Identification of Forty Cations and Nineteen Anions by Circular Thin

Identification of FortyCations and Nineteen Anions by Circular Thin. Layer Chromatography ... drops of7M NHiSCN and extracted with 3 ml. of diethyl et...
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Identification of Forty Cations and Nineteen Anions by Circular Thin Layer Chromatography M. H. HASHMI, MAQBOOL AHMAD SHAHID, A. A. AYAZ, FARHAT RAFIQUE CHUGHTAI, NASlM HASSAN, and ABDUS SUBHAN ADlL West Regional laboratories, Pakistan Council of Scientific and Industrial Research, Lahore, West Pakistan

b Circular thin layer chromatographic methods for identification of 40 cations and 19 anions from 0.5 mi. of unknown solution are described. The metal ions are separated to five definite groups by solvent extraction before their analysis by TLC. The anions are divided into four different groups on the basis of four separate spray reagents. The method is simple and development of a chromatoplate is complete within 2 minutes. The apparatus for the collection of samples of alloys and other metallic surfaces for TLC analysis i s described. Total time of complete analysis of unknown mixture including preparation of s o b tion and extraction is about 2 to 3 hours.

Table 1.

Solvent Extraction of Cations"

+

Test soln. (0.5 ml.) HC1 (coned.) to 7 M final concentration. Extracted with isobutyl methyl ketone and amyl acetate ( 2 : l ) . Chlorides of certain metals are precipitated. Such cations cannot be included in the schemeb I

I

Aqueous layer. Added 5-6 drops of 7 M NH4SCN and extracted with 3 ml. of diethyl ether

Organic layer Group I

I

r

1

Orgaiic layer Group I1

Aqueoui layer. Added 3 ml. of acetylacetone; organic layer is separated after 3 minutes' shaking

I

I Organic layer Group I11

I

M

HALL(4, 6) demonstrated the usefulness of thin layer chromatography in the analysis of mixtures of iron and zinc (4) and of copper and nickel salts ( 5 ) . Though the preliminary results of Meinhard and Hall were not very satisfactory, these authors were still of the opinion that thin layer chromatography would prove useful in inorganic chemical analysis. However, the inorganic field was virtually ignored until 1960. Since then some studies have been reported on the separation and subsequent identification of inorganic ions (2, 3, 7-10) but, generally speaking, these researches have involved only a small nimber of ions. Moreover, the development of a chromatcplate requires 2 hours (10) which makes the method unsuitable for routine analysis. I n the present paper a semimicro analytical method has been developed for separation and identification of 40 metal ions from 0.5 ml. of unknown solution by circular thin layer chromatography. The present method has an advantage over a previously described procedure (2) in which after separation into groups 1-5 by the classical hydrogen sulfide scheme of qualitative analysis, the metal ions in each group are separated by circular TLC (2) which not only requires a large amount (10 ml.) of the unknown solution but also is limited to 19 cations

Aqueous layer. pH adjusted to about 4.5 and extraction with acetylacetone is repeated

EINHARD AND

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ANALYTICAL CHEMISTRY

r

I

Organik layer. Added to Group I11 extract

1

Aqueods layer. Added diethyldithiocarbamate, sodium salt, in excess and extracted with 3 ml. of diethyl ether II 7

I

Organic layer Aquebus layer Group IV Group V 5 The individual metal ions present in each group are given in Table IV. b These include Ag+, Hg+,Pb+, W+6 and T1+. However, sufficient traces of lead remain dissolved for analysis.

and is not a comprehensive scheme. In the present method, the development of a chromatoplate takes 2 minutes which makes the method specially suitable for quick and routine analysis. The apparatus for the collection of samples of alloys and other metallic surfaces for TLC analysis is described. A method for the identification of 19 anions from solution is also included. These anions have been divided into four different groups on the basis of four spray reagents specific for the anions of the group concerned. EXPERIMENTAL

All reagents were of analytical grade or comparable purity. For cations aluminum oxide (D-5, containing 5% calcium sulfate as Materials.

binder, Camag) and silica gel (D-0, without binder, Camag) were used without further treatment for preparation of the thin layers. For anions aluminum oxide S and silica gel S (Hopkin and Williams) were used. The layers were made with Camag applicator having a uniform thickness (ea. 200 microns) and were dried overnight at room temperature (3@32O C.). Apparatus. Circular thin layer chromatographic apparatus (2) was used for development of chromatoplates. Special care was taken to saturate the developing chamber before running the chromatoplates. Preparation of Solution. CATIONS. About 200 mg. of each of t h e following salts of 40 metal ions were mixed together thoroughly with 20 grams of sodium carbonate: Nitrates of Fe+3 Co+*, Zn+2, Te+4, U+e, Zr+', Ni+2:

,ye

ELECTRODE

Group IV PER WIRE LEAD j6'

A.

