K
_{D,Pic}, denotes an individual distribution constant of Pic
^{﹣} into the DCE or NB phase. Also, it was experimentally shown that extraction constants based on the overall extraction equilibria do not virtually contain the
terms in their functional expressions.

Univalent and divalent metal picrates

been extracted by crown compounds (L) into the high-polar diluents, such as 1,2-dichloethane (DCE), dichloromethane and nitrobenzene (NB) [_{z}, dissociates ML^{z}^{+} and zPic^{−} [_{D,A}) of Pic^{−} (=A^{−}) into the diluents has been determined extraction-experimen- tally [_{D,A} definition and the same diluents, the thus-determined K_{D,Pic} values have differed from each other. For example, the logK_{D,Pic} values were −0.94 [_{2} extraction with 18-crown-6 ether (18C6), −1.34 [_{2} one with benzo-18C6 (B18C6) into NB, −2.4_{6} [_{2} one with 18C6 and −4.3_{5} [_{2} one with 18C6 into DCE. Thus, their values have changed over experimental errors with combinations of MPic_{z} and L.

To clarify a reason for such differences, the authors have applied the idea [

ference (Df_{eq}) at extraction equilibrium to an expression of log K_{D,A}, namely

[^{−}. In addition to this, extraction constants, K_{ex}_{±} and K_{ex2}_{±}, have been electrochemically expressed as

to standard formal potentials for the single distribution of A^{−} into the diluent or organic (o or org) phase and the formal potentials for the overall equilibrium, respectively. Also, K_{ex}_{±} and K_{ex2}_{±} have been defined experimentally

by extraction as

On the other hand, from the thermodynamic points of view, these extraction constants are resolved into

_{ML,org} (complex

formation in the o phase) and K_{1,org} (1st-step ion-pair formation in the o one), do not contain the Df_{eq} terms in their expressions, because the constants are of homogeneous systems that all species relevant to the reaction are present in the single o phase [^{z}^{+} has been expressed with K_{D,M} (see Equation (3) at

since K_{D,M} and K_{D,A} are present in the

tually the Df_{eq} ones. Thereby, the extraction constants virtually lose the Df_{eq} terms on their functional expres-

sions. Thus, the above expression, such as

experimentally-evaluated values and theoretically-reproduced ones [

In the present paper, in order to solve the above two contradictions, namely the differences of K_{D,A} caused by experimental conditions of extraction and the contradiction based on the thermodynamic cycles [_{eq} of the extraction constants, K_{ex}_{±} and K_{ex2}_{±}. In course of clarifying this expression, some experimentally-determined constants [_{ex}_{±}, an individual distribution constant (K_{D,ML}) of the complex ion ML^{2+} into the NB phase and that of AgL^{+} into DCE, were also reproduced by calculation. Here, the AgPic and MPic_{2} (M = Ca, Sr & Ba) extraction with L = 18C6 and/or B18C6 [_{eq} values [_{D,A} ones determined by the extraction experiments was discussed based on an electroneutrality-point of view [

(i) Case of the M(I) extraction with L. For the extraction equilibrium,

for the o phase. The concentrations of M^{+} and A^{−} in the o phase were modified as

by using electrochemical equations [

and

see Appendix B in ref [_{o}/[j] denote a standard formal potential of species j {=M(I), A(−I) & ML(I); see the introduction and section 3.3} and the individual distribution constant (K_{D,j}) of j between the two phases, respectively. At least, the

_{D,A} determination. Defining as

with

and

Accordingly, the following equation is derived.

Hence, if the [M^{+}], [ML^{+}]_{o} and [A^{−}] values are determined experimentally, then we can obtain the Df_{eq} values from Equation (6) immediately; the [ML^{+}]_{o} values were calculated here from the relation

^{+}]_{o} £ 0 were neglected in a further computation.

(ii) Case of the M(II) extraction with L. Similarly, we can consider the following stepwise extraction-equili- bria [_{D,A} determination). Therefore, the charge balance equation for the o phase becomes

As described above, this equation was modified to [

Defining as

with

and

We can exactly solve this equation for x based on the mathematical formula [

where _{eq} value from the combination of Equations (6) and (10).

