INDICATOR CONSTANTS* BY I. M. KOLTHOFF
I n the colorimetric determination of pH without buffer solutions it is necessary to know the ionisation constant of the indicator in order to calculate the p a or paH of the solution from the determined ratio of the concentration of the acid to the concentration of the basic form. Often, for indicator acids the following equation is applied : [aH+] =
paH = log
[acid form] KI or [basic form]
[basic form] [acid form]
+ PKI
Similarly for indicator bases we can write: [aH+] = [acid form] -Kw _ - [acid form] [basic form] K I ~ H [basic form] KI and
paH = log
[basic form] acid form
+ PG'
(3)
In equation ( 2 ) Kw represents the ionic product of water and KIOHthe ionisation constant of the indicator base. At fixed temperature the ratio between these two is constant and the constant KI' can be written instead. pKI and pK1' are usually termed as the indicator constant or indicator exponent resp. As a rule it is assumed that its value is equal to the PH of a buffer solution, in which the indicator is 507~ transformed into its alkaline form. Several investigators have determined the constant of various indicators. I n tabulating these values it appears, however, that agreement between different authors is not very close; and it is hard to make a proper choice and to decide which value of p~ to use in our calculations. I n searching for the reason of this apparent disagreement, the following factors have to be considered: a. The values reported by different authors depend upon the accuracy of their measurements and on the care taken in the preparation of standard solutions of known hydrogenion-concentration. As a rule, indicator constants have been determined colorimetrically or spectrophotometrically. The spectrophotometric method is more precise than the usual colorimetric one, though the latter may yield an average result accurate t o within 0.02, if an adequate number of measurements a t varying ratios has been made. It should be mentioned that some authors (like W. & Clark) I. only approximated the pK values to the first decimal place, whereas we are interested in
INDICATOR CONSTANTS
1467
having the second decimal place included. An important factor in this respect is the purity of the indicators used, especially with regard to the presence of other dyestuffs also having an indicator character. Such contaminations should not be present. Some years ago the author determined the indicator constant of bromo cresolgreen, but did not find a constant value at different ratios of the acid and alkaline form. Later it appeared that the indicator was not quite sure. b. Different authors did not work a t the same temperature. It is possible that a better agreement may be obtained, if all data could be reduced to the same temperature. c. The expression of pK1 must be properly defined (equation I). Thermodynamically KI is constant in the equation: [a acid form] [a Hi]= aKI (4) [a basic form] in which the symbol a signifies the activity of the corresponding form or ionconcentration or activity equilibrium constant. The usual procedure of obtaining KI or pK1 is the following: The indicator is added to a buffersolution of known hydrogenion-concentration or, better, hydrogenion-activity and the ratio between the acid and basic form of the indicator is determined in a colorimetric or spectrophotometric way. I n the computation of XI or pK1 the concentration ratio of the acid to basic form (equation 3) is usually used instead of the activity ratio (equation 4). At constant hydrogenionactivity the ratio of activity of the acid to basic form is fixed according to equation (4), and independent of the electrolyte content of the solution. On the other hand the ratio of the concentration of the acid to the basic form, which determines the color or the light absorption of the indicator in the buffersolution changes at constant [aH+] with varying ionic strength. Therefore the pK1 value derived on the basis of equation (3) is more or less conventional, and holds only at the ionic strength of the buffer, in which it has been determined, with increasing ionic strength pK1 decreases, (indicatoracids) whereas it increases with decreasing ionic strength. In infinitely dilute solutions, where the activity- and concentration ratios are the same, pK1 will be identical with paKI. With monobasic indicators (or monoacid indicator bases) the salt influence upon the activity ratio will be less than with dibasic indicator acids (all sulfonphthaleins behave like dibasic acids in their colorchange from the yellow to the alkaline form). Moreover not only the ionic strength of the solution determines the ratio of the activities, but also the kind of ions present has some influence, The whole subject iyhich is closely related to that of the salt error of indicators, is rather complicated and has been extensively discussed in a former paper.' If f I is the activity coefficient of the acid form, and f 2 that of the basic
I. & Kolthoff: I. J. Phys. Chem., 32, 1820 (1928); E. Guntelberg and E. Schiodt: 2. physik. Chem., 135, 393 (1928); J. Sendroy and A. B. Hastings: J: Biol. Chem. 82, 197 (1929):
1468
I. X. KOLTHOFF
From (3) and ( 5 ) it follows that: pa& - PKI
+ log;
(6)
paKI is a constant at varying ionic strength. Though the quantitative side of the problem is rather complicated (comp. lit. ref. I ) , it is evident from the above that values of pKI reported by different authors can be the same only if determined in buffersolutions of the same ionic strength and containing t,he same kind of ions. d. From equation ( I ) it follows that pKI can only be calculated, if pan of the buffersolution is known. As a rule the paH (pH) of solutions is derived from measurements with the hydrogenelectrode on the basis of the equations originally given by S. P. L. Sorensen,* and PH values of buffer solutions reported in literature are all “Sorensen values.” However according to the modern theory of strong electrolytes, this pH expression has no actual significance. In a solution of O.IN hydrochloric acid Sorensen computed a PH according to the theory of Arrhenius equal to 1.038; actually the pH is 1.00and the pax (activity exponent) 1.08i : 0.01. At the present time the latter value is uncertain to within about 0.01and various authors do not use exactly the same standard value.3 The majority uses Sorensen’s data. for the expression of pH, though J. Sendroy and A. B. Hastings4 as well as K. Buch5 related their data of paKI on a paH value of 1.08 in O.INhydrochloric acid or 2.08 in a mixture of o . o ~ Nhydrochloric acid and o.09N potassium chloride respectively. Therefore in order to compare their values with those of others, 0.04 has to be subtracted from their paKI figures. At first sight it seemsmore logical to add to the figures of other authors 0.04 in order to report the corresponding paK, values. However as all data in literature on the pH of buffer mixtures are expressed in “Sorensen-units,” it seems better to adhere t p them though they have no actual significance. As soon as the difference between pH (Sorensen) and paH has been fixed by international agreement, it will be very simple to transform all Sorensen-values into paH by adding a constant factor. Applying this change now would cause more confusion than already exists, since different authors use a slightly different factor. In the following tables a review is given of the pK1 values of indi2. cators (apparent indicator exponents) reported in the literature. As a rule the agreement is not very close. Considering the factors discussed in the foregoing paragraph which influence the value of the apparent indicatorexponents, the author has tried to derive the data under similar conditions of ionic strength and temperature. It will be shown that under these conditions the agreement is much better, and it is possible to find pK1 data with an accuracy of about 0.05.
