the activity coefficients of certain acid-base … · j. sendroy, jr., and a. b. hastings 199 the...

THE ACTIVITY COEFFICIENTS OF CERTAIN ACID-BASE INDICATORS.*

BY JULIUS SENDROY, JR., AND A. BAIRD HASTINGS.

(From the Hospital of The Rockefeller Institute for Medical Research, New York.)

(Received for publication, December 29, 1928.)

At an early stage in the development of the calorimetric method, Ktister (I), Van Cleeff (2), Acree (3), von Szyszkowski (4), and Michaelis and Rona (5) recognized and pointed out the fact that the salt content of the solution influenced the reaction of the indicator. The color of the same indicator in the same buffer solution could be changed by addition of neutral salts. Sorensen and Palitzsch (6) called attention to the fact that it was necessary to consider separately, the “neutral salt effect” on the buffer itself, and on the indicator color. In 1914, Bjerrum (7) suggested that this double effect had to do with the change in the dissociation constant of the buffer, and also of the indicator. He found that the change in the logarithm of the indicator dissociation constant was proportional to the variation in salt concentration.

The literature covering the work done on “salt errors” of indicators will be found in the texts and monographs of Thiel (S), Bjerrum (7), Prideaux (9), Michaelis (lo), Kolthoff (ll), and Clark (12), and will be referred to in connection with the development of the text of this paper. Kolthoff, in 1926, summarized the results in saying that, ‘Various theories have been advanced to explain the salt error, but none of them is adequate for the quantitative interpretation of the behavior of every indicator.” The indicator error caused by different salts has been found to vary in an apparently irrational manner. The question has therefore been allowed to rest as a purely empirical matter. ‘Salt error” has been correlated with percentage salt, equivalent concentration, molecular concentration, and sodium ion concentration. The effect of salt has been determined in most cases at such

* A preliminary report of this work appeared under the above title in the Proceedings of the American Society of Biological Chemists, J. Biol. Chem., 78, p. lxvii (1928).

197

by guest on Decem

ber 28, 2019http://w

ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

198 Indicator Activity Coefficients

high concentrations of electrolyte as to be of little help in biological work, where solutions are seldom used of an electrolyte strength exceeding that of 0.9 per cent NaCl.

It is important to note, however, that in 1921, Brijnsted (13), on the basis of some of Sorensen’s old data, suggested that the behavior of some indicators, including phenolphthalein and neutral red, might be due to the effect of interionic forces in electrolytic solutions. He obtained good agreement between Sorensen’s data and the theoretical equations which he and Bjerrum had developed on the basis of the former’s theory of complete dissociation.

In the present paper we have attempted to utilize recent ad- vances in the theory of solutions to study indicator behavior in the presence of salts. The indicators studied have been brom-cresol green, brom-cresol purple, and phenol red, covering the pH range from 4.0 to 8.2. A theory, originally suggested by BrBnsted, has been further developed and applied to the systematic quantitative investigation of the change in color of these indicators under the influence of certain salts.

THEORETICAL.

The theoretical aspects of indicator color change are sufficiently discussed in the texts referred to above, so that it will be necessary to present here only a brief outline of the situation.

The indicators which we have studied may be structurally represented in two dimensional space as follows :

Phenol red. Brom-cresol purple. Brom-cresol green.

Mol. wt. = 354 Mol. wt. = 540 Mol. wt. = 698

f) ,,,,f) Ci&()Br Br~CX~ zaQBr Bg Y,,

\ \/ \/ C-O

’ I/;’

c-o

’ I//O

c-o

0

’ j//O -s -S --s

\ 0 0 \O 0 \O

Phenolsulfon- Dibromo-o-cresol Tetrabromo-m-cresol phthalein. sulfonphthalein. sulfonphthalein.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

J. Sendroy, Jr., and A. B. Hastings 199

The exact configuration of these compounds with respect to the bromine positions is not known.

According to the original theory of Wilhelm Ostwald, indicators are weak acids or weak bases, in which the color of the undissociated form is different from that in the dissociated or ionized form. There have been some objections to this idea, among them (1) the alkali salts of phenol red are red in the solid form as well as in solution, (2) some indicator color changes show a definite time reaction (they are either ionic reactions of a higher order or more likely not ionic, but molecular reactions), and (3) Beer’s law is obeyed in solutions of solvents other than water.

On the other hand, the school of Hantzsch and his collaborators has evolved the tautomeric or chromophoric theory, according to which the color of an indicator is a function of its constitution; that is, it depends on the equilibrium between a la&one form (such as colorless phenolphthalein in acid solution) and a quinone (such as red phenolphthalein in alkaline solution). However, as Kol- thoff states, the structural change may be a phenomenon parallel to the color change, and yet not really be the cause of it. Also, the correlation between color and pH is not explained according to this theory without some assumption of ionization.

One may combine the two theories as Stieglitz (14) and Kolthoff have proposed. Thus, there is not only an equilibrium between the lactone and quinone forms [LtiQ], but the quinone form will also be in equilibrium with Q- ions and Hf ions [Q+Q- + Hf]. The ions may or may not have the same constitutions as the undissociated molecules, and the final equilibrium constant evolved, although an “apparent” equilibrium constant, yields an expression which agrees with the simple Wilhelm Ostwald form of equation. For example, brom-cresol green will behave in this manner :

‘c’-0 ’ I//O

0 -S

\O

Colorless lactone (weak acid).

Colored acid quinone cresolate (strong acid).

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


0- + K+ ;;

Br Br Br

0 0

Br

CH, CH,

‘11 C

1 i

0 -S-O- + K+

II 0

Colored salt (strong acid).

The sulfonphthaleins are dibasic acids. However, the dissociation constant of the sulfonic acid group is so much stronger than that of the weak phenolic group with which the color change is mainly associated, that they may be and have been regarded as monobasic for most purposes.

