ISSN 0027�1314, Moscow University Chemistry Bulletin, 2013, Vol. 68, No. 4, pp. 191–195. © Allerton Press, Inc., 2013.Original Russian Text © V.M. Ivanov, V.N. Figurovskaya, Y.I. Shcherbakova, 2013, published in Vestnik Moskovskogo Universiteta. Khimiya, 2013, No. 4, pp. 216–220.

191

Chromium(VI) compounds are widely used in ana�lytical chemistry. Indeed, the application of potassiumdichromate as a primary standard (this compoundmeets all the primary standard requirements) resultedin the development of dichromatometry. Complica�tions arise when determining the chromium(VI) con�centration in solutions. In this case, the use of a titri�metric analysis variant with iron(II) salts added inexcess and the determination of unreacted iron(II)with a standard K2Cr2O7 solution is associated witherrors due to the incomplete reversibility of the reac�tion of diphenylamine oxidation�reduction indicatorwith chromium(VI) upon the introduction of a reduc�ing agent, e.g., iron(II) [1].

The photometric method for determining chro�mium(VI) may be an alternative for the titrimetricmethod; however, it is distinguished by insufficientsensitivity. The literature data on molar extinctioncoefficients are scarce while being inconsistent

between each other, i.e., 4610 and 750 for Cr and

Cr2 ions, respectively [1, page 41], 5000 (375 nm)

and 300 (456 nm) for Cr ions and 1500 (349 nm)

for Cr2 ions [2]. The absorption maxima of theseforms are located at 373 [1, page 41], 375, and 456 [2]nm. Despite this, the method is widely used to deter�mine large amounts of chromium in various objects. Itis preferred to use acidic media, although the sensitiv�ity is lower and, under these conditions, the specificityis higher. In this case, oxidation�reduction side reac�tions only occur in the presence of reducing agents,which may be easily addressed. On the contrary, the

sensitivity of determination in the Cr form is sev�eral times higher, but the selectivity is considerably

O42–

O72–

O42–

O72–

O42–

lower due to the poor solubility of many metal chro�mates, including those of Ag+ and divalent metals.

It was shown [3] that chromaticity characteristicsof complexes of many elements are 1.5–2 ordershigher than the coefficients of molar extinction. Thereare no such characteristics for chromium in the litera�ture.

The aim of this work is to determine the chromatic�

ity characteristics of chromium(VI) in the Cr and

Cr2 forms.

EXPERIMENTAL

Reagent and solutions. The initial solution ofK2Cr2O7 was prepared from an accurately weighedsample of recrystallized specimen of chemically puregrade and contained 5.0 mg/mL of chromium(VI).5 M H2SO4 and 0.05 M Na2B4O7 ⋅ 10H2O preparedfrom specimens of chemically pure grade were used.The acidity was varied using mixtures of these solu�tions.

Apparatus. The absorption spectra of solutionswere recorded on a Hitachi U�2900 spectrophotome�ter (l = 1 cm). The optical density was measured on aKFK�3�01 photometer (l = 1 cm), and the chromatic�ity functions were determined on a Spektroton colo�rimeter (OKBA Khimavtomatika, Chirchik, Russia)(l = 0.5 cm); the pH values of solutions were con�trolled by an ESL�43�07 glass electrode on a universalEV�74 ionomer. The following chromaticity functionswere measured: X, Y, and Z are color coordinates inthe XYZ system; L, A, and B are color coordinates inthe CIELAB system; L, S, and T are lightness, satura�tion, and color hue, respectively; W is index of white�ness; and G is the index of yellowness.

O42–

O72–

Chromaticity Characteristics of Chromium(VI) SolutionsV. M. Ivanov, V. N. Figurovskaya, and Y. I. Shcherbakova

Moscow State University, Department of Chemistry, Moscow, Russiae�mail: mvonavi@mail.ru

Received March 1, 2013

Abstract—The light�absorption spectra of solutions of chromium(VI) in the form of dichromate (pH 1–5)and chromate (pH 7–9) have been studied. The solutions have maxima of light absorption at 360 and 380 nm

and molar extinction coefficients of 155 ± 7 and 935 ± 27 for Cr2 and Cr respectively. The chroma�ticity functions of these chromium(VI) forms have been investigated and it has been shown that they are 1.0–1.5 orders of magnitude higher than the molar extinction coefficients. In all cases, the yellowness is maximal.

