1422
Anal. Chem. 1984, 56, 1422-1428
(15) Lazarou, L. A.; Hadjlioannou, T. P. Anal. Chem. 1979, 5 1 , 790. (16) Mark, H. B.; Rechnitz, G. A. "Kinetic in Analytical Chemlstry"; Interscience: New York, 1968. (17) Kolthoff, I. M.; Medalia, A. I. J . Am. Chem. SOC.1947, 7 1 , 3777. (18) Feial. F. "SDOt Tests in Oraanic Analvsis": Elsevier: New York. 1956.
(21) Guilbault, 0.G.; Brignac, P.; Zinner, M. Anal. Chem. 1968, 4 0 , 190. (22) Pilipenko, A. T.; Shevhenko, T. L.; Volkova, A. I . Zh. Anal. Khim. 1977, 32, 731.
Color Changes in Screened Indicators Elisabeth Bosch, Enric Casassas, Alvaro Izquierdo,* and Marti Roses Departament de Qdmica Analhica, Universitat de Barcelona, Barcelona, Spain
Several eff lcient screened lndlcators are prepared by use of complementary trlstlmulus data of different acld-base Indlcators and screenlng dyes. The results show that color changes from one pure acld-base lndlcator and dlfferent dyes, when represented In the complementary chromatlclty dlagram, are on the same chromatic straight ilne. For a varlety of neutrallratlon indlcators the equatlon deflnlng thls line from the color parameters of the indlcator is developed theoretlcally and compared with the experlmentai equatlon. An expression Is developed defining the best screened lndlcator that can be prepared from a given pure acid-base indlcator and dyes in order to obtaln the optlmum color change. Thls optimum color change always occurs between two compiementary colors with the same relative grayness.
The chromaticity system CIE (1,2),which specifies each color by means of three coordinates X , Y, and 2 (R) was developed for characterization of additive colors and it does not allow the treatment, in a simple way, of subtractive colors such as the ones encountered in indicator solution. Reilley et al. ( 3 , 4 )proposed use of absorbance instead of transmittance in the computation of the chromaticity coordinates, designated X,, Y,, and 2, (R,) in this case, thus introducing the complementary tristimulus colorimetry which renders the subtractive color coordinates additive. It is difficult to plot a color point in a X-Y-2 or Xc-Yc-Zc three-dimensional space; therefore, x , y, z (1) or Q,, Qy, Q, (QJ coordinates are usually used ( I - 3 , 5 ) . These coordinates represent the color vector direction and they can be plotted in a x-y or Q,-Q, bidimensional chromatic diagram. The Q, coordinates are constants for each colored species and are independent of the concentration and path length. Since R, coordinates are additive for subtractive color systems, it is possible to calculate easily the coordinates of a mixture of two colored species, like both forms of an acidbase indicator, at any pH value within the color change range (8) and thus the pK, of this indicator ( 4 , 9 ) . To specify more accurately a color, Reilley and co-workers (3) introduced color parameters such as the color concentration, J , which depends on the experimental conditions concentration and path length, and the relative grayness, g, which measures the dirtiness of a color. Complementary tristimulus colorimetry finds an important application in the screening of indicators, since it allows calculation of the concentration ratio that the pure indicator and the screening dye have to hold in order that the screened indicator shows a gray color a t a certain pH value (3,9). The present work studies different screened indicators and it shows 0003-2700/84/0356-1422$01.50/0
that all the screened indicators which may be prepared from the same pure indicator and different screening dyes show color changes that, when plotted in the complementary chromaticity diagram, are on the same straight line. Parameters for this line can be calculated from the color parameters of the pure indicator alone. As a consequence the color changes of all the possible screened indicators to be prepared from this pure indicator can be calculated easily. In this paper equations are proposed to calculate the optimum concentration ratio for a screened indicator prepared from a given pure indicator and different screening dyes in order to obtain the best color change, occurring between two complementary colors with the same relative grayness. For this study the indicators chosen are several semicarbazones and thiosemicarbazones from 1,2-naphthoquinone (NQS), derivatives, i.e., 1,2-naphthoquinone-2-semicarbazone 1,2-naphthoquinone-2-semicarbazone-4-sulfonic acid (NQS4S), 1,2-naphthoquinone-2-thiosemicarbazone-4-sulfonic acid (NQT4S) (studied and described as indicators in a previous paper (IO)), and 1,2-naphthoquinone-2-thiosemicarbazone (NQT), whose characteristics are given here. These compounds have been selected for the following reasons; (a) their color transitions (from yellow shades to reds) take place between noncomplementary colors and this fact makes them specially suited for preparation of screened indicators with dyes; (b) their color change pH ranges are in basic media where only a few two-color indicators are described (11).