In the following treatment, we may most simply consider the indicator as a weak acid, the salt or alkaline form, BA, of which is completely ionized, the acid, HA, not ionized to any significant extent. Consequently, all of the A- anions will be derived from, and equal in concentration to BA. If the activity coefficient of the undissociated acid is assumed to be unity,

(1) K’ = R TA-

where K’ denotes the apparent stoichiometric dissociation constant, K the apparent activity dissociation constant (the value of K’ at infinite dilution), and YA- the activity coefficient of the anion. If p is used to denote negative logarithm, the expression showing the relation between the hydrogen ion activity and the two forms of the indicator will then be the familiar Henderson- Hasselbalch equation:

(2) DA1

p@H+ = PK’ + log [HA]

Also, from Equation 1,

(3) pK’ = pK - pTA- = pK - ApK’

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


and for a dibasic acid,

(4) pKz’ = p& + p’yA- - p’yA- = PIG - ApIG’

The ratio [BA] : [HA] may be altered by change of either paH+ Or Of pK’. In other words, with change in pK’ there is the possibility of an alteration in color of a solution with pan+ un- changed. When Equation 1 is applied to an indicator, BA is calculated as the colored alkali salt. In this case the pK’ indicates both ionic and tautomeric equilibria. Since a constant fraction of BA is presumably tautomerized into the colored form of the indicator under any given set of conditions, this constancy may be incorporated into the general equilibrium constant K’.

That the Debye-Htickel equation makes possible an approximate quantitative calculation of the effect of neutral salts on the apparent dissociation constants of weak acids has been shown in a number of instances. Working with pure buffer solutions, Hastings and Sendroy (15) applied the Debye-Htickel theory to the study of the first and second dissociation constants of carbonic acid. Since then Cohn has studied the second dissociation constant of phosphoric acid (16) and more recently the dissociation constant of acetic acid (17). Simms (18) has recently applied the theory to the investigation of systems of weak electrolytes of organic nature.

The Debye-Hiickel theory of interionic activity (19) is expressed in terms of activity coefficients, and involves the assumption of complete dissociation. When the ions are assumed to function as point charges, the Debye-Hiickel equations reduce to the limiting law of Bronsted and La Mer (20). For a single ion,

(5) - log yion = 0.5 v2 &Y

where y is the activity coefficient, v is the valence of the ion, and p denotes the ionic strength, a unit of concentration introduced by Lewis and Randall (21). Since p = + cv2, where c = molar or molal concentration, a molar solution of NaCl and one of MgS04 of the same strength will be as 1: 1 in molar concentration, but as 1: 4 in ionic strength. Where two ions are involved,

(6) log y’ = 0.5 (v*2 - v12) 4 YZ

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


or for monovalent and divalent ions,

(7)

However, at higher concentrations, the ions must be regarded as finite spheres of rigid size and the Debye-Hiickel equation is:

(8) log Yion = A. v= d/.~

1+04 XCP

where A is a universal constant based on the absolute temperature, the dielectric constant of water, and the Boltzmann distri- bution coefficient; B is the composite constant involving the effective thickness of the ionic atmosphere (about 0.33 X lo8 4; cm.) and the size of the ions (usually about 2 to 5 X 10V8 cm.). C is a “salting out” term or polarization or hydration term for higher concentrations, to take account of the effect of change in dielectric constant of the environment of the particular ions whose activity is being studied. In our work, this last term can probably be neglected without causing any appreciable error, the concentrations here being no higher than P = 0.2.*

EXPERIMENTAL.

Procedure and Methods.

In order to obtain reproducible and constant potentials with the hydrogen electrode, it was necessary to buffer the solutions studied. Accordingly, phosphate and acetate mixtures of definite composition were prepared, diluted to the lowest concentrations indicated in the tables of results (M/210 acetates, and M/150 phosphates), and varying amounts of salt solutions of acetates, phosphates, NaC1, KCl, Na2S04, K804, CaCL, MgCL, and MgSOd were added to increase the ionic strength to about ,u = 0.2. The composition of all stock solutions was checked quantitatively

* It is recognized that differences in the physical and chemical constitution of solutions may cause differences in light absorption, quite apart from the effect of these differences on the ratio of the two forms of indicator as influenced by the reaction of the solution and the apparent dissociation constant of the indicator. The work of van Halban and Ebert (22), however, would seem to indicate that these effects at our concentrations of indicator and salt would be very slight, and probably negligible.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


by standard methods. To study the effect, if there is any, of a non-electrolyte, some experiments were carried out in which a glucose solution was used as diluent. In order to have the concentrations of solutions the same for both electrometric and calorimetric observations, they were diluted -& (9cc. + 1 cc. water) for the electrometric determinations, since the indicator addition produced the same result of dilution for the calorimetric method. The water used for all work was freshly redistilled from acid dichromate. All observations were made at 20 &O.l”, colori- metric determinations being made in duplicate, electrometric until three consecutive determinations showed no greater variation than 0.2 miIlivolt.

In order to avoid difficulty due to the presence of minute amounts of O2 in these dilute solutions, the extra precaution was taken of bubbling hydrogen gas through them before making the electrometric observations. The hydrogen electrode apparatus has already been described (23). The standard solution used to obtain e, the value of the saturated calomel half-cell, was 0.1 N HCI, made from Hulett’s constant boiling acid. The pan+ was assumed to be 1.08. New platinum-coated electrodes were used for each experiment, the e being determined before and fre- quently after all determinations were made.

For connecting bridge, saturated KC1 solution was employed. Our calculations involve the assumption that the liquid junction potential between the solution under investigation and the saturated KC1 was the same in all of the solutions studied, including the 0.1 N HCl used for standardization. When we consider the different ions and ionic strengths involved in these studies, it may be questionable whether such an assumption of zero diffusion potential in each case is justified. However, the error from this source is apparently but slight in the use of the saturated KC1 bridge.

The calorimetric determinations were made by adding 1 cc. of indicator (0.016 per cent brom-cresol green, 0.016 to 0.032 per cent brom-cresol purple, or 0.0075 per cent phenol red) to 9 cc. of the solution, and reading by daylight lamp against bicolor standards, as described in previous papers (24,25). These standards depend only on the relative amounts (measured and known), of indicator in full acid and full alkaline form. Complicating factors, such as the fading of the standards, the assumption of a

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


pK’ value for the indicator, or the consideration of the ionic strength of the standards, as in the case of phosphate andacetate buffer standards, were thereby eliminated. The concentration of indicator made according to Clark, with 1 equivalent of alkali, was only 0.00002 to 0.00006 M, not sufficient to contribute to or affect the buffering power of the solution, or its ionic strength.*

0 0.02 006 008 01 0.14

Ho25 salt per Liter

FIG. 1. Electrometric and calorimetric determinations of buffers at various dilutions.

1 Acknowledgment should be made to the La Motte Chemical Company and to Hynson, Westcott and Dunning for supplying us with pure indicators for these experiments. No further purification was attempted by us. Several successive samples of these indicators gave identical titration curves in accordance with theory as shown by us previously (25). The titration curve of each indicator was theoretical for a solution containing a single weak acid. If other phenolphthalein derivatives had been present in significant proportions they would have measurably distorted the titra-

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE I.

