Ion Asso.ciation between Indicators and Indifferent Electrolytes Michel de Vylder and Wilfried Rigole Laboratory of Physical Chemistry, University of Ghent, Belgium The effect of large concentrations (up to 3M) of indifferent electrolytes on the dissociation equilibrium of the indicators methyl orange, methyl red, and the K-salt of p-(benzylani1ineazo)benzenesulfonic acid was examined. Apart from the equilibrium shift resulting from the alteration of the activity coefficients, it seems that the effect consists in the formation of an ion pair between the anion of the indicator and the cation of the added electrolyte. On the assumption that this ion pair has the same color as the undissociated indicator, values of the dissociation constants of several formed ion pairs could be calculated on the basis of colorimetric measurements.
IT IS VERY HARD to give a systematic treatment of the influence of neutral salts on the color changes of indicators. It depends not only upon the salt content but also on the specific character of the indicator and on the kind and valence of the cations and/or anions present. Particularly, the color change of a definite concentration of an indicator caused by the presence of a neutral salt may occur for two different reasons: The neutral salt may cause a qualitative or quantitative alteration in the color of the acidic, respectively, the basic form OF the indicator, resulting in a change of A,, or in an alteration of the extinction coefficient; or according to the Debye-Hiickel theory, the neutral salt may affect the chemical equilibrium between the colored forms. Indicators in solution may indeed be considered as weak acids (or bases)
the true dissociation constant being given by
The presence of neutral salts will cause alteration in the individual activity coefficients ; the value of the function fH+fx-/jHx will therefore change and since Kl is a true constant the value of K, = (H+)(X-)/(HX) will be altered. Since the color of the indicator is determined by the ratio of the concentrations and not of the activities, the influence of indifferent electrolytes on the dissociation of indicators may be investigated by colorimetric measurements. Experimentally it was found that the color change of the acidic or basic forms of the indicators used was negligible. In solutions in which the indicator is neither completely in the acidic nor in the basic form, small concentrations of neutral salts increase the dissociation of the indicator in the sense and the amount as was expected according to the DebyeHiickel theory. However the dissociation apparently decreases by adding concentrations larger than 0.1M. This paper deals with a closer examination of this latter effect, which leads to a new kind of influence of indifferent electrolytes on the color change of indicators.
mined the pK value of the methyl orange used. Therefore, various concentrations of HCl were added to methyl orange solutions in COz-free water, so that we obtained various degrees in the dissociation of the indicator. The concentration of the red color (acidic form) was measured by means of a Unicam SP500 spectrometer at a wavelength of 510 nm. The basic form (yellow color) was obtained by substraction from the original indicator concentration. At times these results were checked by direct measurements of the yellow color at 420 nm which always showed a complete agreement. If the concentration of the red color is represented by CHX, the concentration of the yellow color by ex-, and the added concentration of the acid by C,, so that C, = CH+ CEX, the pK of methyl orange was calculated in the following way (see Table I). The mean value (pK = 3.41) agrees very well with those recorded in the literature (from 3.37 to 3.47). INFLUENCE OF INDIFFERENT ELECTROLYTES ON THE DISSOCIATION CONSTANT OF METHYLORANGE. Small shifts of the indicator color are best measured with the optical method if the concentrations of both forms are nearly equal. Therefore, a concentration of 0.48 x lO-3M HC1 was added to solutions of methyl orange, so that the pH of the solution approximated the pK. The concentration of methyl orange was about 10-%4. Various amounts of several indifferent electrolytes were added and the apparent dissociation constants colorimetrically determined. The results are shown in Tables I1 to IV. Since theory predicts that log K, should increase linearly with the square root of the ionic strength of the solution, some of these results were plotted us. d c i n Figure 1. Methyl Red as Indicator. COLORIMETRIC DETERMINATION OF THE pK OF METHYL RED. A mean pK value of 4.89 was found, the method being just the same as explained for methyl orange. INFLUENCE OF INDIFFERENT ELECTROLYTES ON THE DISSOCIATION CONSTANT.As the color of methyl red is much less stable than the color of methyl orange, the experiments were restricted to one single electrolyte, KC1. A solution of 1.15 x lO-5M methyl red in 2.574 x 10-5M HC1 was used (Table VI. K-Salt of the p(Benzylani1ineazo)benzenesulfonic Acid. COLORIMETRIC DETERMINATION OF THE pK OF PBBS. The same method as for methyl orange and methyl red yielded a mean pK value of 2.55. INFLUENCE OF INDIFFERENT ELECTROLYTES ON THE DISSOCIATION CONSTANT. Three neutral salts were examined: KC1, NaCl, and BaCh (Table VI). Thymol Blue and Phenolphthalein as Indicators. Measurements were tried also with phenolphthalein and thymol blue as indicators. However, because of a pronounced instability of the color of these indicators, it was quite impossible to get reliable results.