EXPERIMENTAL SECTION Apparatus. For complementary chromaticity coordinated determination an Acta M-VI1 Beckman spectrophotometer with 10-mm cells, to record spectra, and a Rockwell AIM-65 20 K RAM microcomputer were used. The pH of solutions was measured with a Radiometer pH meter (Model PHM64) with a glass/ calomel combined electrode, GK 2401 B. Chemicals. NQS, NQSIS, and NQT4S were synthesized and purified as reported in a previous paper (IO);NQT was prepared according to Luque et al. (12). The characteristics of NQT are the following: mp, 182 OC; IR (KBr) 3420,3270, and 3150 cm-l (NH), 1505,1425,1310,and 965 cm-l (NCS) agree with literature data (13-15). Anal. Calcd for CllN3H90S: 57.1, C, 18.1 N, 3.9 H, 13.8 S. Found: 57.0 C, 16.3 H, 3.9 H, 13.8 S. NQS, NQS4S, and NQT4S were used in aqueous solutions and NQT was used in ethanol/water 1:4 (v/v) solution. The commercial indicators studied were Methyl Orange, Bromocresol Green, Methyl Red, and Phenol Red from Eastman-Kodak (ACS); and the dyes, reported in Table 11, where supplied by Sandoz, except picric acid, Doesder (ACS), and Methylene Blue and Indigo Carmine, Scharlau. Buffer solutions used covered the pH range from 3.3 to 11.8, and they were prepared at the constant ionic strength I = 1 M (16). 0 1984 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984 1423 START
1
7 INPUT INDICATOR DATA
1-
CALCULqTE &PRINT
1 CALCULATE
R,. Q , . J
1
ro OF DYES?
CALCULATE Q;
1 CALCULATE 0
1
Figure 2. Division of chromatlclty diagram in triangles to calculate 0:.
PRINT ALL
1 END
COLOR
8' DYE "2"?
GRIS
DYES ?
Figure 1. Line flows of the COLOR and QFIISprograms.
M pure indicator solutions, at different Procedure. The pH vaIues, prepared from M stock solutions and the appropriate buffer solution (to obtain I = 0.1 M), are added to the cell and its absorption spectrum is recorded. For screened indicators the solution is prepared from lo4 M pure indicator stock solution plus aqueous screening dye (or dyes) solution, the pH adjusted, and the spectrum recorded. Absorbance digital data of each solution is taken from 770 to 380 nm at 10-nm intervals. It has been verified that the dyes used do not show any color change within the pH range studied. The temperature was 25 f 1 "C. Computation Method. The weighted ordinate method, Ax = 10 nm, recomended by Kotrly et al. (5) with the coefficients given by Judd (2) was used. Two linear computer programs written in BASIC were developed, one to compute the chromaticity coordinates, color concentration, and relative grayness (COLORprogram) and the other to compute the screened indicators composition and their color changes (GRIS program) (Figure 1). To compute the relative grayness, g, it is necessary to know the coordinates of the spectrum color (8,") of each color point (Q,).Since there is no linear relationship between Q," and Qyo in the chromaticity diagram, this diagram has been divided in 20 triangles (Figure 2), in such a way that within each triangle Q," can be considered a linear function of Q,". Then, any color point (Q,) is placed by the program in the appropriate triangle and Q," is calculated as an intercept of the line that joints G , and Q, points with the triangle boundary of spectnun colors. To divide the chromaticity diagram into triangles, we have used the coordinates of 20 spectrum colors, given by Judd ( 2 ) . RESULTS AND DISCUSSION Indicators. The complementary chromaticity coordinates (Q,),the color concentration values (J) and the relative grayness (9) of each indicator at different pH values are given in Table I. Figure 3 shows the observed color changes plotted
Figure 3. Color changes of indicators in the complementary chromaticity diagram: (+) NQS; (W)NQS4S; (0)NQT; (A)NQT4S.