Brom-Cresol Green pK’ Change at 20” with Increase of Ionic Strength by Means of Sodium Acetate. Calorimetric Readings with Indi-

cator Concentration = O.OOOO!J M.

Sai?o?e Electro- metric paH+’

Colori- metric

olor ratk log R.

5.08 5.08

5.06 5.08

5.05 5.06

5.04 5.06

Composition. P G ,: I

HCrHaOz NaGHa _______- --

I pyokg. 2

M p&kg. 2

1 0.00130 0.00303 0.00303 0.055 0.21 la 0.00130 0.00303 0.00303 0.055 0.23

2 0.00260 0.00606 0.00606 0.078 0.24 2a 0.00260 0.00606 0.00606 0.078 0.24

3 0.00390 0.00909 0.00909 0.095 0.25 3a s.00390 0.00909 0.00909 0.095 0.25

4 0.00650 0.01515 0.01515 0.123 0.26 4a 0.00650 0.01515 0.01515 0.123 0.26

5 0.01040 0.02424 0.02424 0.156 0.27 5a 0.01040 0.02424 0.02424 0.156 0.26

6 0.01427 0.03333 0.03333 0.182 0.27 6a 0.01427 0.03333 0.03333 0.182 0.27

7 0.01948 0.04545 0.04545 0.213 0.28 7a 0.01948 0.04545 0.04545 0.213 0.29

8 0.02468 0.05757 0.05757 0.240 0.29 8a 0.02468 0.05757 0.05757 0.240 0.30

9 0.03117 0.07272 0.07272 0.270 0 30 9a 0.03117 0.07272 0.07272 0.270 0.31

10 0.03896 0.09093 0.09090 0.301 0.31 10 a 0.03896 0.03090 0.09090 0.301 0.32

-

5.03 5.04

5.03 5.03

5.01 5.02

5.01 5.02

5.01 5.02

5.01 5.01

pK’ indicator. A pK’

4.87 0.05 4.85 0.07

4.82 0.10 4.84 0.08

4.80 0.12 4.81 0.11

4.78 0.14 4.80 0.12

4.76 0.16 4.78 0.14

4.76 0.16 4.76 0.16

4.73 4.73

0.19 0.19

4.72 0.20 4.72 0.20

4.71 4.71

0.21 0.21

4.70 0.22 4.69 0.23

tion curves, except in the improbable case that the impurity had the same pK’ as the pure indicator. The nature of our reproducible results indicates that we were dealing with substances of a considerable degree of purity. In the case of brom-cresol green many early preparations were unusable owing to the presence of an insoluble impurity. With later preparations we had no such difficulty. These melted sharply at 215.5” (Cohen reports 217”; Cohen, B., Pub. Health Rep., U. S. P. H. S., 41,305l (1926)) andgave reproducible titration curves. Brom-cresol purple melted at 243”. The phenol red had no definite melting point; it decomposed at about 240”.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE II.

Brom-Cresol Green pK’ Change at 20” with Increase of Ionic Strength by Means of Sodium Chloride. Calorimetric Readings

with Indicator Concentration = 0.0000% M.

Sample NO.

I

la

2 2a

3 3a

4 4a

5 5a

6 6a

7 7a

8 8a

9 9a

10 10 a

Composi- ion: acetate 8 in Samph 2, Table I,

+ NaCI.

P v5- Electro-

metric paH+.

C&Xi- metric

hr ratio: log R.

PK’ ndicator.

-

--

ApK

M per kg. Hz0

0.00000

0.00000

0.00606 0.078 5.07 0.24 4.83 0.09 0.00606 0.078 5.07 0.24 4.83 0.09

0.00909 0.01515 0.123 5.04 0.25 4.79 0.13 0.00909 0.01515 0.123 5.06 0.25 4.81 0.11

0.01818 0.02424 0.156 5.03 0.26 4.77 0.15 0.01818 0.02424 0.156 5.03 0.26 4.77 0.15

0.02727 0.03333 0.182 5.01 0.27 4.74 0.18 0.02727 0.03333 0.182 5.01 0.27 4.74 0.18

0.04545 0.05151 0.227 5.00 0.28 4.72 0.20 0.04545 0.05151 0.227 5.00 0.28 4.72 0.20

0.06363 0.06969 0.264 4.98 0.30 4.68 0.24 0.06363 0.06969 0.264 4.99 0.30 4.69 0.23

0.08181 0.08787 0.296 4.97 0.31 4.66 0.26 0.08181 0.08787 0.296 4.97 0.31 4.66 0.26

0.10908 0.11514 0.339 4.96 0.32 4.64 0.28 0.10908 0.11514 0.339 4.97 0.33 4.64 0.28

0.13635 0.14241 0.377 4.94 0.33 4.61 0.31 0.13635 0.14241 0.377 4.96 0.34 4.62 0.30

0.16362 0.16968 0.412 0.16362 0.16968 0.412

0.34 4.59 0.33 0.35 4.60 0.32

0.21210 0.21816 0.467

4.93 4.95

4.93 0.36 4.57 0.35

RESULTS.

-

When a ~/15 phosphate solution of about pq+ = 7.4, such as is used for color standards, is diluted in several steps to 30 times its

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE III.

Brom-Cresol Green pK’ Change at 20” with Increase of Ionic Strength by Means of Potassium Chloride. Calorimetric Readings

with Indicator Concentration = 0.00002 M.

Sample No.

t

_-

1 1% lb

Y pHergkg. 2

0.00000 0.00000 0.00000

2 2a

0.00909 0.00909

3 3a

0.01818 0.01818

4 4a

0.02727 0.03030

5 5a

0.04545 0.04545

6 0.06363 6a 0.06363 6b 0.06363

7 7a

0.08181 0.08181

8 0.10908 8a 0.10908 8b 0.10908

9 0.13635 9a 0.13635 9b 0.13635

10 0.16362 10 a 0.16362 10 b 0.16362

11 11 a 11 h

0.19998 0.19998 0.19998

hnposi- :n: acetate in &mph

, Table I, + KCl.

P

-

_-

Electro- metric paH+’

Colori- metric

hr ratio: log R.

PK’ dicator.