'WG'

B. C.

TlNUM ELECTRODE

PAPER PLUG.

LING

Sodium sulfide used as spray reagent Yellow ring of Cd+l Is not visible in photograph because of its light color Chromatogram sprayed with dimethylglyoxlme Stannous chloride-KI used as spray reagent Outer-most yellow ring of rhodium is not visible in the photograph because of its light color Ring X is an interfering ring which appears 20 minutes after spray or on heating, and ia characteristic of the spray reagent and the solvent

CAPILLARY

Table 111.

Solvent A

B

+ y e ELECTRODE

Solvents for Separation of Cations and Anions

Composition Acetone, hydrochloric acid (4M), acetylacetone (45:3:2) Acetone, acid (4M) hydrochloric

Group I, I1

I11

(47:3) Acetone, hydrochloric I V acid (4M), acetylacetone (48: 1 . 5 :0 . 5 ) D Acetone, hydrochloric V acid (4M) (46 :4) E Acetone, hydrochloric V acid (concd.) (47:3 ) Fa n-Butanol, pyridine, Anions water, ammonia (8 :4 :8 : 1) After shaking, the upper layer is used. C

SURFACE

Figure 1 .

UNDER

ANA LYSIS

Sampling capillary

Table II. Spray Reagents for Location of Cations and Anions

Reagent Tannic acid (TAW) Tannic acid (TAg) Stannous chloride-potassium iodide (SC-KI)

Solution 10% in water

lOyoin glycerine-water (1: 1)

Dissolve 5 grams SnClz in 10 ml. concd. HC1 and dilute to 100 ml. with addition of 0.5 gram K I 0.05% in a mixture of 96% ethanol and Phenyl fluorone (Pf) concd. KC1 (3:l) Dithizone (DZc) 2y0 in chloroform 0.5% in 96% ethanol Rubeanic acid (RA) 1%in 96% ethanol Diphenyl carbazide (DC) 5y0 aqueous Potassium ferrocyanide (PF) Saturated solution in 967, ethanol Alizarin (AZ) Peroxide-benzidine (PB) Spray with 5% solution of Nan02 in H20 followed by 1% solution of benzidine in glacial acetic acid Quinalizarin (QAZ) 0 . 05Y0 in 7oy0ethanol Sodium sulfide (SS) 27, aqueous Dimethylglyoxime (DG) 1%in 96% ethanol Rhodizonic acid, sodium salt (SR) 1% aqueous, freshly prepared Hydrogen peroxide-NHa(HA) Mixture of HZOZ(30% w./v.) and concd. NHa (1:l) Sodium cobaltinitrite (SCo) Cobaltinitritea (3 parts) mixed with 1 part of methanol Silver nitrate-fluorescein (SF) 1% solution of AgNOa in HzO; after short drying followed by 0.1% fluorescein in alcohol Silver nitrate (S) Aqueous saturated solution Potassium iodide-HC1 (PH) 10% solhion containing 10 ml. HCl (2M) Ferric chloride (FC) 10% solution containing 10 ml. HC1 (2M) Potassium dichromate (PD) Aqueous, saturated solution containing 10 ml. H2SO* (2M) Sodium nitroprusside (SN) 20%, aqueous Ferrous sulfate (FS) lo%, aqueous solution containing 20 ml. HzSOa (2hf) Cobalt acetate, (CH~COO)ZCO.~HZO, (11.4 grams), lead acetate, (CHaCO.O)lPb 3Hz0 (16.2 grams), sodium nitrite (20 grams), and glacial acetic acid (2 ml.) are mixed and solution is made to 150 ml. with water, centrifuged, and filtered (6). 0