on the chromaticity diagram. The pKa value of each indicator and its complementary chromaticity coordinates, at every point inside the pH range of color change, are related by the equation
where the subscripts a and b refer to the acidic and basic forms of the indicator and the subscript I refers to the mixture of both forms a t any pH value inside the transition range. pKa values are best obtained from that chromaticity coordinate whose values show the greatest variation within the pH range of color change. The results, with their range, are the following: NQS, 9.62 f 0.03; NQS4S, 8.74 f 0.03; NQT, 9.27 f 0.02; and NQT4S, 8.34 f 0.02. The color change pH range of each indicator can be obtained from the plot of A J / A pH vs. pH according to Cacho et al. Figure 4. Dyes. The color parameters of the dyes studied are given in Table 11. Since Indigo Carmine decomposes quickly in basic medium and since the zinc chloride present as double salt in the Methylene Blue available interferes with the color change of the studied indicators, because it forms colored complexes (10, 15), these dyes have not been tested as screening dyes.
(In,
1424
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984 -
Table I. Complementary Chromaticity Values for the Color Changes of Some Acid--Base Indicators substance NQS (5.10 x 10-5 M)
NQS4S (4.92 x
M)
NQT (3.16 x 10-5 M)
NQT4S (4.42 X
lo-'
M)
PH 1.155 5.287 6.554 8.050 8.866 9.221 9.506 9.870 10.002 10.317 11.217 12.650 1.140 3.357 6.531 7.392 7.882 8.210 8.500 8.625 8.874 9.013 9.533 9.903 12.782 1.167 5.595 7.308 8.226 8.453 8.667 8.943 9.160 9.311 9.519 9.686 10.561 11.761 13.230 1.110
3.347 6.503 7.400 7.940 8.178 8.361 8.520 8.781 9.082 9.452 9.834 10.250 10.703
QX
0.145 0.145 0.144 0.143 0.140 0.137 0.137 0.135 0.134 0.133 0.132 0.132 0.151 0.150 0.150 0.147 0.142 0.139 0.135 0.134 0.131 0.131 0.128 0.128 0.127 0.139 0.141 0.147 0.156 0.163 0.170 0.181 0.193 0.198 0.206 0.210 0.224 0.222 0.222 0.140 0.140 0.146 0.155 0.165 0.170 0.176 0.180 0.186 0.190 0.192 0.194 0.194 0.193
QY
0.053 0.054 0.054 0.069 0.122 0.162 0.196 0.226 0.236 0.248 0.259 0.257 0.034 0.036 0.040 0.052 0.075 0.099 0.120 0.128 0.142 0.148 0.162 0.167 0.170 0.123 0.129 0.146 0.183 0.210 0.237 0.282 0.321 0.341 0.371 0.387 0.434 0.436 0.436 0.078 0.079 0.108 0.156 0.229 0.268 0.299 0.326 0.360 0.386 0.403 0.410 0.412 0.408
Q, 0.802 0.802 0.801 0.788 0.738 0.701 0.667 0.639 0.630 0.618 0.609 0.611 0.816 0.814 0.810 0.801 0.783 0.763 0.745 0.738 0.726 0.721 0.710 0.706 0.703 0.738 0.730 0.707 0.661 0.628 0.593 0.537 0.486 0.461 0.423 0.403 0.341 0.342 0.342 0.782 0.781 0.746 0.689 0.606 0.562 0.525 0.494 0.454 0.424 0.405 0.396 0.394 0.399
J
g
0.285 0.285 0.286 0.299 0.365 0.440 0.533 0.650 0.692 0.760 0.845 0.851 0.280 0.279 0.285 0.316 0.356 0.419 0.484 0.523 0.601 0.638 0.756 0.795 '0.836 0.409
0.39 0.39 0.39 0.51 0.64 0.63 0.62 0.60 0.58 0.56 0.55 0.54 0.28 0.30 0.40 0.45 0.52 0.56 0.54 0.53 0.50 0.50 0.48 0.48 0.47 0.62 0.68 0.82
0.411
0.420 0.456 0.475 0.501 0.550 0.602 0.639 0.688 0.716 0.836 0.872 0.877 0.525 0.528 0.544 0.601 0.662 0.711 0.766 0.815 0.879 0.943 0.982 1.002 1.011 1.014
1.01
1.10 1.18 1.23 1.27 1.25 1.22 1.20 1.08 1.05 1.05 0.50 0.50 0.77 1.04 1.09 1.07 1.06 1.03 0.99 0.94 0.92 0.91 0.90 0.90