* S. P. L. Sorensen: Compt. rend. du Lab. Carlsberg, 8, 23 (1909). See also the new edition of W. M. Clark: “The Determination of Hydrogen Ions” (1928). a A discussion of the confusion in the expression of the, acidity and the uncertainty in the standard paH values is given in a paper in Rec. Trav. chlm., (1930). J. Sendroy and A. B. Hastings: J. Biol. Chem., 82, 198 (1929). K. Buch: SOC. Scient. Finnica, 2, 29 (1926).
1469
I S D I C A T O R CONSTASTS
In the first column the temperature is given, in the second the method used: in the third the kind of buffer mixture; in the fourth the pIiI value (holding in the particular buffersolution); in the fifth the author. I t should be mentioned that in the determinations a series of buffers of varying pH was used, so that the ionic strength is not constant but changes between t w o limits. In the discussion an average value of the ionic strength belonging to the reported pRI value has been selected. Bromphenolblue Temperature
Room temp. (Xbout z j'?) (Libout18'?) (About 18'?) (zoo) iIj0)
i30°1 130')
Method used
Type of buffer
Spectrophotom. Clark and Lubs Sorensen , Acetate Colorirn. .Clark and Lubs ) >
, ,,
,> ,,
1)
1
J ) J ) >
Author
PKI
Rrode6 Prideaus' 4.10 V1W 4.1 Clark and I.uhhn 4.00 + IiolthoffIo 4.10 0.1Gillespie" 4.1 Van hlstine'?
4.05 4.0
+
I n the Clark and Lubs buffers the ionic strength is of the order of o . o j 0.2. From the results in t,he table it will be seen that at room temperature ( I j" to 30') various authors find a pIi, value at a n ionic strengt'h between 0.05 and 0 . 2 of 4.00 to 4.10. I n a biphthalate buffer of an ionic strength of about o.oj, the value of 4.00 at zoo + j o seems most reliable. In a recent' paper, E. Guntelberg and E. Schiodtl determined the following constant of bromphenolblue: KO= (CH) (alkaline form) (acid form) in dilute solutions of hydrochloric acid in the presence of potassium and sodium-chloride a t 18". As we are reporting; (aH+) (alkaline form) KI = (acid form) we have t o add to the pK,values of Guntelberg and Schiodt pfA = - log f H a t the corresponding salt concentrations, since (aH+) = CHfH On the other hand, as all values are related t o Sorensen data, 0.04 must be subtracted from the figure found in thie way: pK1 = ph'o PfH - 0.04 (7) Guntelberg and Schiodt determined pX, in very dilute hydrochloric acid in 0.06, in the citrate buffers of the order
+
C. Brode: J. Am. Chem. SOC.,46, 481 (1924). E. B. R. Prideaux: J. SOC.Chern. Ind., 45, 664. , 678. . 697 _ . (1926). Arch. phys. biol., 4 28j (1926). O W . M. Clark and H.+A.L d s : J. Bact., 2 , I , 109, 191 (1917). IOI. M. Kolthoff: Rec. Trav. chim., 43, 144 (1924). l l L . J. Gillespie: J. Am. Chem. Soc., 42, 742 (1920); Soil Sci., 9, 115 (1920). '*E. Van Alstine: Soil Sci., 10, 467 (1921).
* F. VI&:
~
I470
I. M. KOLTHOFF
the presence of O.IX, o.zN, o.gN and I N potassium chloride resp. They also worked a t larger salt-concentrations ( z and 3N potassium chloride) and 3-4 and gN sodiumchloride resp. which data will not be considered here. The value of -log fn in potassium chloride solutions are given by H. S. Harned and N. J. Br~rnbaugh.’~These are slightly different from those, calculated on the basis of an equation given by K,Bjerrum and A. UnmackI4 -log f E = 0.196 q0-0.166~ -0.003 (18Oin KC1) The values of pfH in potassiumchloride solutions according to Harned and Brumbaugh (2;”) and Bjerrum and Unmack (18’) are reported in the following table; and an average value will be used in our calculations. pfH in potassium chloride solut,ions Concentration KC1
pfH (H. and B.)
pfH (Bj.& U.)