Cd+2, Bif3, Pb+2, Hgi2, Cu+l Laf3 K+, Lie, Cs+, Rb+, Ba+2, SrC2: Caf2: MsfZ Ce+3, T h + 4 , Sef4, Al+3, the chlorides of Mn+2, Pd+2, Pt+*, Ru+3, Ge+4, A u + ~ , Sb+K, Sn+4, Ga+3, together with sodium arsenite, chromium sulfate, titanium sulfate, vanadyl chloride, and molybdic acid. Rhodium metal was fused with potassium bisulfate and was mixed with the above. The mixture thus obtained was fused in a platinum crucible, allowed t o cool, and extracted 3 to 4 times with hot dilute nitric acid. The solid left behind was treated with concentrated nitric acid and the solution thus obtained was mixed with the previous solution. The solid mass still left behind was treated with a mixture of H N 0 3 (concd.) and HC1 (concd.) ( 1 : 3 ) and the solution was mixed with the previous solution in nitric acid. The final solution obtained was concentrated by boiling which also eliminated excess acids. ANIONS. iiqueous solutions of sodium or potassium salts of 19 anions (Cf. Table V) were prepared for TLC analysis. The collection of samples of alloys and other metallic surfaces was carried out by a sampling capillary shown in Figure 1 which consists of a platinum VOL 38, NO. 1 1 , OCTOBER 1966

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Table IV. Group

Cation

Rt

Color and spray reagent*

Values of Cations

Solvent *

Sensitivity,

Maximum amount,

W3.O

rI3.d

Remarks

A

I (Chloride group)

Fe +3 Au +a

1.00 0.71

Mo+' V +6

dull violet (TAW) grey to black (TAW) grey to black (SC-KI) dark yellow (TAW) dark blue (TAW)

Ga+3 Sb +6 As +3

Te Ge +4

0.62 0.51

0.06 0.3 0.3 0.6 0.9

24 15 15 67 38

red orange (DZc)

0.98

2.0

50

red orange (DZc) yellow (DZc) dark brown (SC-KI) red (Pf)

0.53 0.51 0.51 0.40

2.5 6.0 0.3 0.7

%} 10 20

heat slightly after spraying clears after spray with glacial acetic acid or by heating afterwards must be sprayed with glacial acetic acid and heated must be heated after spray

A I1 (Thiocyanate group)

I11 (Acetylacetone group)

Pd +2 Pt +4

yellowish brown (RA) reddish purple (RA)

0.95 0.90

0.9 0.3

E}

c o +2

dark brown (RA)

0.85

0.2

26

Zn + 2 Sn +4

red-violet (DC) blue (without spray) red violet (DC) violet (DC)

c u +2

reddish brown (PF) reddish brown (RA)

Ru + 3 U +e

blue (RA) brown (PF) violet (AZ) yellow (PF) violet (AZ) violet (AZ) dark blue (PB) violet (QAZ) violei; (QAZ)

Ti+' Zr +4 Cr +3 La+3 ~ 1 + 3

0.4

26

0.93 0.67 B 0.94

0.3 0.3

30 30

0.15 0.15

6 6

0.51 0.48 1.00 0.39 0.44 0.85 0.51 0.39 0.70

0.1

25 50 50 40 40 40 20 25 6

1 .o 1.0 2.0 1.3 1.3 1.0 2.0 1.0

ap ears after a few minutes or on {eating; sprayer is acidified before use distinct color in NH3 vapor, while Pd and Pt fade out a t 20 pg. or more

in HC1 vapor; turns blue in NHa vapor sprayer acidified on silica gel plate on silica gel plate on silica gel plate only

C IV (Diethyldithiocarbamate group)

v

(Aqueous group)

Cd+Z Bi+3 Pb +2 Se +4 Rh +2 Ni+2 Mn +2

tan to black (SS) tan (SC-XI) yellow (SS) dark brown (SS) brown (SS) red (SC-KI) yellow (SC-KI) red (DG) brown yellow (DG) blue (PB)

Sr+2 Ba+Z Th+4 Ce+3 Mg+2

D ON ALUMINA PLATE red (SR) 0.40 2.2 red (SR) 0.00 2.8 blue violet (AZ) 0.50 1.7 blue violet (AZ) 0.40 2.0 1.3 yellow (HA) 2.0 green black (TAg) 0.70 2.5 violet (AZ)

K+ Rb+ Cs: Li

yellow (SCo) blackish brown (SCo) orange brown (SCo) dark brown (SF)