-

_-

A pK’

--

3.00606 0.078 5.07 0.22 4.85 0.07 3.00606 0.078 5.09 0.24 4.85 0.07 3.00606 0.078 5.07 0.24 4.83 0.09

0.01515 0.123 5.06 0.24 4.82 0.10 0.01515 0.123 5.04 0.25 4.79 0.13

0.02424 0.156 5.04 0.27 0.02424 0.156 5.03 0.26

4.77 4.77

0.15 0.15

0.03333 0.182 5.03 0.29 4.74 0.18 0.03636 0.191 5.02 0.29 4.73 0.19

0.05151 0.227 5.02 0.30 4.72 0.20 0.05151 0.227 5.01 0.31 4.70 0.22

0.06969 0.264 5.01 0.31 4.70 0.22 0.06969 0.264 4.99 0.32 4.67 0.25 0.06969 0.264 5.00 0.32 4.68 0.24

0.08787 0.296 5.00 0.34 4.66 0.26 0.08787 0.296 5.00 0.34 4.66 0.26

0.11514 0.339 4.99 0.34 4.65 0.27 0.11514 0.339 4.99 0.35 4.64 0.28 0.11514 0.339 4.98 0.35 4.63 0.29

0.14241 0.377 4.98 0.35 4.63 0.14241 0.377 4.98 0.35 4.63 0.14241 0.377 4.98 0.36 4.62

0.16968 0.412 4.98 0.35 4.63 0.16968 0.412 4.97 0.36 4.61 0.16968 0.412 4.98 0.36 4.62

0.20604 0.460 4.97 0.36 4.61 0.20604 0.460 4.97 0.36 4.61 0.20604 0.460 4.96 0.37 4.59

0.29 0.29 0.30

0.29 0.31 0.30

0.31 0.31 0.33

-.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE IV.

Brom-Cresol Green pK’ Change at’ 20” with Increase of Ionic Strength by Means of Sodium Sulfate. Calorimetric Readings with

Indicator Concentration = 0.00002 M.

SaNmoq1e Chmposi-

ion: acetate 9 in Sampb 2, Table I, + NazS0~

P

Electro- metric paH+

COlOri- metric

:olor ratio: 1ogR.

PK odicator. A pK’

1 la

M rergkg. 2

0.00000

0.00000

0.00606 0.078 5.06 0.24 4.82 0.10 0.00606 0.078 5.09 0.24 4.85 0.07

2 0.00303 0.01515 0.123 5.06 0.25 4.81 0.11 2a 0.00303 0.01515 0.123 5.06 0.25 4.81 0.11

3 0.00606 0.02424 0.156 5.05 0.26 4.79 0.13 3a 0.00606 0.02424 0.156 5.03 0.26 4.77 0.15

4 0.00909 0.03333 0.182 5.04 0.27 4.77 0.15 4a 0.00909 0.03333 0.182 5.03 0.27 4.76 0.16

5 0.01515 0.05151 0.227 5.01 0.28 4.73 0.19 5a 0.01515 0.05151 0.227 5.03 0.29 4.74 0.18

6 0.02424 0.06969 0.264 5.01 0.30 4.71 0.21 6a 0.02424 0.06969 0.264 5.00 0.30 4.70 0.22

7 0.02727 0.08787 0.296 5.00 0.31 4.69 0.23 7a 0.02727 0.08787 0.296 4.99 0.31 4.68 0.24

8 0.03636 0.11514 0.339 4.99 0.32 4.67 0.25 8a 0.03636 0.11514 0.339 4.99 0.32 4.67 0.25

9 0.04545 0.14241 0.377 4.98 0.33 4.65 0.27 9a 0.04545 0.14241 0.377 4.98 0.33 4.65 0.27

10 0.05454 0.16968 0.412 4.98 0.34 4.64 0.28 10 a 0.05454 0.16968 0.412 4.97 0.34 4.63 0.29

11 0.06666 0.20604 0.454 4.95 0.35 4.60 0.32 11 a 0.07070 0.21816 0.467 4.96 0.35 4.61 0.31

12 0.08060 0.24786 0.498 4.94 0.36 4.58 0.34

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE V.

BTOm-CTeSOl Green pK’ Change at 20” with Increase of Ionic Strength by Means of Potassium Sulfate. Calorimetric Readings with

Sax’e

-

tit a* 2,

.-

d

hnposi- ,n: acetate in Sample Table I,

k K&304.

1 la

d rergkg. 2

0.00000

0.00000

2 2a

0.00228 0.00228

3 3a

0.00455 0.00455

4 4a

0.00682 0.00682

5 5a

0.01137 0.01137

6 0.01591 6a 0.01591

7 7a

0.02046 0.02046

8 0.02727 8a 0.02727

9 9a

10 10 a

11

0.03409 0.03409

0.04091 0.04091

0.05303 -


p. Electro- metric p”IH+’

-

00

_-

Cdori- metric lor ratio: 1ogR.

PK’ dioator.

-

_-

A pK’

I.00606 0.078 5.07 0.24 4.83 0.09 j.00606 0.078 5.07 0.24 4.83 0.09

I.01288 0.113 5.07 0.25 4.82 0.10 I.01288 0.113 5.07 0.25 4.82 0.10

1.01969 0.140 5.06 0.25 4.81 0.11 I.01969 0.140 5.06 0.26 4.80 0.12

3.02652 0.163 5.05 0.26 4.79 0.13 0.02652 0.163 5.05 0.27 4.78 0.14

0.04015 0.203 5.04 0.27 4.77 0.15 0.04015 0.203 5.04 0.28 4.76 0.16

0.05379 0.232 5.03 0.29 4.74 0.18 0.05379 0.232 5.02 0.30 4.72 0.20

0.06742 0.26C 0.06742 0.26C

5.02 0.30 4.72 0.20 5.02 0.31 4.71 0.21

0.08787 0.08787

0.29f 0.29E

5.01 0.32 4.69 0.23 5.00 0.32 4.68 0.24

0.10833 0.32E 0.10833 0.32s

4.67 0.25 4.67 0.25

0.12879 0.12879

4.66 0.24 4.66 0.24

0.16514

0.35: 0.35s

0.40( 4.98

0.34 0.33

0.34 0.34

0.35 4.63 0.21 -

-

- -

original volume, and the calorimetric pan+ is read against the original ~/15 standards at each dilution, with indicator concentrations constant, the result obtained with phenol red is such as is

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

Indicator Activity Coefficients

TABLE VI.