+
RESULTS AND DISCUSSION
Figure 1 shows that in very dilute salt solutions, the indicator curves approach the theoretical slope. Indeed from the Debye-Huckel theory, it follows for the limiting curve that
EXPERIMENTAL
+
4;
log Kl = log K, 1.012 (3) Methyl Orange as Indicator. COLORIMETRIC DETERMINAwhich applies to the dissociation constant of a weak acid in TION OF THE pK OF METHYL ORANGE. In order to investigate the presence of a concentration c of a uni-univalent neutral the precision of our measurement procedure, we first deter1234
ANALYTICAL CHEMISTRY, VOL. 43, NO. 10, AUGUST 1971
Table I. Concn of methyl orange, x 10-5~ 0.408 2.420 1.020 0.510 0.850 0.850 1.700 0.850 0.850 1I020 2.040 1.020
Colorimetric Measurement of pK of Methyl Orange at Different Degrees of Dissociation
Concn of HC1, X 10-4M 2.017 2.270 2.780 2.780 4.792 4.820 4.792 4.820 4.792 6.050 12.61 50.44
Extinc. at 510 nm 0.088 0.537 0.246 0.124 0.248 0.253 0.525 0.263 0.530 0.322 0.730 0.440
cHX,
x 10-5~
0.132 0.830 0.403 0.204 0.258 0.469 0.974 0.496 1.004 0.612 1.464 0.938
Table 11. Apparent Dissociation Constants of Methyl Orange by Adding Indifferent Electrolytes to a Solution of 1.700 x 10-5M Methyl Orange in 47.92 X 10-5M HCI KC1 NaCl LiCl Concn Concn Concn added, K, X added, K, X added, K, x M 103 M 103 M 103 ... 0.350 ... 0.350 ... 0.325 0.005 0.405 0.0053 0.377 0,00456 0,362 0.0124 0.453 0.0153 0.405 0.00912 0.377 0.0496 0.481 0.0410 0.424 0.0456 0,427 0.1240 0.507 0.0595 0.438 0.0912 0,427 0.2480 0.490 0.0910 0.445 0,1032 0,411 0.4960 0.427 0.1032 0.427 0.1907 0,416 0.9618 0.319 0.3479 0.405 0.6325 0.362 1.OOO 0.314 0.5852 0.319 0.6731 0,336 1.347 0.270 1.031 0.250 1.161 0.268 1.924 0.224 1.071 0.224 1.346 0.224 2.001 0,216 1.566 0,167 1.265 0.257 2.555 0.108 2.530 0.113 0.086 2.641 3.777 0.079 3.133 0.068 5.060 0.056 Table 111. Apparent Dissociation Constants of Methyl Orange by Adding Indifferent Electrolytes to a Solution of 0.8500 X 10-5M Methyl Orange in 47.92 X 10-5M HCI KBr NaBr LiBr Concn Concn Concn added, K, X added, K, X added, K, x M 103 M 103 M 103 0.406 ... 0.412 ... 0.341 0.511 o.o& 0.475 0.0055 0.0121 0.414 0.0199 0.0220 0.534 0.447 0.520 0.0680 0.0550 0.555 0.0995 0.571 0.1360 0.491 0.1100 0.1990 0.3339 0.507 0.426 0.555 0.5004 0.2482 0,422 0,475 0.5112 0.414 0.6216 0.3982 0.372 0.7636 0.381 0.331 0.7262 0.4775 0.324 0.331 1.013 0.272 0.9122 0.7090 0.286 0.258 1.228 0.220 0.9120 0.252 1.160 0,209 1.464 0.170 1.044 0,209 1.425 0.174 0.152 2.046
salt at 25 “C ( I ) . However, deviation from this theoretical slope appears rapidly. At larger concentrations (from 0.1M) of neutral salts, deviations should occur, because the activity coefficients no longer obey the limiting law of Debye-Huckel. They are influenced by several factors such as hydration and the size of the ionic radii. Therefore, we have compared our curves (1) A. J. Rutgers, “Physical Chemistry,” Interscience, London, 1954.