Table 11. Complementary Chromaticity Values for Some Screening Dyes abbreviations used in (2.1. no. dye this paper (20) picric acid PA 10 305 Solar Yellow BG 19 555 SY Pyrazol Blue G PB Solar Blue 2GLN SB Cartasol Blue 2GF CB 24 400 Indigo Carmine 73 015 IC Methylene Blue MB 52 015 Xilene Blue VS XB 42 045 Sandolan Turquoise E-AS 42 080 ST Alizarine Light Green GS AG 61 570
C, mgiL
26.6 45.0 43.4 31.4 26.7 24.6 14.0 10.1 16.6 60.0
Screened Indicators. The method proposed by Flaschka (9) and by Reilley et al. (3) has been used for calculating the
Q X
0.164 0.152 0.408 0.434 0.463 0.499 0.587 0.592 0.594 0.428
QY
0.013 0.048 0.451 0.435 0.432 0.422 0.381 0.375 0.371 0.336
Q,
J
g
0.824 0.800 0.141 0.132 0.107 0.078 0.031 0.033 0.036 0.235
0.253 0.630 1.191 1.178 0.893 0.817 0.620 0.298 0.365 0.872
0.05
0.62 0.36 0.34 0.26 0.19 0.07
0.08 0.09
1.45
composition of the screened indicators. In accordance with this method, a mixture of i colored species will yield a gray
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984 lor2
color if it complies with the following equation:
+ Ci miJiQri
QrbJb
n CVriJ[
=0
(2)
Qrb'
1
where J{ is the color concentration of the colored species "i" in the mixture and (3) Vri = Qri - GI Applying eq 2 to a screened indicator prepared by mixing a volume of stock solutions of indicator at a given pH and volumes of screening dyes "1"and "2",at volume ratios, from screening dye to indicator equal to ml and m2, respectively, the following equations are obtained (9):
(4)
(5)
where J I , Vxr, Vy, refer to the indicator at the pH of the gray point of the mixture and ml, J1,V x l ,Vyl, m2, J2,Vxz, and Vs2 refer to the screening dyes "1" and "2", respectively, at the same pH. Screened indicators with two dyes and with a single dye have been prepared. In the single-dye case the end point depends only on the dye used, because there is a unique intermediate form of the indicator which, mixed with the dye, can give a gray color. The coordinates of this intermediate form can be determined by the intersection of the line that joins the dye color point Qrl and GI with the line which represents the color change of the indicator. From eq 1 the end point pH value of the screened indicators can be calculated. From it and from eq 2 the mixture composition can be derived by means the following relation:
m1=--
1425
= J b
+
C miJi i
These expressions allow the calculation of the limits of the color change of the screened indicator. (We will indicate the screened indicator with the slanted prime to differentiate it from the single indicator). The plot in the chromaticity diagram of the calculated color changes for various screened indicators prepared from the same indicator and different dyes shows that all the color points of the acidic and the basic forms of the different screened indicators are on the same straight line, independent from the end point pH value and from the screening dyes used. This is a general behavior for all screened indicators, shown by the ones proposed in this paper and confirmed with several other screened indicators commonly used which have been prepared from commercial indicators whose coordinates, experimentally determined, agree with known literature data (4,18,19) and from screening dyes. Coordinates for these dyes are reported in Table I1 and in ref 19 (Figures 5 and 6). The equation of this straight line may be derived as follows: The slope of the line which represents the color change of a screened indicator is given by