Brom-Cresol Green pK’ Change at 20” with Increase of Ionic Strength by Means of Calcium Chloride. Calorimetric Readings with


Sai%-?e

1 la

M per kg. Hz0

0.00000

0.00000

0.00604 0.078 5.08 0.24 4.84 0.08 0.00604 0.078 5.09 0.24 4.85 0.07

2 0.00312 0.01540 0.124 5.05 0.25 4.80 0.12 2a 0.00312 0.01540 0.124 5.04 0.26 4.78 0.14

3 0.00624 0.02478 0.157 5.03 0.27 4.76 0.16 3a 0.00624 0.02478 0.157 5.04 0.28 4.76. 0.16

4 0.00937 0.03414 0.185 5.01 0.29 4.72 0.20 4a 0.01025 0.03679 0.192 5.01 0.30 4.71 0.21

5 0.01561 0.05287 0.230 4.99 0.31 4.68 0.24 5a 0.01538 0.05218 0.228 5.01 0.31 4.70 0.22

6 0.02186 0.07160 0.267 4.98 0.33 4.65 0.27 6a 0.02153 0.07063 0.266 4.96 0.32 4.64 0.28

7 0.02810 0.09034 0.300 4.96 0.34 4.62 0.30 7a 0.02769 0.08910 0.298 4.96 0.33 4.63 0.29

8 0.03747 0.11844 0.344 4.95 0.35 4.60 0.32 8a 0.03691 0.11677 0.341 4.93 0.33 4.60 0.32

9 0.04684 0.14654 0.382 4.92 0.35 4.57 0.35 9a 0.04614 0.14445 0.380 4.92 0.34 4.58 0.34

10 0.05620 0.17464 10 a 0.05536 0.17212

0.417 0.415

0.473 0.470

4.91 0.35 4.56 0.36 4.90 0.34 4.56 0.36

11 0.07286 3.22460 11 a 0.07177 3.22135

4.88 0.36 4.52 0.40 4.89 0.35 4.54 0.38

Composi- .ion: acetate ts in Sampl 2, Table I,

+ CaC12.

shown in Fig. 1. The apparent slight pffn+ change is in the direc- tion of an increase with dilution. The same procedure with a

F2

-

-

P di- Electro-

metric PaH+.

- -Y-

Colori- metric

:dor ratio log R.

PK’ ndicatotor A pK’

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE VII.

Brom-Cresol Green pK’ Change at 20” with Increase of Ionic Strength by Means of Magnesium Chloride. Calorimetric Readings with

Indicator Concentration = 0.00002 hf. -- - ___ Composi-

tion: aoetat

sal21f a8 in Electro- Colori-

Sample 2, P 4 metric metric

oh ratic PK’

ndioatm A pK’ Ta$;.\,+ PaH+. log R.

-

.e

--

0

/

I

- ___ __

Y per kg.Hz

1 0.00000 0.00604 kO78 5.07 0.24 4.83 0.09 la 0.00000 0.00604 0.078 5.07 0.24 4.83 0.09

2 0.00327 0.01585 0.126 5.03 0.26 4.77 0.15 2a 0.00327 0.01585 0.126 5.03 0.26 4.77 0.15

3 0.00655 0.02568 0.160 5.02 0.28 4.74 0.18 3a 0.00655 0.02568 0.160 5.01 0.29 4.72 0.20

4 0.00982 0.03549 0.188 5.00 0.30 4.70 0.22 4a 0.01090 0.03875 0.197 5.00 0.30 4.70 0.22

5 0.01527 0.05185 0.228 4.97 0.31 4.66 0.26 5a 0.01527 0.05185 0.228 4.97 0.31 4.66 0.26

6 0.02181 0.07147 0.267 4.95 0.32 4.63 0.29 6a 0.02181 0.07147 0.267 4.96 0.32 4.64 0.28

7 0.02836 0.09110 0.302 4.94 0.33 4.61 0.31 7a 0.02836 0.09110 0.302 4.95 0.32 4.63 0.29

8 0.03708 0.11728 0.343 4.92 0.34 4.58 0.34 8a 0.03708 0.11728 0.343 4.93 0.33 4.60 0.32

9 0.04580 0.14345 0.379 4.90 0.34 4.56 0.36 9a 0.04580 0.14345 0.379 4.91 0.34 4.57 0.35

10 0.05672 3.17618 0.420 4.88 0.35 4.53 0.39 10 a 0.05672 3.17618 0.420 4.90 0.34 4.56 0.36

11 0.07198 3.22198 0.471 4.86 0.35 4.51 0.41 11 a 0.07198 3.22198 0.471 4.87 0.35 4.52 0.40

- -

~/15 phosphate mixture of pan+ about 6.4 and brom-cresol purple yields a similar result. On the other hand, with a ~/7 acetate mixture of po(n+ about 5.0 and brom-cresol green, the curve ob-

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


tained indicates, with reference to the original standard, a pQ(n+ decreasing with dilution.

An inspection of the electrometric dilution curves shows that there is no essential difference in the behavior of the phosphates and acetates, but that the above outlined difference is due to the fact that the buffer salts have other, though lesser, effects on the indicators than the effect exerted through pffn+. In each case, dilution of the buffer results in an increase of the actual po(n+ determined electrometrically. The calorimetric and electrometric observations agree at one point only; namely, at the concentration of salt corresponding to that of the calorimetric stand-

TABLE VIII.

Brom-Cresol Green pK’ at SO" with Addition of Glucose. Calorimetric Readings with Indicator Concentration = 0.00008 M.

t

_-

Chmposi- ion: acetate

as in Sample 2,

r$20k.+

Afpal.

0.0000

0.0111 0.0222 0.0333 0.0555 0.0888 0.1333 0.2000

_-

-

B

Electro- metric P’=H+.

Colori- metric

color ratio: log R.

PK’ ndicator.

0.00604 0.078 5.07 0.24 4.83 0.00604 0.078 5.08 0.25 4.83 0.00604 0.078 5.07 0.24 4.83 0.00604 0.078 5.07 0.25 4.82 0.00604 0.078 5.07 0.24 4.83 0.00604 0.078 5.06 0.25 4.81 0.00604 0.078 5.07 0.24 4.83 0.00604 0.078 5.05 0.24 4.81

ApK

0.09 0.09 0.09 0.10 0.09 0.11 0.09 0.11

ards used for the color readings. Increased concentration again causes a divergence of the two curves, but the discrepancy is of a different sign. Thus the relative salt concentrations of the unknown material and the color standard determine the magnitude and the algebraic sign of what is known in the literature as “salt error.” In the sense in which it is used in this paper, this is the difference between the calorimetric and the electrometric readings : P”H+(C) - wH+(e>.