K,
a
0.68 0.66 0.61 0.60 0.46 0.45 0.44 0.42 0.41 0.40 0.28 0.08 Log K,
x 10-3~ 0.420 0.420 0.423 0.414 0.406 0.388 0.350 0.341 0.325 0.400 0.451 0.438
PK 3.38 3.38 3.37 3.38 3.39 3.41 3.45 3.47 3.49 3.40 3.36 3.36
Methyl orange
0.5
1,o
15
mol^
Figure 1. Effect of some indifferentelectrolytes on dissociation constant of methyl orange Table IV. Apparent Dissociation Constants of Methyl Orange by Adding Indifferent Electrolytes to a Solution of 0.8500 X 10-5M Methyl Orange in 48.20 X 10-5M HCI Concn Concn Of KN03, of BaClz added, M K , X lo3 added, M K , x 103 ... 0.341 ... 0.341 0.0050 0,409 o.ooo1 0.394 0.0225 0.472 0.0098 0.491 0.0627 0.518 0.0488 0.510 0.2195 0.567 0.1175 0.499 0.3249 0.583 0.2233 0.403 0.6810 0.589 0.4113 0.321 1.008 0.597 0.4970 0.264 1.515 0.589 0.5811 0.233 0,7843 0.206
ANALYTICAL CHEMISTRY, VOL. 43, NO. 10, AUGUST 1971
1235
Conc. red color i n mole/, x105
Difference EXPER.- THEOR
0.5
c
0.3
/
P
c
/
0.5
Figure 2a. Calculated values of concentration of undissociated methyl orange in comparison with those measured by colorimetry Table V. Apparent Dissociation Constants of Methyl Red by Adding KCI to a Solution of 1.15 X 10-6M Methyl Red in 2.574 X 10-5M HCl Concn of KCl added, M K, x 105 ... 1.293 0.0219 0.0676 0.2247 0.3493 0.4516 0.6008
1.670 1.968 2.061 1.968 1,766 1.650
Table VI. Apparent Dissociation Constants of PBBS by Adding Indifferent Electrolytes to a Solution of 1.540 X 10-5M PBBS in 3.044 X 10-3M HCI Concn Concn Concn of BaClz of KC1, of NaCl added, M K, x lo3 added, M K, X lo3 added, M K, X l o 3 0.0061 0.0273 0.1112 0.3762 0,9324 1,639 2.213
3.380 3.840 4.228 3.988 3.590 2.676 2.300 1.968
...
0.0131 0.0655 0.1489 0.4327 0.7912 1.527 2.478
2.290 2.824 3.052 2.961 2.444 1.954 1.353 0.879
. I .
0.0100 0.0173 0.0675 0.1223 0.3869 0.4721 0.7188
2.290 2.750 3.012 3.225 2.823 2.290 1.854 1.578
with the values of the activity coefficients from Robinson and Stokes (2) where allowance already was made for these influences. However, there was no agreement at all between the apparent dissociation constants following from our colori(2) R . Robinson and R. Stokes, “Electrolyte Solutions,” Butterworths, London, 1959. 1236
Cone. N a C l Conc.