The b¢ values were evaluated from the relation,

extraction experiments [_{+} from the experimental data [

According to previous papers, the two of the three extraction constants have been defined as ^{I}A-L extraction system [^{II}A_{2}-L extraction one [_{ex}_{±} (or logK_{ex2}_{±}) equals

These two kinds of extraction constants contain the Df_{eq} terms as parameters in their functional expressions[

[_{ex} has been expressed as _{eq} and spontaneously became an expression electrochemically-standardized at

In the above functions, some contradictions have been observed in the former cases: see Appendix in ref. [

_{eq}, because

the resulting component equilibrium-constant K_{2,org} does not relate with Df_{eq} [_{2,org} and K_{ex} are the constants at

comes _{eq} term does not disappear, where _{eq}.

In order to cancel such contradictions, we assume here that the two extraction constants are functions without Df_{eq}, as well as that of K_{ex} [

and

That is, by our traditional sense, it is proposed here that complicated equilibrium constants, such as K_{ex}, K_{ex}_{±} and K_{ex2}_{±}, do not contain the Df_{eq} terms in their functions. This means that these constants are ordinarily defined without Df_{eq}or under the condition of

The relations in ^{−} [^{+}, R_{4}N^{+}, M^{2+} and ML^{2+}, in Df_{eq}. As an example, the thermodynamic relation for M(II)

can be rearranged into

Overall equilibrium & Its cycle^{b} | Relation |
---|---|

^{c} | (a) |

(b) | (b) |

^{d} | (c) |

(d) ^{d} | (d) |

^{d} | (e) |

(f) | (f) |

^{a}k = ex±, ex2±, ML,org, ML,w, & 1,org, where the symbol “w” shows a water phase; ^{b}Thermodynamic cycle; ^{c}Ref. [^{d}Ref. [

Therefore, the relation (c) in _{eq} of K_{D,M} equals that of K_{D,A} in the extraction system of Equation (13). Also, we can rewrite Equation (13) to

Consequently, Equation (14) or (13) does not contain the Df_{eq} term and is virtually expressed with only the standard formal potentials (at

_{eq} values were calculated from Equation (4) and the experimental log K_{D,Pic} values in

Here,

Data no. | logK_{ex} | logK_{ex}_{±} | logK_{D,A} | logK_{ML,DCE}^{a}_{ } (I_{DCE}^{c}/10^{−5}) | logK_{1,DCE}^{b} | logK_{D,ML} |
---|---|---|---|---|---|---|

1A^{d} | 5.55 | 0.17^{e} ± 0.03, −0.5_{1} | −2.70 | 5.68^{f} (0.64) | 5.38^{e}, 6.0_{5} | 3.05^{f} |

1B^{g} | 5.17 ± 0.01 | 0.25 ± 0.09 | −2.33 ± 0.03 | 5.76 (0.40) | 4.92 | 2.76 |

1C^{g} | 5.336 ± 0.004 | 0.5_{1} ± 0.1_{0} | −2.60 ± 0.05 | 6.03 (1.1) | 4.82 | 3.3 |

2^{g} | 5.07 ± 0.01 | −0.13 ± 0.09 | −1.68 ± 0.02 | 5.38 (0.55) | 5.20 | 1.73 |

Data no. 1A | 1B | 1C | 2 | |
---|---|---|---|---|

0.10 | 0.078 | 0.094 | 0.040 | |

0.09_{3} ± 0.01_{3} | 0.07_{4} ± 0.01_{2} | 0.08_{9} ± 0.01_{2} | 0.040 ± 0.005 |

Data no. 1A | 1B | 1C | 2 | |
---|---|---|---|---|

^{*} | 0.17 | 0.25 | 0.52 | -0.13 |

Data no. 1A | 1B | 1C | 2 | |
---|---|---|---|---|

^{*} | 1.36 | 1.44 | 1.7 | 1.06 |

^{§} | 2.94 | 2.70 | 3.2 | 1.74 |

^{a}Values calculated from ^{b}Values calculated from^{c}Unit: mol dm^{−3}; ^{d}Ref. [^{e}Values re-calculated from the same data as that reported before. See ref. [^{f}Additionally determined values which were calculated from the same data as that reported before. See ref. [^{g}Data obtained from additional extraction experiments. Experimental conditions and data analyses are essentially the same as those reported on ref. [^{−3} HNO_{3}.