Keywords: chromate ions, dichromate ions, optical and chromaticity characteristics

DOI: 10.3103/S0027131413040056

O72–

O42–

,

192

MOSCOW UNIVERSITY CHEMISTRY BULLETIN Vol. 68 No. 4 2013

IVANOV et al.

Procedure. The standard solution of K2Cr2O7 in theamount of 1–5 mL and the required amounts of sulfu�ric acid or sodium tetraborate solutions were intro�duced into 25�mL volumetric flasks, water was addedto the mark followed by mixing and pH control, thespectra of light absorption were recorded, and theoptical density or chromaticity characteristics weremeasured.

Calculations. The coefficients of molar extinctionfor chromium(VI) forms were calculated by the least�squares method using Origin 6.0 software. The molarcoefficients of chromaticity functions were calculatedby analogy with the coefficients of molar extinction inthe range of the linearity of the function at a variablechromium concentration (l = 0.5 cm).

RESULTS AND DISCUSSION

Acid–Base Characteristics

Despite the stability of chromium(VI) in solutions,its behavior is rather complicated and includes notonly monomerization�dimerization

Cr → Cr2 ,

but also the protonation of these ions. It is believed [1,

page 15] that the transformation of Cr into

Cr2 occurs through a protonation step to form

HCr followed by dimerization. The equilibrium

2 Cr + 2 H+ = Cr2 + H2O

is rather mobile and established quickly. The acidsthemselves differ in strength at the second stage of dis�sociation as follows [1, page 15; 4]:

HCr2 = H+ + Cr2

K2 = 2 × 10–2 (pK2 = 1.70),

HCr = H+ + Cr

K2 = 3 × 10–7 (pK2 = 6.52).

O42– O7

2–

O42–

O72–

O4–

O42– O7

2–

O7– O7

2–

O4– O4

2–

For the reaction

Cr2 + H2O = 2 HCr = 2 H+ + 2 Cr ,

the equilibrium constant is equal to 7.9 × 10–13 [5,page 259]. For H2CrO4, the following data are givenpK1 = 4.72; pK1 = 6.04; pK2 = 6.57; pK2 = 6.43; logβ2

= 11.29 and logβ2 = 12.47. This inconsistency cannotbe considered satisfactory. At the same time, the num�ber of methods used to determine these constants islimited; in particular, it is not possible to use an infor�mative and sensitive method, such as spectrophotom�etry, which, in this case, allows one to study only thedimer�to�monomer transformation, not the degree ofprotonation of these forms. At the same time, one mayassume that dichromate ions are predominantlyformed at pH < 1, while chromate ones are formed atpH > 7.5.

Absorption Spectra

The absorption spectra in acidic medium (pH 1.0)have a minimum at 310 nm, a maximum at 360 nm, anda shoulder of very low intensity at 450–470 nm. Theabsorption spectra in alkaline medium (pH 8.5–9.2)have a minimum at 310 nm and one intense maximumat 380 nm (Fig. 1). The curves intersect in two isobesticpoints (340 and 450 nm). Although solutions of

Cr have yellow coloration, whereas those of

Cr2 are orange colored, the maximum of light

absorption of Cr2 solutions is located in a shorterwavelength region. Most likely, the color may beexplained by the presence of a second maximum thatis hardly used for analysis.

Wavelengths of 360, 380, and 450 nm were chosen

as characteristic of individual Cr2 and Crforms and for their mixture, respectively.

O72– O4

– O42–

O42–

O72–

O72–

O72– O4

2–

0.90

300

0.70

0.50

0.30

0.10

340 380 420 460 500 540 580

A

λ, nm

1

2

Fig. 1. Spectra of light absorption of chromium(VI) solutions at pH of (1) 1.0 and (2) 9.2. Solutions contain 1 mg of chromiumin 25 mL.