Hg+z

0.91 0.82 0.56 0.40 0.20 0.97 0 50 Of59

3.0 3.0 2.5 2.0 traces 2.0 0.6 0.3 4.2 2.8

0.40 0.33 0.24 0.91

2.0 2.2 3.5 0.4

15 15 50 120 20 30

3 q 35

11 35 10 20 20 20 8

"40405'1

after spray expose to NHs vapors for 15-20 minutes

fades soon but reappears on heating

appears with difficulty on strong heating "I+, if present, interferes. It may be removed by boiling the solution with NaOH before spotting

4

E ON SILICAPLATE peach (RA) red (RA) red violet (AB) blue violet (AZ) blue violet (AZ) blue violet (AZ) yellow (HA) brown black (TAg) a

0.88 0.00 0.89 0.80 1.00 1.00

1.3

2.0 0.8 1.0 1.3 1.5 1.0 1.5

fade out; reappears on heating appears on exposure to ammonia vapors and heating

Cf. Table 11.

* Cf. Table 111.

Represents the minimum amount of the metal ion in volume of the liquid spotted before extraction. Loss due to extraction has not been taken into account. d Represents the maximum amount of each metal ion which does not interfere with the succeeding rings when all metal ions of a particular group are present to their maximum amount.

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ANALYTICAL CHEMISTRY

electrode placed in a glass tube drawn into a capillary a t one end. The capillary is made to touch the 10% sodium citrate electrolyte solution in order to draw a small amount into the capillary. The platinum electrode is adjusted to remain in contact with the electrolyte solution held by the capillary and is brought in contact with the metal surface under analysis and a 4.5-volt battery is connected between the metal surface and platinum electrode taking care that the platinum electrode always acts a3 a cathode. dfter 1 minute the capillary is withdrawn from the metal surface and the electrolyte from the capillary is transferred to a micro test tube for solvent extraction and TLC analysis. Procedure. The metal ions in the test solution were separated into five different groups by extracting about 0 5 ml. of the test 3olution by the procedure of R e s t and Mukherji (11). The solution was allowed to stand for 2 to 3 minutes and the organic layer was separated with the help of m “dgla” micrometer syringe. Extritction was repeated at least three times to remove completely the cations of the group concerned. The first extraction of each group was performed somewhat quickly (1 to 2 minutes) and the extract was preserved for analysis. Attempts were made to include as many metal ions in the extraction procedure as possible. As a result, the present scheme includes 40 metal ions instead of 35 covered by the original scheme (11). The extraction scheme is given in Table I. For the extraction of group I11 cations, extraction is repeated twice. In the first eytraction in strong acid medium, Cu+*, U+6, Crf3, and are not extracted properly so the pH is adjusted to 4.5 with the addition of sodiuni hydroxide and the eltraction is repeated. For analysis both extracts are combined. The analysis of cations and anions of individual groups as carried out by circular thin layer chromatographic apparatus ( 2 ) . Development of the chromatoplate is complete in 1 to 2 minutes. The plate IS then dried and sprayed with the appropriate reagent to locate the position of different rings.

RESULTS

AND DISCUSSION

I n Table I1 are given spray reagents used for the location of different cations and anions on thin layers ( I ) . Treatment with ammonia can be carried out simply by exposing the plates to ammonical vapors. Five different solvents have been used for the separation of metal ions of various groups while anions of all the four groups can be separated by one solvent (Table 111). The R, values, sensitivity, and maximum amount of cations and anions of different groups are reported in Tables 11’ and V, respectively. In certain groups, more than one spray reagent has been used. I n such cases,

Table V.

Group

Anion

I

I1

R, Values of Anions

Color and spray reagent”

yellow (S) orange (S) yellow (S) blue (FC) yellow orange (S) black (S) blue (S) brown (S) brown (S) brown (FC) bluish green (SN) black (S) red violet (SN) brown (PH) yellow (PH) yellow (PH) yellow brown (PH) black (S)

I11

IV a

b

MaxSensi- imum Solventb tivity, amount, pg. rg*Rf F

brown (FS) yellow (PH) green (FC) blue (FC) brown (FC) brown (FC) brown (PD) green (PD) yellow (S)