0.09
o.oj6
0.08
0.11
o.oj5
0.09 0.08 0.03
0.2
N 9
0.5
s
0.10
O.Oj0
I
N
0.046
o
0.1
pfH (average)
027
The following table gives the values of pKc of bromphenolblue according t,o Guntelberg and Schiodt and the corresponding data for pK1 computed on the basis of equation ( 7 ) ; Bromphenolblue (Colorim.) Electrolyte Concentration 0 0.05
3 (K
0.1”
”
o,
‘1
”
I.
”
”
PKc
PKI(G.&S.j
~ K (Kolthoff) I
4 . I3
3.80 3.i3
4.09 3.84 3.ii
4.00 __
3.72
3.71
-
C1)
4.10
3.7 -
The value pKI (Kolthoff)’ has been derived from former studies on the salt error of bromphenolblue. From the above it seems justifiable to accept the following values of pK1 of bromphenolblue at zoo 5’ in solutions with an ionic strength smaller than 0.05.
*
Ionic strength
0.05
PKI 4.00
0.01
4.06
0.00
4.10
It may be mentioned that Guntelberg and Schiodtl in their excellent paper make the following statement : “It is evident that bromphenolblue ’3Harned and Brumbaugh: J. Am. Chem. Soc., 44, 2729 (1922). 14 N.Bjerrum and A. Unmack: Det. Kgl. Danske Videnskab Selskab., 9,
I (1929).
INDICATOR COSSTASTS
1471
behaves as a monobasic acid; its curve lies between that of carbonic acid and benzoic acid and has the expected form; its anion seems to have a remarkable high activity coefficient." We are sure, however, that bromphenolblue behaves as a dibasic acid in its color change from yellow to purple though it must be admitted that the dependence of the ratio of the activity coefficient of the mono and divalent anion upon the ionic strength of the solution is quite abnormal and differs from that of other divalent acids (also other sulfonphthaleins) so far investigated. Bromocresolgreen Temperature
Method used
30°
Room temp. 20°
Type of buffer
PK
Author
Spectrophotoni. Clark and Lubs 4.68
2 70
>)
I,
,)
Citrate Acetate
Colorini.
If
f,
3 8"
Holmes and Snyder1& 4 47 B. CohenI6 4.7 Prideaus7 4.6~(4.48) Hastings, Sendr oy 4.68(4.;2) and Robson:7
The values in the table from Hastings' c.8. work are corrected for the difference between pH and paH; the original data are given in parentliesij. From the figures in the table, it, will be seen that there is an excellent agrc'enient between the pIi1 values. Xt an ionic strength of 0 . 1 t o 0.15 pK1 betwen I j oand 30' is equal t o 4.46 i 0 . 0 2 . At decreasing ionic strengths pIi1 increases; J. Sendroy and -1.B. Hastings' extrapolate at an ionic strength of zero at 20' a value of 4.92, or corrected for the Siirensen value 4.88, whereas from work on the salt error of brorncresolgreen" the author arrives at 4.90. The close agreement bet ween all yalues is within the experimental error, C hlorphenolred Temperature Method used 30' Spectrophotoni. SO'
Colorirn.
,,
Type of buffer
Clarks and Lubs Acetate and
PKI
5.98 j.98 (6.02)
Author
R . C'ohen'c Hastings, and IIob~on~7
Citrate j.89(5.93) From these figures it follows that at an ionic strength of about 0.1 pIi1 = 6.00 - o . o o j i t - z o o ) Csing the data found from the salt error" of chlorophenolred, we extrapolate at an ionic strength of zero: pK1 = paKI = 6.2j (zoo) '6 W.C. Holmes and E. F. Snyder: J. Am. Chem. Soc., 47, 2 2 1 , 226, 2232 (1925). 3g0
17
B. Cohen: Public Health Reports, 42, 3051 ( 1 9 2 j ! . A. B. Hastings, J. Sendroy and W.Robson: J. Biol. Chem. 65, 381 (1925).
I472
I. hl. KOLTHOFF
Bromcresolpurple Temperature
Method used
>, ,,
Room temp. (2j0?)
Jl
Type of buffer
Spectrophotom. Citrate(S0rensen)
I8O
l!
I
Clark and Lubs
Colorimetr.
2 O0
I)
3 oo
,,
2 O0
Room temp. (about 2 5’1)
11
1)
1S o 20°
f l 1)
>
) >
,, ,,
”
,,
hcetate;citrate
)J
,,
38O
1,
,l
,,
,,
~ K I Author 6.15 Buch5 (6.19) 6.3 6.3 6.3 6.2 6 6.28
6.3 6.07
6.1 j
Prideaus7 Brode6 Clark and Lubs9 Gillespiell Barnett and BarnettI8 S-an hlstine12 Kolthoff’O Hastings,
(6. I 9) Sendroy 6.0; and Robson (6.09)
Using the author’s value (6.07) and his data on the salt error of bromcresolgreen’ and extrapolating by means of the simple Debye-Huckel equation, it is found that at an ionic strength of zero: paKI = 6.07 0.28 = 6 . 3 j o ( 1 j 0 ) ; or with the temperature modulus of Hastings C.S. 6.33 at zoo, whereas Sendroy and Hastings4 arrived a t the value 6.42 (6.46) and K. Buch5 at 6.38 at 20’. From this and the work referred to, the values of pK1 a t various ionic strengths have been derived, and are accurate to within 0.05.
+
pKI Bromcresolpurple a t Yarious Ionic Strength Ionic Strength 0
0.005 0 .OI
PKI 6.40-0.05 (t-20) 6 . 3 0 - 0 . 0 0 5 (t-zo) 6.28-0.005 (t-20)
Ionic Strength 0.05
0.1
PKI 6.21-0 .OOj ( t - 2 0 ) 6.12-0 , 0 0 5 (t-20)
Bromthymolblue Temperature
Method used
Room temp. ” (about z j ’ ? ) ” (about 18’?)