The experimental data and the results obtained are given in Tables I to XXIII inclusive. The values of pK’ of the indicators were calculated according to Equation 2 from the electrometric

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE IX.

Brom-Cresol Purple pK’ Change at 20” with Increase of Ionic Strength by Means of Sodium and Potassium Phosphates. Calorimetric

Rea&ngs with Indicator Concentrakon = 0.00005 M.

SaNmople Electro-

metric PaH+.

Colori- metric

OOh ratio: log R.

PK' indi-

cator. A pK’

1 la

M per M per kg.H?O kg.WzO

0.00144 0.00057 0.00314 0.056 0.00144 0.00057 0.00314 0.056

6.69 0.30 6.39 0.07 6.69 0.30 6.39 0.07

2 0.00288 0.00113 0.00628 0.079 6.68 0.29 6.39 0.07 2a 0.00288 0.00113 0.00628 0,079 6.67 0.30 6.37 0.09

3 0.00433 0.00170 0.00943 0.097 6.66 0.29 6.37 0.09 3a 0.00433 0.00170 0.00943 0.097 6.65 0.29 6.36 0.10

4 0.00576 0.00227 0.01256 0.112 6.64 0.28 6.36 0.10 4a 0.00576 0.00227 0.01256 0.112 6.64 0.30 6.34 0.12

5 0.00866 0.00340 0.01886 0.137 6.61 0.28 6.33 0.13 5a 0.00866 0.00340 0.01886 0.137 6.58 0.29 6.29 0.17

6 0.01299 0.00510 0.02829 0.168 6.57 0.27 6.30 0.16 6a 0.01299 0.00510 0.02829 0.168 6.58 0.30 6.28 0.18

7 0.01732 0.00680 0.03772 0.194 6.55 0.27 6.28 0.18 7a 0.01732 0.00680 0.03772 0.194 6.56 0.29 6.27 0.19

8 0.02165 0.00850 0.04716 0.217 6.52 0.27 6.25 0.21 8a 0.02165 0.00850 0.04716 0.217 6.53 0.28 6.25 0.21

9 0.02598 0.01020 0.05658 0.238 6.50 0.26 6.24 0.22 9a 0.02598 0.01020 0.05658 0.238 6.51 0.27 6.24 0.22

10 0.03174 0.01247 0.06913 0.263 6.48 0.26 6.22 0.24 10 a 0.03174 0.01247 0.06913 0.263 6.49 0.26 6.23 0.23

11 0.03754 0.01475 0.07677 0.277 6.46 0.25 6.21 0.25 11 a 0.03754 0.01475 0.07677 0.277 6.46 0.24 6.22 0.24

12 0.04330 0.01700 0.09431 0.307 6.44 0.23 6.21 0.25 12 a 0.04330 0.01700 0.09431 0.307 6.44 0.23 6.21 0.25

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE X.

Brom-Cresol Purple pK’ Change at 20” with Increase of Ionic Strength by Means of Sodium Chloride. Calorimetric Readings with


Sam&lye

1 la

Composi- tion:

phosphate as in

Sample 3, Table IX, + N&l.

r per kg.HzC

0.00000

0.00000

0.00948 0.097 6.65 0.28 6.37 0.09 0.00948 0.097 6.60 0.29 6.31 0.15

2 0.00914 0.01862 0.136 6.59 0.28 6.31 0.15 2a 0.00914 0.01862 0.136 6.58 0.28 6.30 0.16

3 0.01828 0.02776 0.167 6.56 0.28 6.28 0.18 3a 0.01828 0.02776 0.167 6.53 0.28 6.25 0.21

4 0.02742 0.03690 0.192 6.52 0.27 6.25 0.21 4a 0.02742 0.03690 0.192 6.51 0.27 6.24 0.22

5 0.04570 0.05518 0.235 6.48 0.26 6.22 0.24 5a 0.04570 0.05518 0.235 6.46 0.26 6.20 0.26

6 0.06398 0.07346 0.271 6.43 0.24 6.19 0.27 6a 0.06398 0.07346 0.271 6.42 0.24 6.18 0.28

7 0.08226 0.09174 0.303 6.38 0.22 6.16 0.30 7a 0.08226 0.09174 0.303 6.38 0.22 6.16 0.30

8 0.10968 0.11916 0.345 6.34 0.20 6.14 0.32 8a 0.10968 0.11916 0.345 6.35 0.21 6.14 0.32

9 0.13710 0.14658 0.383 6.31 0.18 6.13 9a 0.13710 0.14658 0.383 6.31 0.19 6.12

10 0.16452 0.17400 0.417 6.28 0.15 6.13 10 a 0.16452 0.17400 0.417 6.29 0.17 6.12

0.33 0.34

0.33 0.34

P

Electrc- metric PaH+.

Colori- metric

0101 ratio: log R.

PK’ ldioator. A pK’

pan+ and the calorimetric readings of the samples against bicolor standards. The standards were marked in terms of the logarithm of the ratio of the alkaline to the acid form of the indicator. The values of pK’ so calculated involve the experimental errors in determination of pan+ electrometrically and calorimetrically, which

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XI.

Brom-Cresol Purple pK’ Change at 20" with Increase of Ionic Strength by Means of Potassium Chloride. Calorimetric Readings with

Indicator Concentration = 0.00005 JX.

Cyyi-

phosphate as in

Electrc- P G metric PK’ A pK’

PaH+. idicator.

C&Xi- metric

31or ratio: log R.

0.28 0.29

0.27 0.28

0.27 0.28

0.27 0.27

0.26 0.26

0.24 0.25

wrkg.HzO

1 0.00000 0.00948 0.097 6.64 6.36 0.10 1% 0.00000 0.00948 0.097 6.65 6.36 0.10

2 0.00910 0.01858 0.136 6.58 6.31 0.15 2a 0.00910 0.01858 0.136 6.59 6.31 0.15

3 0.01820 0.02768 0.166 6.56 6.29 0.17 3a 0.01820 0.02768 0.166 6.56 6.28 0.18

4 0.02730 0.03678 0.192 6.52 6.25 0.21 4a 0.02730 0.03678 0.192 6.53 6.26 0.20

5 0.04550 0.05498 0.234 6.49 6.23 0.23 5a 0.04550 0.05498 0.234 6.48 6.22 0.24

6 0.06370 0.07318 0.270 6.44 6.20 0.26 6a 0.06370 0.07318 0.270 6.44 6.19 0.27

7 0.08190 0.09138 0.302 6.42 6.19 0.27 7a 0.08190 0.09138 0.302 6.42 6.18 0.28

8 0.10920 0.11868 0.344 6.37 6.16 0.30 8a 0.10920 0.11868 0.344 6.38 6.15 0.31

9 0.13650 0.14598 0.382 6.35 6.13 0.33

10 0.16380 0.17328 0.416 6.32 6.14 0.32 10 a 0.16380 0.17328 0.416 6.32 6.12 0.34

may be 0.01 unit in each case, or even 0.02 for calorimetric observations. The change in pK’ with variation of ionic strength was then plotted against d;, and the curve drawn through the points was extrapolated to zero ionic strength. This was done for each salt used to vary the ionic strength. The results are

0.23 0.24

0.21 0.23

0.22

0.18 0.20

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XII.