0.00 0.00 0.00 0.00 0.10 0.25 0.52 0.63 0.76

0.50 0.00 0.27 0.52 0.62

0.65 0.37 0.00 0.10 0.74 0.21 0.65

0.2 0.5 0.3 1.0 0.1 0.5 1.0 0.7 0.5 0.9 1.5 0.3 2.5 1.0 0.2 3.0 0.2 0.7 1.0 2.7 0.3 0.2 2.0 0.2 2.5 0.8 0.2

Remarks

5.0 7.0 2.0

3.0 3.0 7.5 8.0 17.0 20.0 21.0 20.0 5.0 8.0 8.0 8.0 8.5 3.0 4.0

on prolonged heating

4.0 6.0 9.0 10.0 13.0 3.5

Cf. Table 11. Cf. Table 111.

it is necessary to run a separate chromatogram for each spray reagent. The sensitivity in Table IV indicates the minimum amount of the metal ion which must be present before extraction. While determining the sensitivity on chromatoplate, the loss due to extraction has not been accounted for. The maximum amount (cf. Table IV) indicates the upper limit of each metal ion which does not interfere with the succeeding rings when all metal ions of a particular group are present in their maximum amount. For circular TLC analysis, it is essential that the amount of metal ions and anions spotted on thin layers must lie between sensitivity and the maximum amount (cf. Tables IV and V). The maximum diameter to which the solvent is allowed to spread is about 1 inch and R, values are measured with a fine geometrical divider of the type generally used by draftsmen. To minimize the error, R, values are evaluated by measuring the diameter of the rings obtained on spraying. Special care must be taken in applying spots on chromatoplates because the spot size is of great importance. Spots of smaller size give better results. When analyzing an unknown mixture, it is not necessary to run standard chromatograms because the sequence of separation of different cations and anions remains the same, although

their R, values may differ slightly from those given in Table IV and V. Aluminium oxide was used as adsorbent throughout except from the separation of cations of group V and anions of group 1V for which silica gel was employed. The anions have been divided into four different groups on the basis of four separate spray reagents-viz. silver nitrate, potassium iodide-HC1, ferric chloride, and potassium dichromate. The position of certain anions can also be made visible on thin layers with sodium nitroprusside or ferrous sulfate (cf. Table V). The positions of nine anions of group I are revealed by spraying the chromatoplate with silver nitrate. Though AsOz-, AsOl-, and H2P04- have the same R j value, h s 0 4 - i s confirmed by its orange color while H2P04- and hsO2give yellow color. AsOz- is confirmed to be in group IV by its green color with potassium dithromate. H:PO,is confirmed by its blue color when the chromatoplate is sprayed with ferric chloride. The anions of group I1 are made visible by potassium iodide-HC1 solution and the presence of anions of other groups do not interfere. Spray reagent for group I11 anions is ferric chloride which gives color with ferricyanide, ferrocyanide, sulfocyanide, acetate, phosphate, and iodide. Iodide is conVOL. 38, NO. 1 1 , OCTOBER 1966

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firmed by its brown color with silver nitrate in group I. Both ferrocyanide and phosphate give blue color, have same R, value and remain at the centre. However, phosphate can be confirmed by its yellow color with silver nitrate while ferrocyanide does not give any color. The anions of group IV are detected by spraying the chromatoplate with potassium dichromate. The sampling capillary was successfully employed for taking samples from the surface of the following alloys. The few drops of the solution contained in the sampling capillary were transferred

directly to the TLC plate and the spot ww developed for the suspected group or transferred to a micro test tube for solvent extraction. The elements thus detected are given against each alloy. (1) Nicrome

(2) Chroma1 (3) Brass (4) Misch’s metal

(Ni+*, Cr+a, Fe+a) (&+a, Ni+*) (Cu+2, Zn+2) (Cefa)

LITERATURE CITED

(1) “Chromatography,” p. 132, E. Merck, Darmstadt, 1965. (2) Hashmi, M. H., Shahid, M. A., Ayaa, A. A.,Talanta 12, 713 (1965).

(3) Jakovljevir, M. H., TadiE, I . P., Mikrochim. Acta 1965,937, (4) Meinhard, J. E.,Hall, F. N., ANAL, CHEM.21, 185 (1949). (5) Ibid., 22, 344 (1950). (6) Miller, C. C., Magee, R. J., J . Chem. soc. 1951, 3183. (7) TadiE, I. P., JakovljeviE, M. H., Mikrochim. Acta 1965, 940. ( 8 ) Seiler, H., Helv. Chim. Acta. 45, 381 (1962). (9) Ibid., 46, 2629 (1963). (10) Seiler, H.,Seiler, M., Zbid., 43, 1939 (1960). ~~-..,.