,J
J J
”
Colorim.
ZOO
1So 20°
Room temp. 1s
Type of buffer
~ K I
Author
Spectrophotom. Phosphate( Sorensen) 7.06 Buchj
18’
,, ,, ,,
,I
Clark and Lubs Boric acid:borax Clark and Lubs
,, J)
tJ
(7.10) 7. I 7.10 7.0 7.1
Prideaux? RrodeB T’lM Clark and Lubs9 7.08 Kolthofflo 7. I O Gillespie” 7.10 Van hlstine’*
G. D. Barnett and C. W. Barnett: Proc. SOC.Exp. Biol. Med., 18, 127
(1920/21).
I473
ISDICATOR CONSTANTS
The influence of the temperature between 15' and 30' is negligibly small. The agreement between various authors is very satisfactory. By means of the data of the salt error of bromthymolbluel and the simple Debye and Huckel equation a pK1 at an ionic strength of zero of 7.29 is found, whereas Buch arrives at 7.37. This extrapolation t o infinitely dilute solution is uncertain t o at least o.oj in pK1. Combining the data on the salt error of bromthymolblue with the figures in the table, we find the following pKI values at various ionic strength: pKI bromthymolblue
Ionic Strength 22
0.0025
7 21 7 I9 7 I3 7.10 (Clark and Lubs phosphate buffer) 7 06 (Order of Sorensen phosphate ) 7 04
0.ooj 0.01
0.oj 0.1
0.1; 0 . 2
Phenolred Temperature
Method used
Type of buffer
~ K I -4uthor
Spectrophotom. Phosphate(Sorensen) 7 86 Buch5 11 Clark and Lubs j . 9 0 Brode6 Room temp. ,, Phosphate; borate 7.9 Prideaux' " (about 18'?) Colorim. Clark and Lubs 7.87Barnett and ZOO ChapmanIQ 1) ,, 7.78 Barnett and 2 oo Barnettla 11 ,, 7.9 Clark and Lubsg zoo 1, ,, 7 . j 2 Gillespie'l 29O I 8"
2jo
Room temp. " (about z j"?) I jo
2 oo
38O
1,
11
7.7 6 TT-u?O
t
,)
j . 9 Van Alstine"
,, 1'
,1
7.8j Kolthoff" Phosphate(Sorensen) 7 .j 4 (7.78) Hastings, Sendroy and 1, " 7.61 (7.65) Robson" ,)
From the salt error1 and the Debye-Huckel equation the pK1 value of phenolred at infinitely dilute solution a t I jo has been computed from Kolthoff's figure in the table and a value of 8.06 found. Using Hastings" C.Y.temperature modulus, this figure at zoo would be 8.02, whereas Sendry and Hastings4 obtain 8.00 (8.04 for paH in 0.1s HCI of 1.08) at the same temperature. There is perfect agreement between these two data. At an ionic strength of zero: p I i ~= 8 . 0 0 - 0 . 0 0 7 (t-20) G. D. Barnett and H. 6. Chapman: J. .Im. Med. Assoc., 70, 1062 (1918). *OH. Wu: Proc. SOC.Exp. Biol. hled., 21, 111 (1g23/24).
I474
I. M. KOLTHOFF
Comparing the data in the table a t the same temperature and ionic strength, we find an agreement of 0.04 between most of them, which is very satisfactory. From the above and the salt error of phenolred the following pKI table has been derived : Ionic strength
~ K I
(ZOO)
0
8.00-0.00;
0.002j
0.1
7.95 7.91 7.92 7.84 7 81
0.Ij
7 77
0.2
7.75
0.OOj 0.01
0.05
(t-20)
Clark's phosphate buffers Sorensen's phosphate buffers
0.Ckesolred
Method used
Temperature
Room temp. " (about
25'?)
1,
'' (about
18'1)
2 oo
1
,, ,. ,,
O
>-
1Sa
Room temp.
~ K I Author
Spectrophotom. Clark and Lubs 8 . 2 0 > Borate 8.2 Palitzsch 8.30 C'olorim. Clark and Lubi 8.3 1,
24
Type of buffer
11
(25'7)
Brode6 Prideaux7 T1&>8
('lark and I,ubj9
8.08 Ciillespie" 8.17 Kolthoff'o
8.3
Tan Ailstinel*
I n comparing the different values, it should be remembered that the ionic strength of the phosphate buffers a t a pH near 8.0 is of the order of 0.15, whereas the same of the borate-boric acid solutions is about 0.0j. Clark's value probably holds for borate solutions; a t higher ionic strength the pK1 will be smaller. The most probable value at 20' and an ionic strength of 0.0j is 8.30, and of 0.15 8.20, both 0.05. I t is desirable to have a more extended investigation on this indicator.
*
m. Cresolpurple (Acid range) Temperature
Method used
Type of buffer
30'
Spectrophotom.
Clark and Lubs buffers Alkaline range Clark and Lubs
3 oo
,,
pK I
,5I
8 32
Author
B. Cohen'*
I,
INDICATOR CONSTANTS
Thymolblue (Acid range) Room temp. ” (about 25O?) Spectrophotom. Clark and Lubs ” (about 18O?) ,, !, tt ” (about 2 s 0 ? ) 2,
11
Colorim.