Q.,"'- G., S=
-J'
J
QxL - Gx
Applying eq 7 to an indicator and n - 1 screening dyes and substituting into (11) gives n-1
Gy) + C J((Qyi
J,'(Qya
-
J,'(Qxa
- Gx)
- Gy)
i
S=
(12)
n-1
+ Ci Ji'(Qxi - G x )
According to eq 2 and 3 it can be written n-1
CJi'(Qri - GI) = -JI'(Qrl
JI VI1
i
J1 VI1
(10)
lor2
-
GI)
(13)
Introducing (8) and (13) into expression 12 gives
where JIand VI, refer to the end point of the indicator and ml,J1,and VI, refer to screening dye. Since the color vectors in the three-dimensional complementary color space are additive, it is possible to foresee the utility of a hypothetical screened indicator from a previous calculation of its color change by the following equations, which give the coordinates of a mixture of colored species at different concentrations
C '
S=
>Ja(Qya Ca
c,'
- Gy)
-
CII -JICQ,I CI
- Gy)
(14)
CI'
-Ja(Qxa Ca
- Gx) - -JI(Q~I - Gx) CI
In this equation any intermediate form of the indicator is treated according to its own color, although chemically it is a mixture of two forms. Therefore ca = cI and c,' = c i and (14) become Ja(Qya
S=
Ja(Qxa
- G y ) - JI(QYI - G y ) - Gx) - J I ( Q ~ I - Gx)
(15)
If the intermediate form of the indicator is considered really as a mixture of its acidic and basic forms, eq 7 and 8 can be applied and results in where Q;, J{,and c[ (concentration) refer to the mixture and Qri, J i , and ci refer to the stock solutions. Then c{/ci is the dilution factor of the colored species. If we consider the n colored species to be the acidic or basic form of the indicator and one or two screening dyes, we can write, according to ( 7 ) and (8) QraJa
QrL = Ja
+
1 or 2 miJiQri i 1 or 2
E
+ Cc miJi
where JI = qJa (1 - Q)Jb (17) and q is the mole fraction of the indicator in acidic form. Substituting these expressions into eq 15, the following is obtained
(9)
Ja(Qya
S =
Ja(Qxa
+ Jb(Qyb - G y ) - Gx) + Jb(Qxb - G x ) - Gy)
(18)
1426
ANALYTICAL CHEMISTRY, VOL. 56,NO. 8, JULY 1984
t,
Figure 4. Color concentration changes of indicators wkh p H (+) NQS; (B) NQS4S; (e)NQT; (A)NQT4S.
08
“Yi
I
I
I
I
1
I
0.2
I
, 9 ,I
, ,
OS3
1
1
Q,
1
I
,
,
, I , ,
0.4
,,
I
,I
“1----I 0.3
t
F-l
1
0.351
-
0.3
I
Figure 8. Color changes calculated for some screened indicators with dlfferent dyes (one or two). The gray point pH values are given together with the dyes. (A) Methyl Orange with CB pH 4.04; I C pH 3.79; MB pH 3.44; MB/PA pH 3.0, 2.5; (0) Bromocresol Green with Cochenille Rot A pH 4.62; Phenosafranin pH 4.52; Victoriarubin 0 pH 4.49; Phenosafranin/Alizarin-ViolanolR pH 4.25; Alizarin-Violanol R pH 3.80; (0) Methyl Red with CB pH 5.51; IC pH 5.38; MB pH 5.19; MB/PA pH 4.7, 4.5, 4.0; (0) Phenol Red with CB pH 7.17; MB pH 7.39; AG pH 7.42; MB/PA pH 8.5, 9.0.
-
0.4
I
NOS
0.35
0.25
0.3
~
0.2
Os3
Q,
0.4
Figure 5. Color changes calculated for some screened indicators with different dyes (one or two). The gray point pH values are given together NOS with SB pH 9.1 1; CB pH 9.40; PB/CB pH 9.0, 9.2; the dyes: (0) CB/ST pH 9.6, 9.8, 10.0, 10.2; (0) NQS4S with PB pH 8.03; SB pH 8.90; PB/CB pH 8.2, 8.4, 8.6, 8.8, 9.0; (0)NQT with XB pH 8.99; ST pH 9.0; AG pH 9.01; CBlST pH 8.8; ST/PA pH 9.2, 9.4, 9.6, 9.8, 10.0, 10.2; (A)NQT4S with CB pH 7.84; XB pH 8.28; ST pH 8.30; CB/ST pH 8.0, 8.2; ST/PA pH 8.4, 8.6, 8.8, 9.0, 9.2, 9.4.