1.o
1.5 mole/( I
Figure 26. Subtraction of experimental curve from the theoretical one metric measurements and those calculated with the activity coefficients from Robinson and Stokes. This is shown in Figure 2a where the curve for a solution of methyl orange with NaCl is given as a n example. This effect was also noticed by Sidgwick and coworkers (3) and by V. V. Palchevskii (4) who report it without explanation. It appears that the difference between the theoretical and practical curves is nearly proportional to the added concentration of neutral salt (Figure 26). Therefore, the possibility of an ion pair formation between the anion of the indicator and the cation of the indifferent electrolyte was presumed. Assuming this ion pair to have the same color as the undissociated form of the indicator, the value of the dissociation constant of the ion pair may easily be found as follows. At equilibrium we have
and
(MX)
(M+)
+ (X-)with KZ = (M+>(X-) (MX) ~
f”
(5)
where (M+) represents the concentration of the added cation. frepresents the mean activity coefficient of the ions while the activity coefficient of the chargeless molecule is omitted, as it may not differ appreciably from one. If 2 = (H+) (HX) represents the added concentration
+
(3) N. V. Sidgwick, W. J. Worboys, and L. A. Woodward, Proc. Royal SOC.London, 129,537 (1930). (4) V. V. Palchevskii, Vesm. Leningrad. Uniu., Fiz. Khim., 1962 (3), 125.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 10, AUGUST 1971
Table VII. Calculation of Dissociation Constant of Ion Pair Presumed by Adding NaCl to a Solution of 1.700 X loS6 Methyl Orange in 47.92 X 10-6M HCI R(Co1orAdded imetry), NaC1, M f2 10-6M K2 0.942 0.331 0.852 0.0053 0.913 0.382 0.780 0.0153 0.894 0.260 0.0410 0.690 0.880 0.312 0.654 0.0595 0,874 0.307 0.0910 0.605 0.891 0.274 0.1032 0.602 0.913 0.375 0.3479 0.487 1.012 0.326 0.5852 0,452 1,100 0.355 1.031 0.430 1.150 0.316 1.071 0.430 1.252 0.314 0.434 1,566 0.352 0.491 1 ,379 2.555 0.281 0,498 1.435 2.641 1.481 0.288 3.133 0.546 Mean value: K2 = 0.319 (standard deviation u = 0.04).
Table IX. Values of Dissociation Constants of Ion Pairs Presumed by Adding Indifferent Electrolytes to PBBS Mean Kz =
Table VIII. Values of Dissociation Constants of Ion Pairs Presumed by Adding Indifferent Electrolytes to Methyl Orange Mean Kz = mean
concentration of indicator and R; Kl may also be found colorimetrically in the absence of added electrolyte; J:* is taken from Robinson and Stokes. Table VI1 proves the reliability of the above theory: for all concentrations of NaCl added to methyl orange, a constant value was found for K2. The same was true for all indifferent electrolytes and for all three indicators investigated. Tables VIII, IX, and X summarize the values of the dissociation constants of the ion pairs. The values of Kl X K2 in the next to the last column are inserted for the following reason. The values of K2 for a common cation show rather large deviations. It was observed that it results from the fact that they strongly depend on the value of K l , that is remeasured for each electrolyte but with little accuracy. However, the product is more constant, so we divided it by the more accurate value obtained without electrolyte to get the mean.
Added electrolyte
Experimental
K,,X lowa 0.350 0.406 0.341 0,325 0.412 0.325 0.341 0.341
KC1
KBr KN03 NaCl NaBr LiCl LiBr BaClz
(Ki X K2) Kl X Kz, 0.388 X
K2, derived 0.379 0.322 0.365 0.319 0.271 0.770 0.737 0.052
X
10-3
0.133 0'13' 0.125
0.334
0"04 0.112
0.278
0'250
0.644
0.251 0.018
0.053
(KIX K z ) Added
electrolyte KC1 NaCl BaCh
Experimental
Ki, X 0.388 0.229 0.229
Kz
Ki X K2,
derived 0.394 0.352 0.050
0.133 0.081 0.011
x lo-*
0.282 X IO-* 0 472 ~
0.286 0.041
Table X. Value of Dissociation Constant of Ion Pair Presumed by Adding KCl to Methyl Red Mean Kz =
Ki X Kz Added electrolyte KC1
Experimental
KI,X 0.129
Kz derived 0.565
KI X K2,
0.129 X
X
x
0.073
0.565
of acid, the first equation gives
(H+) = 1
z
CONCLUSIONS
(X-) +-f" Kl
Because of the above results, it may be assumed that the color change, caused by the presence of a neutral salt in a solution of methyl orange, methyl red, or the K-salt of p (benzylani1ineazo)benzenesulfonic acid, is due, apart from a small equilibrium shift owing to the activity coefficients, to the formation of an ion pair between the anion of the indicator and the cation of the added salt. The conclusion of V. V. Palchevskii ( 4 ) that methyl orange is unfit for the colorimetric detection of pH in concentrated salt solutions may thus be remedied by evaluating the influence of the electrolyte from the known dissociation constants.
The concentration of undissociated indicator (red color) is given by
R
=
(HX)
+ (MX) (7)
from which
(M+) (8) R/KX-)f"l - Z/Ki (X-lPl In this relation, R = (HX) (MX) may be found by Kz =
+
colorimetry;
+
(X-)equals the difference between the total
RECEIVED for review February 1, 1971. Accepted April 2, 1971.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 10, AUGUST 1971
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