Born-Cresol Purple pK’ Change with Increase of Ionic Strength by Means of Sodium Sulfate. Calorimetric Readings with

Indicator Concentration = 0.00003 by-.

i

.-

Composi- tion:

?iP phosphate Electrc- Colori-

as in Sample 3,

CL 4 metric metric PK’ P=H+. olor ratio: ndioator A pK’

Table IX, log R.

t N&04. -- pa ks.HnC

1 0.00000 0.00946 0.097 6.65 0.29 6.36 0.10 la 0.00000 0.00946 0.097 6.66 0.29 6.37 0.09

2 0.00270 0.01754 0.132 6.61 0.29 6.32 0.14 2a 0.00270 0.01754 0.132 6.61 0.28 6.33 0.13

3 0.00539 0.02563 0.160 6.57 0.28 6.29 0.17 3a 0.00539 0.02563 0.160 6.57 0.28 6.29 0.17

4 0.00809 0.03371 0.184 6.55 0.27 6.28 0.18 4a 0.00809 0.03371 0.184 6.55 0.27 6.28 0.18

5 0.01348 0.04988 0.223 6.50 0.26 6.24 0.22 5a 0.01348 0.04988 0.223 6.51 0.27 6.24 0.22

6 0.01887 0.06605 0.257 6.47 0.26 6.21 0.25 6a 0.01887 0.06605 0.257 6.48 0.27 6.21 0.25

7 0.02426 0.08222 0.287 6.46 0.27 6.19 0.27 7a 0.02426 0.08222 0.287 6.45 0.26 6.19 0.27

8 0.03234 0.10548 0.325 6.42 0.25 6.17 0.29 8a 0.03234 0.10548 0.325 6.42 0.25 6.17 0.29

9 0.04043 0.13073 0.361 6.39 0.23 6.16 0.30 9a 0.04043 0.13073 0.361 6.38 0.23 6.15 0.31

10 0.04851 0.15499 0.393 6.36 0.22 6.14 0.32 10 a 0.04851 0.15499 0.393 6.36 0.22 6.14 0.32

given in Table XXIV. Considering the uncertainty attached to such extrapolations from even the most dilute solutions with which these experiments were performed, the agreement of pK for the different solutions is fairly good. The average pK values thus obtained were then used as the basis for calculating A pK’.

-

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

J. Sendroy, Jr., and A. B. Hastings

TABLE XIII.

217

Brom-Cresol Purple pK’ Change with Increase of Ionic Strength by Means of Potassium Sulfate. Calorimetric Readings with

Indicator Concentration = 0.00003 x.

%?

Composi- tion:

phosphate as in

Sample 3, Table IX, + KzSOa.

P G Eleotro- metric PmH+.

Colori- metric

dor ratio: log R.

1 la

‘wkg.HzO

0.00000

0.00000

0.00948 0.097 6.66 0.30 0.00948 0.097 6.66 0.30

2 0.00227 0.01629 0.127 6.62 0.30 2a 0.00227 0.01629 0.127 6.62 0.29

3 0.00454 0.02310 0.152 6.60 0.29 3a 0.00454 0.02310 0.152 6.60 0.29

4 0.00681 0.02991 0.173 6.57 0.28 4a 0.00681 0.02991 0.173 6.57 0.28

5 0.01135 0.04353 0.208 6.54 0.28 5a 0.01135 0.04353 0.208 6.56 0.27

6 0.01589 0.05715 0.239 6.51 0.27 6a 0.01589 0.05715 0.239 6.53 0.27

7 0.02043 0.07077 0.266 6.49 0.26 7a 0.02043 0.07077 0.266 6.49 0.26

8 0.02724 0.09120 0.302 6.46 0.25 8a 0.02724 0.09120 0.302 6.46 0.25

9 9a

10 10 a

11

12

0.03905 0.11163 0.334 6.42 0.23 0.03905 0.11163 0.334 6.44 0.24

0.04086 0.13206 0.363 6.39 0.22 0.04086 0.13206 0.363 6.41 0.23

0.04697 0.15038 0.388

0.410

6.40

0.05297 0.16838 6.38 -

PK’ ndicator A pK’

6.36 0.10 6.36 0.10

6.32 0.14 6.33 0.13

6.31 0.15 6.31 0.15

6.29 0.17 6.29 0.17

6.26 0.20 6.29 0.17

6.24 0.22 6.26 0.20

6.23 0.23 6.23 0.23

6.21 0.25 6.21 0.25

6.19 0.27 6.20 0.26

6.17 0.29 6.18 0.28

6.18 0.28

6.17 0.29

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XIV.

Brom-Cresol Purple pK’ Change with Increase of Ionic Strength by Means of Magnesium Chloride. Calorimetric Readings with


Cotyoyi-

phosphke 88 in

Sample 3, Table IX, + MgC12.

per kg.HzC

0.00000

0.00000

LL 4 A pK’ Electro-

metric PaH+.

COlOri- metric

01or rat.io: log R.

PK’ ndicator

6.63 6.64

0.28 0.28

6.35 6.36

0.00329 0.00329

6.44 6.44

0.13 0.12

6.31 6.32

0.00657 0.00657

6.30 6.31

0.04 0.03

6.26 6.28

0.01094 0.01094

6.19 6.19

-0.05 -0.07

6.24 6.26

0.01641 0.01641

6.09 6.10

-0.13 -0.15

6.22 6.25

1 0.00948 0.097 0.11 la 0.00948 0.097 0.10

2 0.01934 0.139 0.15 2a 0.01934 0.139 0.14

3 0.02918 0.171 0.20 3a 0.02918 0.171 0.18

4 0.04230 0.206 0.22 4a 0.04230 0.206 0.20

5 0.05871 0.242 0.24 5a 0.05871 0.242 0.21

6 0.07840 0.280 0.27 6a 0.07840 0.280 0.27

7 0.09810 0.313 0.32 7a 0.09810 0.313 0.28

8 0.12764 0.357 0.35 8a 0.12764 0.357 0.32

9 0.15715 0.396 0.36 9a 0.15715 0.396 0.35

10 0.18670 0.432 0.36 10 a 0.18670 0.432 0.38

In Figs. 2 to 4, curves were drawn through the experimental points determined for each salt, and all were extrapolated to the same average pK value.