(11) West, P.W., Mukherji, A. K., ANAL. CHEM.31, 947 (1959).

RECEIVEDfor review March 21, 1966. Accepted June 21, 1966.

Separation of Alkyl Sulfides by Liquid-Liquid Chromatography on Stationary Phases Containing Mercuric Acetate WILSON L. ORR Mobil Oil C o p , Field Research Laboratory, Dallas, Texas

A liquid-liquid chromatographic method is described by which alkyl and cycloalkyl sulfides can be separated from most other classes of organic compounds occuring in petroleum and similar complex materials. The stationary phases consist of mercuric acetate in aqueous acetic acid. n-Hexane is the mobile phase. Hydrocarbons and many other compound types are quickly eluted. Sulfides are delayed according to distribution constants which are proportional to the molecular weight or carbon-number. Sulfides with carbon-numbers up to 18 can be separated. Thiols are irreversibly adsorbed and are not recovered.

A

chromatographic method (LLC) has been developed which gives separations of alkyl sulfides from complex mixtures. Alkyl and cycloalkyl sulfides as a group can be completely separated from most other compound types, including saturated and aromatic hydrocarbons, thiophenes, condensed thiophenes, thiols, and aromatic sulfides. The method is applicable to alkyl sulfides with carbon-numbers up to about 18. Alkyl sulfides can be resolved on a carbonnumber or molecular weight basis. A difference in carbon-number of four is sufficient for complete separation; compounds differing by two carbon atoms can be almost completely resolved under optimum conditions. The method is particularly useful for the isolation of low concentrations of LIQUID-LIQUID

1558

ANALYTICAL CHEMISTRY

sulfides from complex materials such as petroleum, petroleum fractions, extracts of bituminous rocks, etc. It is useful also for the small-scale purification of synthetic or commercial sulfides. The use of heavy metal salts, particularly those of mercury, for the separation, purification, and identification of organic sulfur compounds is well known (1-3, 6, 7). The works of Challenger et al. (S), Birch and McAllan (I), and Emmott (4), pointed out the advantages of mercuric acetate over mercuric chloride for sulfide separations because of the water solubility of the mercuriacetates. Lower molecular weight sulfides can be extracted quantitatively from hydrocarbon solutions by using an excess of mercuric acetate in batchwise extractions. Because precipitates are not formed, there is a clean separation between the hydrocerbon and aqueous mercuric acetate phases. Furthermore, fractional extractions with a limited quantity of mercuric acetate will partially fractionate sulfide mixturese. g., cycloalkyl sulfides extract more readily than alkyl sulfides of comparable molecular weight (4). The composition of the mercuric acetate phase determines the molecular weight range of sulfides which can be extracted effectively. However, all previous work has been preparative and only qualitative observations have been reported. Birch and McAllan (1) used an extractant containing about 21y0 mercuric acetate in water slightly acidified with acetic acid. This reagent was reported to extract 5-thianonane (di-n-butyl sulfide) completely from

light petroleum solutions but would not extract an appreciable amount of 7thiatridecane (di-n-hexyl sulfide). Emmott (4) used a reagent composed of 28y0 mercuric acetate in 67y0 acetic acid. The higher content of acetic acid appears to facilitate the extraction of higher molecular weight sulfides since this reagent was reported to extract 7,9 dimethyl 8 thiapentadecane (dicapryl sulfide) effectively. From the literature observations on batch-wise extractions, it was evident that the adaptation of the same phases to liquid-liquid chromatographic systems would greatly extend the usefulness of mercuric acetate separations if the complexing reactions were rapidly reversible. Distribution Behavior of Sulfides between Mercuric Acetate a n d nHexane Solutions. The separation of solutes by liquid-liquid chromatography depends on the distribution of solutes between two liquid phases, one stationary (s) and the other mobile (m). Regardless of the complexity of molecular interactions within the system, the distribution constant, K , which is defined as the equilibrium concentration of the substance in the stationary phase divided by the concentration in the mobile phase :

-

-

-

where [C]. and [C], represent the total amount of the solute per unit volume regardless of molecular state in the respective phases.