This expression shows that the slope of the line for the different screened indicators can be calculated from the indicator color parameters and that the slope is independent from the gray point pH value and from the screening dyes used. These dyes only define the limits of the color change, but this one is always on the same line. Figure 7 shows experimental color points at various pH values obtained from some screened indicators prepared from the same indicator (NQS, NQS4S, NQT, NQT4S) and different screening dyes. Equation 18 has been tested by comparing the calculated S values (Scdcd) with the values obtained by lineal regression from the color points plotted in Figures 5 and 6 (Stheor) and with those obtained from the experimental color points plotted
O
C
N05-4S
0.15
0.30
n,,
0.35
Flgure 7. Experimental color changes of some screened indicators with different dyes (one or two). The gray point pH value and the pH value of the points represented are given: NQS with (A)CB pH 9.40 (pH points: 5.30, 7.40, 9.30, 9.53, 12.70); (0)PB/CB pH 9.2 (pH points: 5.30, 7.40, 9.22, 12.60); NQS4S with (A)PB pH 8.04 (pH points: 3.28, 7.90, 12.88); (0)SB pH 8.91 (pH points: 7.40, 8.90, PB/CB pH 8.6 (pH points: 3.40, 12.60); NQT with (A)ST 12.80); (0) pH 9.00 (pH points: 5.69, 8.58, 8.87, 10.97); (0)ST/PA pH 9.2 (pH points: 5.70, 8.60, 9.18, 11.03); (0)STlPA pH 9.8 (pH points: 5.66, 8.92, 9.69, 10.92); NQT4S with: (A)CB pH 7.84 (pH points: 5.30, 7.74, 8.62, 10.50); (0)ST pH 8.30 (pH points 5.30, 8.14, 8.42, 10.52); (0) CB/ST pH 8.0 (pH points 5.29, 7.73, 8.10, 8.42, 10.51).
in Figure 7 (Sexptl). Results are shown in Table 111. Equation 18 defines the spectrum colors of the screened indicator color change, which are the same for all the screened indicators prepared from the same indicator. Also, it allows, given a series of screening dyes with known color parameters,
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
1427
Table 111. Comparison of Screened Indicators Lines Evaluated by Various Methods b
indicator
%alcda
theor
NQS NQS4S NQT NQT4S Methyl Orange Methyl Red Phenol Red Bromcresol Green
-0.237 0.398 -19.3 -7.16 -9.90 -24.7 6.30 0.776
-0.236 0.399 -19.4 -7.14 -9.88 -25.1 6.36 0.776
Se.xptlc
-0.231 0.378 -18.6 -4.52d
a Scaled, slope calculated from eq 18. b stheor, slope calculated from Figures 5 and 6. s e P t l , slope calculThis deviation is imputed to the ated from Figure 7. fast decomposition of the NQT4S in basic medium.
rapid determination, on the graph (see Figure 8) and without numerical calculation, of the color changes of the different screened indicators which can be prepared with these screened dyes and, then, the comparison of these color changes in order to select the best fit to the problem at hand. Comparison of Screened Indicators. The color distribution on the chromaticity diagram is not uniform and it does not allow the direct comparison of the quality of color changes because the distances on different regions of this diagram have nonequivalent physical meanings. However, all the screened indicators color changes have a color point in common: the gray point. The relative grayness, g, which is a measure of the gray proportion in a color (3))of the acidic and basic form of various screened indicators can be used to compare them. If a spectrum color is considered with chromaticity coordinates R,O (spectrum colors will be designed with a degree sign) and different amounts of gray color are added to it, the color point moves to Rcl, Rc2,and Rc3(Figure 9) on a straight line parallel to the gray color line. Projection of these points on the chromaticity diagram gives the Qrl, Qr2,and Qr3points. The addition of the gray decreases the color luminosity. This depends on the Y, coordinate according to Y, = Y," gYco (19)
uX Figure 8.