2 oo
!,
Ij o
Room temp.
,,
HCl+o.osK SaCl
,,
I475
Brodee Frideaux’ I .5 Holmes and Snyderls I.7 Clark and Lubsg 1.64 f o . 0 3 Kolthofflo 1.75
I.7 5
I.7
Van illstinel2
The difference between the figures of Holmes and Snyder (1.5) and the other data reported is very striking. The reason is that the former authors used thymolblue in concentrated hydrochloric acid as a completely acid solution for comparison. According to their statement the dissociation is incomplete in solutions with less than 207~ hydrochloric acid. Other authors probably worked with a less acid solution of comparison. Kolthofflo used only 0 . 2 5 K,Van Alstine’2 I . jN hydrochloric acid. It seems to the author, that the concentration of the strong acid in the solution for comparison should not be larger than 0.jS,as in such a liquid the thymolblue is more than 9970 transformed into the acid form. More acid and also neutral salts affect the color intensity and to some extent the shade also. Thus it was hydroobserved that the intensity of the red form of thymolblue in 0.01s chloric acid containing 0.09spotassium chloride, is about 80% of that in the salt free acid solution. Even the effect of O.OIXpotassium chloride is noticeable. Sodium chloride has about the same influence, and lithium chloride even a little more. I n solutions containing more than about IX neutral salt, it is almost impossible to make comparisons of the color of the indicator with that in salt-free solutions. These peculiarities of the indicator will be discussed in a later paper with regard to a study of the structure of the acid form of thymolblue. It seems that the acid form of thymolblue is an internal salt of the sulfonic group and the basic quinoid thymol group (oxonium-or carbonium). The acid form then behaves as an amphoion. In agreement with this view is the fact that the salt error of thymolblue (acid range) is extremely small and comparable with that of methyl orange, According to KolthoffZ1the influence of the temperature upon the ionisation is negligibly small between 15’ and 30’. From the above it is justifiable to conclude, considering the indicator in 0 . 2 5 to o.gN hydrochloric acid to be completely present in the acid form, that a t an ionic strength between zero and 0.5 and a t 20’ i IO’. pKI 21
=
1.65 i 0.05.
“Indicators.” Translated by S . H. Furman, p. 92 (1926).
1476
I. M . KOLTHOFF
Thymolblue (Alkaline range) Temperature
Method used
Type of buffer
~ K I Author
Room temp. (zs0?) Spectrophotom. Clark and Lubs 8.90 Brodes 1, 11 " (about zs0?) 8.91 Holmes and SnyderI5 11 11 " (about 18"?) 8.91 Prideaux7 Colorim. 1, 8.9 Clark and Lubsg 20' 2 5-30' ,, 1, 8.82 Gillespie" 1, ,t 8.96 Kolthoff'O 15' 11 1, (9.0) Van Alstine'? Room temp. From this list we may conclude that at an ionic strength of 0.06 to 0.09 pK1 is equal to 8.93 k 0.03. The temperature effect is very small (KolthoffZ1), therefore this figure may be used between 15' and 30'. Considering the salt error1 of thymolblue, it can be computed that a t an ionic strength of zero pKI will be equal t o 9.20 0 . 0 ; .
*
(Azo indicators) Methylorange Temperature
Method used
Room temp. (IS'?) Spectrophotom "
2 5' 2 So 25 O
2 So
IS0 2 4'
37' 18'
(18"?)
,>
,,
Conductom Colorim
Type of buffer
Citrate (?) ,1
Acetate
9,
1)
,I
I,
1
,I
,l
1)
1,
Citrate
PKI 3.18
Author
Prideaux' V1M 3.53 Thiel and 3.37 Dassler22 (4.82) Winkelblechz3 Tizard?l 3.37 Salm25 3.34 Tizard and 3.57 J5'hist onz6 3.43 3.28 3.52
11
,, Kolthoff 2 7
The agreement between the data of Tizard, V1&;, Salm, Kolthoff, and Thiel and Dassler is satisfactory. Considering that Tizard and Whiston found a decrease of pK1 between I j o and 37' of 0.14 for each degree increase in temperature, we find at zoo; 3.50 (VIBs); 3.50 (Tizard and Whiston); 3.49 (Kolthoff); 3.41 (Salm); 3.43 (Thiel and Dassler). The salt error of methyl orange is extremely small (Kolthoff'), therefore for practical purposes we may assume that p I i ~is constant to within 0.04 at ionic strengths between o and 0.5. 22 A. Thieland A . Dassler: Ber. 56, 1667 (1923);Thiel, Dassler and F. Wulfken: Fortschr. Chem. phvsik. Chem., 18, Heft 3 (1929). 23K. fi-inkelblech: Z. physik. Chem., 36,j69 (1901). zrH. T. Tizard: J. Chem. Sac., 97, 2477 (1910). 26 Salm: 2. physik. Chem. 57 471 (1906). 9eH. T. Tizard and J. R. IU'histon: J. Chem. Soc., 117, rjo (1920). 97 I. M. Kolthoff: Rec. Trav. chem., 44,68 (1925).