MOSCOW UNIVERSITY CHEMISTRY BULLETIN Vol. 68 No. 4 2013

CHROMATICITY CHARACTERISTICS OF CHROMIUM(VI) SOLUTIONS 193

Influence of pH

The influence of pH on optical density is illustratedin Fig.2. One may distinguish two plateaus of opticaldensity: at pH of 1.3–5.0 (A360 = 1.38 ± 0.02; A380 =0.97 ± 0.02; n = 15) and at pH of 7.1–9.3 (A360 =2.35 ± 0.07; A380 = 2.53 ± 0.04; n = 7); and in theisobestic point A450 = 0.19 ± 0.02 (n = 7). These valuesvalidate the choice of wavelengths for studying anddetermining individual forms of chromium(VI).

Calibration Plots and Coefficients of Molar Extinction

The linearity ranges of calibration plots depend onthe chosen form of chromium(VI): they are 0.5–2.5 mgin 25 mL (1.92 × 10–4–0.96 × 10–3 M as recalculated

for chromium dimer) for Cr2 and 0.1–0.5 mg in

25 mL (7.69 × 10–5–3.84 × 10–4 M), as well as 0.5–2.5 mg

in 25 mL (3.84 × 10–4–1.92 × 10–3 M) for Cr asrecalculated for chromium(VI). The molar extinctioncoefficients were calculated from calibration plots andequations for them (Table 1).

O72–

O42–

Upon measuring the optical density in the isobesticpoint (450 nm), the following molar extinction coeffi�cients were obtained: 113.6 (pH 1.0) and 230.5 (pH 9.2)

for Cr2 and Cr forms, respectively. It isimportant to note that the slopes of calibration plotsdepends on how the chromium(VI) concentration is

expressed; they are higher for Cr2 when the con�centrations are expressed in mg/25 mL, but lowerwhen the concentrations are expressed in M due to thedimerization of chromium(VI) in acidic medium. It isnot known whether the authors of other publicationstook this into account. For comparison, Table 2 con�tains the optical densities in the absorption maxima ofthese forms, with the chromium concentrations beingexpressed in mg per 25 mL of solution.

Chromaticity Characteristics

The chromaticity characteristics were determinedfor solutions that obey the Beer’s law (Tables 3 and 4).Equations of the dependence of the chromaticityfunctions on concentrations were derived based onthese data (Table 5).

O72– O4

2–

O72–

3

00

2 4 6 8 10

1

2

A

pH

1

2

3

Fig. 2. Effect of pH on the optical density of chromium(VI) solutions at (1) 360, (2) 380, and (3) 440 nm. The solutions contain5 mg of chromium in 25 mL.

Table 1. Equations of calibration plots (CPs) and molar extinction coefficients for chromium(VI) forms (n = 5)

Chromium(VI) form

Linearity range of CPλ, nm pH Equation of CP

(C is expressed in M) ε

mg in 25 mL M

0.5–2.5 (1.92–9.6) × 10–4 360 0.9 A = 309.1C 155 ± 7

380 0.9 A = 223.7C 112 ± 3

0.1–0.5 (0.77–3.84) × 10–4 360 380

9.2 9.2

A = 578.8C A = 944.3C

580 ± 13 935 ± 27

Cr2O72–

CrO42–

194

MOSCOW UNIVERSITY CHEMISTRY BULLETIN Vol. 68 No. 4 2013

IVANOV et al.

Table 2. Data for calibration plots at different acidity

Chromium(VI) concentrationpH A360 A380

mg in 25 mL M × 104

0.5 1.92 0.9 0.126 0.089

1.0 3.85 – 0.230 0.170

1.5 5.77 – 0.354 0.217

2.0 7.70 – 0.470 0.340

2.5 9.62 – 0.600 0.434

0.1 0.77 9.2 0.044 0.076

0.2 1.54 – 0.090 0.140

0.3 2.31 – 0.135 0.218

0.4 3.08 – 0.175 0.290

0.5 3.84 – 0.224 0.364

Table 3. Chromaticity characteristics of chromium(VI) solutions at pH of 3.6

Concentration*Characteristic

0.5 1.0 1.5 2.0 2.5

X 84.82 83.29 82.29 81.13 79.66

Y 87.77 87.04 86.91 86.46 85.70

Z 95.14 87.34 80.57 74.36 67.97

L 95.06 94.75 94.70 94.50 94.18

A –2.30 –3.85 –5.53 –6.89 –8.33

B 5.40 10.08 14.79 19.10 23.60

S 5.87 10.79 15.79 20.30 25.03

T 113.10 110.90 110.50 109.80 109.40

W 92.33 87.99 83.33 78.96 74.29

G 8.80 16.10 22.94 28.90 34.91

* Horizontal row contains chromium concentration in 25 mL.