^{*}.

^{*} ^{§}.

Also, we estimated Df_{eq,av} from Equation (6) with Equation (5), where Df_{eq,av} denotes an average value for each run.

The both values, expressed as

Average I values of the extraction systems in ^{−3} for the no. 1A [_{ex}_{±} = 0.3_{1} ± 0.1_{4} and logK_{D,Pic} = −2.54 ± 0.07;

_{DCE} range of (0.40 - 1.1) ´ 10^{-}^{5} mol×dm^{−3} (see the data in

in the same I_{DCE} range. The symbol, I_{DCE}, refers to the average ionic strength of the DCE phase; the same is true of I_{NB} (see

_{2} (M = Ca, Sr & Ba) by 18C6 and B18C6 into NB.

The Df_{eq} values were calculated from Equation (4) with the logK_{D,Pic} values in

Df_{eq,av} values were estimated in the same manner. The above findings are listed in

For the 18C6 extraction systems, the

Except for the

cial equilibrium-potential differences, Df_{eq}, based on Equation (4) are essentially the same as those based on

Equation (6). The differences between

charge balance equation between extraction experiments (see Appendix II) and electrochemical (or theoretical)

treatments, namely _{2} for L = B18C6, while that was 0.02_{9} for 18C6; these values

were the maximum of the B18C6- and 18C6-M(II) extraction systems. Practically, the

On the basis of the above facts, _{eq} value obtained from the distribution process of

We obtained the log K_{ex}_{±} values of the AgPic extraction with B18C6 into DCE from the relation (a) in

ponding logK_{ML,DCE} value in

The K_{D,AgL} calculation can be an indirect proof of K_{ex}_{±} without Df_{eq}. First, the log K_{D,AgL} values (namely

Next, the logK_{D,AgL} values were reproduced by using the equation,

_{D,AgL} values can be well

reproduced. From the results of

Pic-B18C6 extraction system.

Moreover, an average _{9} ± 0.2_{3}. From this value and the _{D,AgL} values again, using the above relation [_{D,AgL} values (= 3.1 & 2.7, respectively) of nos.

1A and 1B were close to those in

The logK_{ex}_{±} values for the M(II)-B18C6 extraction into NB were calculated from the relation (c) in

These _{ex}_{±} values in

been determined by the procedure [

without Df_{eq} is satisfied. In this calculation,

[_{CaL,NB} = 11.2, logK_{SrL,NB} = 13.1, logK_{BaL,NB} = 13.4 for L = 18C6 [_{CaL,NB} = 9.43, logK_{SrL,NB} = 11.1 and logK_{BaL,NB} = 11.6 for L = B18C6 [_{D,M} values were calculated from

the modified form of Equation (3),

The following discussion is similar to that from _{D,AgL} at L = B18C6 (

ues were 0.48 for the Ca-18C6 [_{D,18C6} = −1.00 [_{D,B18C6} = 1.57 [_{ex2}_{±} values [

The calculated

As similar to _{D,ML} becomes the indirect proof of logK_{ex2}_{±}

without Df_{eq}. Then, the logK_{D,ML} values at 298 K were estimated from the

The thus-calculated

logK_{D,ML} values in

L | M | logK_{ex}_{±} | logK_{D,A} | logK_{1,NB} (I_{NB}^{b}/10^{-}^{4}) | logK_{D,ML} | logK_{ex2}_{±}^{c} |
---|---|---|---|---|---|---|

18C6 | Ca | 5.44 | −1.43 | 5.9 (8.9) | 0.8_{8} | −0.5 |

Sr | 6.9_{2} | −0.98 | 5.3 (4.8) | −0.1_{7} | 1.6 | |

Ba | 7.3_{5} | −0.69 | 4.9 (5.9) | −0.9_{9} | 2.7^{d} | |

B18C6 | Ca | 2.7_{1} | −1.92 | 5.0 (6.9) | 2.6_{2} | −2.3 |

Sr | 4.34 | −1.34 | 4.7 (2.3) | 1.4_{4} | −0.4 | |

Ba | 5.0_{1} | −1.17 | 4.1 (2.1) | 1.6_{1} | 0.9^{d} |

18C6 extraction system | B18C6 extraction system | |||||
---|---|---|---|---|---|---|