I477
INDICATOR CONSTANTS
E. Guntelberg and E. Schiodt' det'ermined pK, of methylorange a t different ionic strengths in dilute hydrochloric acid at 18'. From their data the corresponding pK1 has been calculated (for details concerning this procedure compare under bromphenolblue). Alethylorange (data of Guntelberg and Schiodt-18') Electrolyte concentration 0
o , 1 3 KCl 0 . 2
PKo
PKI
Electrolyte concentration
PKo
PKI
3.49 3.37 3.36
3'45 3.41 3.41
0 . 5 KC1
3.43
3.46 3'57
I
KCl
3.58
At an ionic strength of zero and a temperature of 20' the value of pKI according to the experiments of Guntelberg and Schiodt would be 3.42. From all reported figures it may be concluded, that at an ionic strength between o and 0.5. pIC1 = 3.46 + 0.04 - 0.014 (t-20') (1 5-30') Dinieth?llaniinoazobenzene (Methyl yellow) Though this indicator on account of its slight solubility is hardly suitable for the colorimetric determination of pH, some data of its pIC1 will be reported for the sake of completeness. Prideaux' found spectrophotometrically at room temperature (about, 1 8 ~ 7 pK1 ) = 3.31 (citrate buffer); whereas from the work of Guntelberg and Schiodt the following data have been computed. Dimethylaminoazobenzene (18") Electrolyte concentration 0
0.1SEicl
PKC
PK1
3'29 3.30
3'25 3.34
Electrolyte concentration
0.5sKC1 I
" "
PKo
PKI
3.36 3.40
3.40 3.39
N e t hylred Temperature
Method used
Type of buffer
~ K I
Room ternp.(zj"?) Spectrophotom Clark and Lubs j . 0 5 ,, '' (*\bout I&'"?) Citrate 4.95 1, 2j0 4.92 Colorim
30°
Jf
ZOO
tf
I j O
Room temp.
18' IjO
2 oo
3 0' 40°
( 2 5 O ? )
>I 1)
,,
Author
Brode6 Prideaux' Thiel and Dassler?? Clark and Lubs 4.96-j.0 Gillespie'l >I 5.I Clark and Lubs8 If 5.05 Kolthoff?* ,, 5.1 Van Alstine'2 Acetate 4.98 Tizard?' f> 5.13 TizardZ4reported by Gillespie
1,
11
1)
,I
7)
fl
j.10
5.05
4.98 f, 11 4.93 50' 2R I. M. Kolthoff: Rec. Trav. chim., 43, 144 (1924); 44, 75 (1925).
I478
I. M. KOLTHOFF
From Tizard's work it may be inferred that pKI decreases 0.006 for each degree increase in temperature. According to Kolthoffi5 the salt error of methyl red is negligibly small at ionic strengths between o and 0.5. From this and all data reported in the table, it may be concluded that an ionic strength between o and 0.5; pK1 = 5.00 0.05 - 0.006 (t-20) One-color indicators Nitrophenols p Dinitrophenol ( 1 oxy. 1.6 dinitrobenzene)
*
I n the following table the figures reported in the literature have been reduced to a temperature of 20' by using the temperature modulus of pKI of 0.006 given by L. hIichaelis and A. Gyemant.2B Besides the type of buffer the ionic strength has also been reported. /3 Dinitrophenol a t zoo Type of buffer
Ionic strength and salt
Acetic acid
order of
Acetate
0.025
Method used
Colorimetr.
0.001
(3. 7z0?) 3.56 3.38 or
0.15 (XaC1) 0.5 (NaC1)
'J
'I
0.001
3.57? 3.34 3.66
0.00 5-0.08
3.54
0.5 ( X U )
>)
HC1 Clark and Lubs hlonopotassium citrate Monopotassium citrate
pK1 3.68
Jl
0 .I
'I
0.25
Elecxond. J'
3.46
Author
Michaelis and Gyemant2 1'
ll 'J
JJ JJ
Kolthoff 30 'J
3.03 3.79 3.60
I t may be mentioned that there is a fairly large deviation in the set of pKI values calculated from the measurements of Michaelis and Gyemant. Still their average value at an ionic strength of 0.001of 3.68 agrees very closely with that of Kolthoff (3.66), and the average of the conductivity data obtained by Bader and Holleman resp. From the figures it can be concluded, that a t an ionic strength of 0.001; pKI
= 3.6;
pK1
= 3.50 rt 0.05
f 0.03
- 0.006
(t-20)
and a t an ionic strength of - 0.006 (t-20)
8 . Gyemant and L. Michaelis: Biochem. Z., 109, 1 6 j (1920). I. M. KolthotT: Pharmrtc. Weekbl., 60, 949 (1923). 31R.Bader: Z. physik. Chem., 6,289 (1890). 32 A. F. Holleman: Rec. Trav. chim., 21, 428 (1902). 28
30
0.1:
I479
ISDICATOR CONSTANTS
The salt error is relatively large; especially a t higher salt-concentration is the pK1 value very uncertain. The indicator is not very useful a t high electrolyte content of the solution. crDinitropheno1
(I
: z :4)
at
20’
Type of buffer Ionic strength and salt
Method used
PKI
Acetate
Colorimetr.
4.05
0.00 j-0.0j
,, ,,
2,
0 . 5 (KC1) 0.15 (SaC1)
1,
0.5
__
Clark and Lubs
,, -
3.85 4.11
,,
0.05-0.08
Elec. cond.
0,001
2,
0.001
9,
Kolthoff 3o 12
3.92 3.80
,,
(IWl)
0. j
ff
3.95
>f
0
12
3.84
,, ,,
”
Author
Michaelis and GyemantZ9
4.13 4.03
3,
RadeP H~lleman~~
The agreement between Rader’s value (electr. conduct of solution) and Kolthoff’s figure at an ionic strength of zero is very close, under these conditions: pK, = 4.10 f 0.03 - 0.006 (t-20’) Ionic strength =
0.1:
pK1
= 3.90
0.5: pK1 = 3.80
yDinitropheno1 (1:z:5) at zoo Type of buffer Ionic strength and salt Method used
Acetate 19
1,
0.15(KaC1)
,l
__ __
j.06 5.00
>,
0 . 5 (SaC1)
Clark and Lubs
PKI
Colorimetr. 5.14
0.03
,,
5.12
Elec. cond.