Table 4. Chromaticity characteristics of chromium(VI) solutions at pH of 9.0

Concentration*Characteristic

0.5 1.0 1.5 2.0 2.5

X 79.47 82.27 82.04 81.21 80.15

Y 82.99 87.04 87.61 87.63 87.26

Z 88.38 86.89 81.69 76.57 72.08

L 93.01 94.75 94.99 95.00 94.84

A –3.69 –5.80 –7.26 –8.88 –10.20

B 6.37 10.40 14.49 18.27 21.46

S 7.36 11.91 16.22 20.32 23.80

T 120.10 119.20 116.70 115.90 115.60

W 89.84 86.98 83.02 79.07 75.64

G 9.68 15.15 21.02 26.00 29.99

* Horizontal row contains chromium concentration in 25 mL.

MOSCOW UNIVERSITY CHEMISTRY BULLETIN Vol. 68 No. 4 2013

CHROMATICITY CHARACTERISTICS OF CHROMIUM(VI) SOLUTIONS 195

It can be seen from Table 5 that the coefficients ofchromaticity functions are higher than the molarextinction coefficients; however, in contrast to the lat�ter, they either decrease (the functions X, Y, Z, L, A, S,T, and W) or increase (the functions B and G) with anincrease in the concentration of analyte as opposed tothe calibration plots in photometry. We determined thechromaticity functions at a layer thickness of 0.5 cm,whereas the molar extinction coefficients were deter�mined at a layer thickness of 1 cm (due to peculiaritiesof calorimetry apparatus). Due to the absence ofapproaches for calculating the chromaticity charac�teristics at different layer thicknesses, one may onlyspeak of the tendency of the chromaticity characteris�tics to change upon changes in the layer thickness.

REFERENCES

1. Lavrukhina, A.K. and Yukina, L.V., in Analiticheskayakhimiya khroma (Analytical Chemistry of Chrome),Moscow, 1979.

2. Sharlo, G., Metody analiticheskoi khimii (AnalyticalChemistry Methods), Moscow, 1965, p. 911.

3. Ivanov, V.M. and Kuznetsova, O.V., Russ. Chem. Rev.,2001, vol. 70, no. 5, pp. 357–372.

4. Averbukh, T.D. and Pavlov, P.G., Tekhnologiyasoedineniya khroma (Technology of Chrome Com�pounds), Leningrad, 1967.

5. Osnovy analiticheskoi khimii. Prakticheskoe rukovodstvo(Fundamental Analytical Chemistry: Practical Man�ual), Zolotov, Yu.A., Ed., Moscow, 2003.

Translated by M. Makarov

Table 5. Linear equations of calibration plots for chromaticity characteristics of chromium(VI) solutions at pH of 3.6 and 9.0

FunctionChromium(VI) concentration (pH of 3.6) Chromium(VI) concentration (pH of 9.0)

mg in 25 mL M mg in 25 mL M

X –1.248C + 85.983 –3244.6C +85.983 –1.959C + 85.267* 78.044C + 80.938*

Y –0.472C + 88.192* –1227.1C + 88.192* –0.878C + 88.306* 2375.1C + 83.767*

Z –6.732C + 101.27 –17502C + 101.27 �10.579C + 96.62 –11165C + 93.998

L –0.201C + 95.241* –522.56C + 95.241* –0.376C + 95.292* 1017.2C + 93.345*

A –1.51C – 0.85 –3925.7C – 0.85 –1.61C – 2.336 –4185.7C – 2.336

B 4.543C + 0.964 11811C + 0.964 3.804C + 2.785 9891.2C + 2.785

S 4.783C + 1.204 12437C + 1.204 –4.128C + 3.538 –10732C + 3.538

T –0.85C + 113.29* –2209.8C + 113.29* –1.230C + 121.19* –3197.8C + 121.19*

W –4.511C + 96.913 –11728C + 96.913 –3.631C + 93.803 –93.803C + 93.803

G 6.502C + 2.824 16904C + 2.824 5.148C + 4.925 13383C + 4.925

* Equations are nonlinear, and correlation coefficient R2 < 0.9.