Graphical calculation of the screened indicators color changes from the same indicator knowing its screened indicators line.
yc t
+
Then, the variation in R, coordinates will be
and then
\
7
LC
Relative grayness g is an achromatic measure. It allows the comparison of screened indicators (prepared from the same or from different indicators) through the difference between the limiting colors of their color changes, which cannot be compared from the length of the line representing the color change. It has been observed that end point detection is very difficult with screened indicators which show acidic or basic form colors with relative grayness higher than 20, because they show gray color in a large pH range. The comparison between two screened indicators with the same end point pH value, prepared from different indicators, ought to be done comparing the relative grayness of the grayest form of each indicator because the pH range in which the indicator shows gray color depends mainly on this form. Condition for the Best Color Change in Screened Indicators. Among all the possible screened indicators to be prepared from an indicator and two screening dyes, the best is the one that shows acidic and basic colors with the same grayness. This best indicator shows the whole color change between two achromatically equivalent complementary colors.
Flgure 9, Complementary chromaticity diagram in relation to threedimensional complementary color space.
This screened indicator shows gray color at a pH that can be calculated in the following way: Equalizing the relative grayness of the acidic and basic colors of the indicator given by eq 21, inserting Q:, and Qr< values obtained from eq 7 as applied to the mixture with two screening dyes, introducing eq 13 and 8, and rearranging, we obtained
Considering the intermediate form, I, of the indicator as a mixture of acidic and basic forms, according to eq 3,4,5, 16, and 17 the following relations can be written:
1428
ANALYTICAL CHEMISTRY, VOL. 56, NO. 8, JULY 1984
ml = m2 = -
qJaDa2
qJaDla
+ ( l - q)JbDb2 JlDlZ
+ ( 1 - q)JbDlb
(24)
Table IV. Screened Indicators with Gray Point at pH,
screened indicator
(25)
J242
where
pH,
NQT4S/PA/ST 0.10/0.09/0.12 g in 100 mL water
8.58
NQT/PA/ST 0.10/0.19/0.26 g in 100 mL ethanol
9.61
PH value g theor g obsd
5.31 7.70 8.60 10.54 5.68 8.58 9.54 11.93
3.2 6.9 109 3.2 4.0 7.7 206 4.0
3.3 7.6 109 4.ga 4.0
7.6 96 3.8
a This deviation is imputed to the fast decomposition of the NQT4S in basic medium.
as screened indicator for end point detection can be concluded. If ga and gb are low (g < 20) the system is useful for pH values
By substituting eq 23, 24, and 25 in eq 22 and rearranging, the following equation is obtained: --= 4
A(1 - 4 )
Bq - C(1- 4) Dq - E(1 - 4 )
(31)
near pHo, but if they are high (g > 20), the system will not be use because all the screened indicators prepared from it will have the acidic or the basic form too gray, and these screened indicators will show gray color in a large pH range. Table IV shows the results obtained for the best screened indicators that, according to this criterion of equal low relative grayness, can be prepared from NQT or NQT4S and the screening dyes Sandolan Turqueoise E-AS and picric acid. Therefore these two mixtures, whose composition is given in Table IV, can be recommended as good screened indicators for end point detection in a very narrow pH range around 8.58 and 9.61, respectively. Registry No. NQS, 15687-37-3; NQS4S, 36307-95-6;NQT, 22051-53-2;NQT4S, 59558-95-1; PA, 88-89-1;SY, 8005-72-9; PB, 12235-72-2; SB, 89998-31-2; CB, 2429-74-5; IC, 860-22-0; MB, 61-73-4; XB, 129-17-9; ST, 3486-30-4; AG, 4403-90-1; Methyl Orange, 547-58-0;Methyl Red, 493-52-7; Phenol Red, 143-74-8; Bromcresol Green, 76-60-8.
LITERATURE CITED
Only the positive solution of eq 31, which is quadratic in q, has a physical meaning. This solution is
Since q / ( l - q ) = [H+]/Ka,where Ka is the acid dissociation constant of the indicator, the end point pH value, pHo, of a screened indicator with acidic and basic form of the same relative grayness is given by
(33) When pHo for a specific indicator/screening dyes system is known, Q,,', Qrb', g,, and gb can be calculated. From ga and gb values (which will be equal) the usefulness of the system
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RECEIVED for review September 27, 1983. Accepted March 5, 1984.