5 ,I9
0.07
0.001
,,
),
5.I9
. Author
Michaelis and Kruger33 1) 2,
Kolthoff30 Bader3l Holleman32
From the above the following figures have been computed:
Ionic strength Zero
,>
”
; pK,
o
Ij
(SaC1)
o 5 (SaC1) 33
= 5
20
*o
03 - o 0 0 4 j (t-zo)
i o 03 = 5 06 i. o 03 = 5 00 =ko 03 = 5
0 0;
IZ
L. Michaelis and Kriiger: Biochem. Z., 119, 30; ( 1 9 2 1 )
1480
I.
M, KOLTHOFF
p. Kitrophenol at
20'
Type of buffer Ionic strength and salt
Method used
~ K I
Acetate Approx. 0.05 Phosphate 0.006-0.0;
Colorimetr.
7.13 7.15
19 1,
0.08-0.10
0.5 (KaC1) order of 0.001
1,
__ __
ff >I
-
,3
-
f,
,,
Author
Rlichaelis and Gyemant?g >I
Kolthoff 3o 7.00 I1 7.08 Rfichaelis and Gyernant?' Electr.cond. 7 . 2 2 H. Euler and Bolin34 11 7 . 2 4 Holleman32 >> LundBn35 7.22 ,> 6.98 Bader3I 7.08 H a n t ~ s c h ~ ~ 11
, j
From the above it will be seen that the pKI value of p. nitrophenol is uncertain to within at least 0.1.According to 3Iichaelis and Gyemant the salt error at an ionic strength of 0.1 is negligibly small. According t o this statement, pK1 should be 7.15 (Llichaelis 8- G) or 7.00 (K) at an ionic strength between 0.0 and 0.1.The data in the literature on the electrical conductivity of p. nitrophenol solutions do not allow us to decide which is correct, as the latter show a variation between 6.98 and 7.24. The temperature modulus between rg0-300 derived from the work of AIicharlis and Gyemant is in good agreement with that calculated from the conductivity experiments of H a n t ~ s c hand ~ ~LundCn3j respectively: pK1 = ;.16 - 0.011 (t-20') (XI and G) At the present time, however, it is impossible to decide which pXI value is most reliable. It may be possible that p. Kitrophenol usually contains another nitrophenol, which is hard to remove by recrystallisation. m . Sitrophenol (reduced with teniperature modulus of Michaelis and Gvemant to 20') Type of buffer Ionic strength and salt Phosphate 0.0 1-0.03
Method used
C'olorinietr.
pK
8.33
Author
Nichaelis and G ~ e r n a n t ? ~
!, 10.0j)
Borate Phosphate Phosphate -
,, >I
, >I
0.01-0.03
f'
0.003-0.0 I 0.05-0.1 0
0.05 (KaCl) 0.1
"
0.2
"
0.5
"
-
I
__
0.001
-
0.OOI 0.001
,; ,I ,I f,
,, 11
Elect. cond. ,I 1)
8.33 8.3 I 8.29
8.3 I 8.26 8.21
8.16 8.1j 8.13 8.04 7.99
8.35
I1
Xichaelis and K r U g d 3 Iiolthoff Michaelis and Kruger33 ,I I>
,, ,,
,,
Holleman3* BadeP Lund61P
H. Euler and Bolin: Z. phvsik. Chem., 66, 7 1 (1909). H. Lund6n: J. chim. phys:, 6, j74 (19071; 2. physik. Chem., 70, 253 (rgIo). 3 8 A .Hantzsch: Ber., 32, 3066 (1899). 34
s5
1481
INDICATOR CONSTANTS
Here the agreement betTveen Michaelis and Gyemant of Kruger, Kolthoff (both colorimetrically) and LundCn (conductometrically) is yery satisfactory; the conductivity data of Holleman and of Bader seem to be too high. It should be remembered that the application of the conductivity method t o such a \Teak acid as m. nitrophenol is rather precarious. Traces of impurities affect the readings relatively much. The temperature modulus derived from Michaelis’ work (0.008) differs somewhat from that of LundCn’s experiments (0.013). From the above, it may be concluded that between a temperature of 15’ t o 30’ and an ionic strength of pKI = PICI = p I i ~= pKI =
0.
0.1 0.2
0.5
8 . 3 j f 0.03
- 0.01
(t-20’)
8.25
8.18 8.1;
From all that has been said of the nitrophenols it appears that the pK1 value of dinitrophenols is rather dependent upon the electrolyte content of the solution. At an ionic strength between o and 0 . j the data are not known vith the same degree of accuracy as those of the sulfonphthaleins or the azoindicators. The pKI value of p. nitrophenolisuncertaintomithino.1 j . Therefore in the application of the nitrophenols according t o the method of JIichaelis there is generally an uncertainty in the results of at least’ 0.1 on account of the uncertain value of the indicator constants. I t seems that the following one color indicators have advantages over the nitrophenols. Their salt error is smaller (quinaldinred excepted), whereas the color change takes place from colorless to red or vice versa. -1summary of the indicator properties as determined by the author is given in the following list : Name indicator
Ionic strength
2 . 4 . z’4”’’Pentaniethoxgtriphenyl~arbinol”~ 1.86 i 0 . 0 j +0.008(t.20) 0-0.1 2 . 4 2’4’2’”’’ Hexa ” 3 . 3 2 *0.03+0.00; (t-zo) 0-0.1 ,> j . 9 0 (20’) 2.4.6 2 ’ 4 ’ 2 ’ ” ” Hepts ” 0 . 0 j-0.I Quinaldinred3* 2.63-0.007 (t-20’) 0 1) 2.73 0.00j
>,
,,
,, Pina~hrom~~
2.90
0 .I
3.10
O.j(KC1)
7.3 4-0.0 I 3 (t-2 0’)
0.014
Discussion and Summary The indicator constants are a function of the ionic strength of the solution. At infinitely dilute solution the indicator-constant is equal to the thermo-
3.