M = Ca | Sr | Ba | M = Ca | Sr | Ba | |

0.088 | 0.061 | 0.044 | 0.12 | 0.082 | 0.072 | |

0.080 ± 0.008 | 0.051 ± 0.008 | 0.036 ± 0.006 | 0.097± 0.008 | 0.059 ± 0.008 | 0.04_{2}± 0.01_{0} |

18C6 extraction system | B18C6 extraction system | |||||
---|---|---|---|---|---|---|

M = Ca | Sr | Ba | M = Ca | Sr | Ba | |

^{*} | 5.4 | 7.0 | 7.6 | 2.7 | 4.4 | 5.3 |

L = 18C6 | B18C6 | |||||
---|---|---|---|---|---|---|

M = Ca | Sr | Ba | M = Ca | Sr | Ba | |

^{*} | -2.1 | -2.2 | -2.3 | -1.3 | -1.3 | -0.5 |

^{§} | 0.9 | -0.1 | -0.8 | 2.7 | 1.5 | 1.9 |

^{a}Ref. [^{b}Unit: mol dm^{−3}; ^{c} values: see ref [^{d}Values re-calculated from the data in ref [^{ }

^{*}

^{*}. ^{§}.

The above calculation results for the AgPic and MPic_{2} extraction with L indicate that the assumption of Equations (11) and (12) without Df_{eq} is essentially valid. In other words, the overall extraction constants, K_{ex}_{±} and K_{ex2}_{±}, must be expressed rationally as functions without Df_{eq}.

The above handling based on

_{2}Cl_{2} [

and

As examples, thermodynamic points of view suggest the following cycles for the above equilibria:

with

and

with_{D,j} values are expressed as

functions with the Df_{eq} ones.

The relation, _{D,M} or K_{D,A} was standardized at _{4}As^{+}BPh_{4}^{-} assumption [_{D,C} cancels out K_{D,A} in (E12c):

Similarly, K_{D,T} cancels out K_{D,A} in (E13c), where T^{-} denotes another anion. That is,

equilibria, (E14) & (E15), one can handle them in the same manner as that described above for the AgPic and MPic_{2} extraction with L, respectively.

We can easily see that the K_{D,H} and K_{D,Pu} values cancel out the K_{D,Cl} one in (E16c). That is,

It was demonstrated that the Df_{eq} values calculated from the experimental logK_{D,Pic} ones are in agreement with or close to those more-accurately done from the charge balance equations for the species with M(I) in the DCE phase and with M(II) in the NB one, except for some cases. This demonstration indicates that the plots of _{D,A}

values and then the first-approximated Df_{eq} ones. These results will give an answer to how one explain the differences in K_{D,A} among extraction experiments of various MA or MA_{2} by various L. Also, we clarified that the assumption of Equations (11) and (12) is valid for the AgPic and MPic_{2} extraction with 18C6 and/or B18C6. This eliminated the contradictions [_{eq} from the thermodynamic cycles. Moreover, the present work indicates a possibility that the proposed handling can be applied to various extraction systems with neutral ligands at least.

The authors thank Mr. Tomohiro Amano, Mr. Satoshi Ikeda and Mr. Yuki Ohsawa for their experimental assistances.

The basic extraction model [

and

Consequently, these component equilibria yield those of _{D,M}), _{D,ML}), _{D,L}) and _{D,A}). An extraction of HPic, _{ex,HPic}), was added in the

[Pic^{-}] calculation. The distribution [

The case (ii) [

and

where the distribution of _{D,M}), _{D,ML}) and_{ex,HPic} value was included in the calculation.

The both models, (i) & (ii), do not contain supporting electrolytes in the o phases. This point is a large difference from corresponding electrochemical measurements [

The K_{D,A} values have been determined extraction-experimentally using the following equations [

for ^{+}) or for ^{2+}). Hence, the plots of

versus

give the K_{D,A} value with the K_{ex} ones for the MA- and MA_{2}-L extraction systems, respectively. Here, the

^{z}^{+}], [L]_{o} and [A^{−}] values are

calculated by a successive approximation [

employed for the approximation:

[

Similarly, the K_{ex}_{±} values have been evaluated from the other arranged form of Equation (A15),

for