3 7 1 . &I. Kolthoff: J. Am. Chem. SOC., 49, 1218 (1927). bl. Kolthoff: Biochem. Z. 199,77 (1928);J. F. MacClendon: J. Biol. Chem 59,437
381.
(1929). 39
I. hl. Kolthoff. J. Am. Chem. SOC.,50, 1604 (1928).
1482
I. M. KOLTHOFF
dynamic activity constant (exponent), the latter being a real constant at any electrolyte content of the solution. It should be mentioned that pKI not only depends upon the ionic strength but also on the type of ions present. Therefore for each indicator a set of data should be derived, which hold a t different ionic strength of various electrolytes, as has been done by Sendroy and HastingsZ0 for bromcresolgreen, bromxresolpurple and phenolred. For most practical cases, however, it will do to indicate pK1 quite generally at ionic strengths below 0.1 and neglect the specific ion effect. This has been done in the following table, in which the data discussed in the previous paragraphs have been summarized. Indicator constants at
20'
~ K atI ionic strength of
Indicator
0
m. Cresolpurple Thymolblue Bromphenolblue Bromcresolgreen
0.01
0.05
(1.52
0.1
O.j
'..j'
1.6;
1.65 1.6; 3 . 8 j 3.75 (KC1) 4.66 4.50 (KC1,l
1.65 (15-30') 4.10 ( I 5 - 2 5 ' ) 4.90 ( I 5-30')
4.06 4.80
4.00
6.25-0.00j (t-20)
6.15
6.05 6.00
4.70
4.42 (KaCl)
C hlorphenolred
j.9 (IiC1) 5.85 (SaC1)
Bromcresolpurple
6.40-0.00j
Bromthymolblue
7 . 3 0 (IjO-30')
Phenolred
8.00-0.007
Cresolred m. Cresolpurple Thyniolblue
8.46 (at 30')
(t-20)
6.28 6.21 6.12
j . 9 (KC1)
j . 8 (KaC1) 7.19 7.73
(t-20') 7.92 7.84
6.9 (KCl) 6.8 (NaCl) 7.81 i . 6 (KCI) 7.10
7.j 0.
8.32 ( 3 0 7 9.20 ( I j-30')
RIethylorange 3.46-0.014 (t-20) Diniethvlaminoazobenzene 3.2 j 5 .oo-0.006 (t-zo) Rlet hylred
9.01
8.9 j
8.90
3.46
3.46
3.46 3.46 3 . 3 4 3.40 (KC1) 5.00
___
/3 Dinitrophenol ( I :z :j ) 3.;0-0.006 (t-zo) ( I :z :4)4.10-0 006 j t - 2 0 ) a >, ( 1 : 2 : j ) j . 2 o - o . o o ~ jit-20) Y ( ; : o o to ; , I j ) - o , o I I ( t - 2 0 ) p Sitrophenol >> 8.35-0.01 (t-20) m. .~ 2 . 4 . 2 ' 4 ' 2 " Penta methyosytriphen~lcarbinol 1.86 2.4.2'"2''4'' Hem 2.1.6 2'4'2''4" Hepta
Quinaldinred Pinachrom
(SaC1)
8.30 8.25
"
3.32
+ 0.008 +
3.50 3.95 3.90 3.80 (liC1) 5.12 5.10 5.00 (SaC'1) 8.30 8.2 j
(t-20)
0.007 j t - 2 0 )
1.86 1.86
j.90
"
2.63-0.007
(t-20')
7.34-0.013
(t-20)
5.00
2.80
8.1 j (SaC'1)
1.86 1.86 5.90 2.90
7.34
3.10 (KC1)
ISDICATOR CONSTANTS
I483
All constants are related to the Sorensen values and not to the activity of hydrogen ions; at infinitely dilute solution 0.04 should be added to the reported value to find the thermo-dynamical constant paK. (aHf) (a acid form) aIi = (a alkaline form) The figures in the table are supposed to be accurate within a t least o.oj. As has been pointed out in a former paper, methylorange and methylred are ideal for accurate pH determinations as their indicator constant is almost independent of the ionic strength, if the latter is smaller than 0.5. I n many practical cases, the concentration and type of ions in the unknown are not given, and then especially the application of methylorange and methylred is advantageous. It should be remembered that methylorange reacts in a specific way with biphthalate or phthalic acid, therefore citrate solutions should be used instead of Clark’s buffers, if solutions of known pH are applied for comparison. I t seems that the methoxy triphenyl carbinols, pinachrom and thymolblue (acid range) are also very advantageous, since the salt influence at an ionic strength below 0.1 is very small or negligible. Manneapohs, January, 1950.