0.02298 0.02298

0.02954 0.02954

0.03939 0.03939

0.04923 0.04923

0.05908 0.05908

6.01 6.01

-0.18 -0.18

6.19 6.19

5.92 5.95

-0.22 -0.23

6.14 6.18

5.85 5.87

-0.26 -0.27

6.11 6.14

5.80 5.81

5.75 5.75

-0.30 -0.30

-0.35 -0.33

6.10 6.11

6.10 6.08

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XV.

Brom-Cresol Purple pK’ Change with Increase of Ionic Strength by Means qf Magnesium Sulfate. Calorimetric Readings with


1 la

2 2a

3 3a

6 6a

7 7a

8 8a

9 9a

10 10 a

Composi- tion:

phosphate as in

Sample 3. rable IX, + MgSOh.

per kg.HzO

0.00000

0.00000

P Electro- metric PaH+.

Cdori- metric

olor ratio: log R.

PK' Idicator. A pK’

0.00948 0.097 6.65 0.28 6.37 0.09 0.00948 0.097 6.63 0.27 6.36 0.10

0.00227 0.01857 0.136 6.51 0.17 6.34 0.12 0.00227 0.01857 0.136 6.51 0.16 6.35 0.11

0.00455 0.02766 0.166 6.41 0.10 6.31 0.15 0.00455 0.02766 0.166 6.41 0.09 6.32 0.14

0.00758 0.03978 0.199 6.32 0.03 6.29 0.17 0.00758 0.63978 0.199 6.32 0.03 6.29 0.17

0.01136 0.05493 0.234 6.25 -0.04 6.29 0.17 0.01136 0.05493 0.234 6.25 -0.02 6.27 0.19

0.01591 0.07311 0.270 6.18 -0.08 6.26 0.20 0.01591 0.07311 0.270 6.18 -0.07 6.25 0.21

0.02045 0.09130 0.302 6.13 -0.11 6.24 0.22 0.02045 0.09130 0.302 6.13 -0.12 6.25 0.21

0.02727 0.11856 0.344 6.06 -0.15 6.21 0.25 0.02727 0.11856 0.344 6.07 -0.15 6.22 0.24

0.03409 0.03409

0.04091 0.04091

0.14584 0.382 6.02 -0.18 6.20 0.26 0.14584 0.382 6.02 -0.17 6.18 0.28

0.17312 0.416 5.97 -0.21 6.18 0.28 0.17312 0.416 5.97 -0.20 6.17 0.29

DISCUSSION.

A search of the literature revealed only one paper containing data which could be used in estimating the pK’ variation of these indicators at different ionic strengths. Lepper and Martin (26)

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


studied the “salt error” of phenol red at 18”. They diluted phosphate and bicarbonate buffers with water and NaCl solutions, and determined pan+ electrometrically and calorimetrically. Their calorimetric solutions were diluted 10 per cent, whereas the electrometric samples were not. On the assumption that pK’ of phenol red = 7.78 for the phosphate color standards they used, the pK’ values at the different ionic strengths have been calculated from their Tables I to V, and are given in our Table XXV. Fig. 5 indicates the correspondence of the two sets of studies. The agreement is good at higher ionic strengths, but Lepper and

TABLE XVI.

Brom-&sol Purde pK’ at .2020” with Addition of Glucose. Calorimetric Readin& with Indicator Concentration =-0.00006 M.

%?

-7

C;g,“p”‘- phosphate

a8 in

kFl::“i + glucoseY.

a

0.01256 0.112 6.61 0.27 6.34 0.12 0.01256 0.112 6.62 0.27 6.35 0.11 0.01256 0.112 6.61 0.27 6.34 0.12 0.01256 0.112 6.60 0.26 6.34 0.12 0.01256 0.112 6.58 0.27 6.31 0.15 0.01256 0.112 6.59 0.25 6.34 0.12 0.01256 0.112 6.56 0.25 6.31 0.15 0: 01256 0.112 6.55 0.23 6.32 0.14

-

--

G Eleotro- metric pmH+.

c

T

cbloli- metric

olor ratio: log R.

PK’ indicator. A pK’

Martin’s results for phosphate mixtures alone do not fit in well with the rest of the data.

Unit of Electrolyte Concentration.-The ionic strength principle enunciated by Lewis and Randall (21) is to the effect that in dilute solutions, the activity coefficient of an ion is a function of the total ionic strength only. This principle has been questioned by Bronsted and La Mer (20) and more recently by La Mer and his collaborators (27, 28) for salts involving symmetrical and unsym- metrical high valence types, but in general it seems to hold fairly well for uni-univalent salts even in higher concentrations than 0.001 M. The ionic strength p is a unit of concentration which takes into account the number and valence of the ions present

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XVII.

Phenol Red pK’ Change at 20” with Increase of Ionic Strength by Means of Sodium and Potassium Phosphates. Calorimetric Readings

with Indicator Concentration = 0.00002 M.

SaN+Tle

1 la lb

-I-.-/

M P@ M P@ kg.HirO kg.HzO

0.00039 0.00163 0.00527 0.073 0.00039 0.00163 0.00527 0.073 0.00056 0.00145 0.00491 0.070

7.64 -0.35 7.99 0.05 7.63 -0.35 7.98 0.06 7.43 -0.53 7.96 0.08

2 0.00078 0.00325 0.01053 0.103 7.62 -0.33 7.95 0.09 2a 0.00078 0.00325 0.01053 0.103 7.63 -0.33 7.96 0.08 2b 0.00078 0.00325 0.01053 0.103 7.65 -0.32 7.97 0.07 2c 0.00112 0.00290 0.00982 0.099 7.45 -0.53 7.98 0.06

3 0.00116 0.00488 0.01579 0.126 7.61 -0.32 7.93 0.11 3a 0.00116 0.00488 0.01579 0.126 7.63 -0.33 7.96 0.08 3b 0.00169 0.00435 0.01472 0.121 7.44 -0.53 7.97 0.07

4 0.00193 0.00813 0.02632 0.162 7.61 -0.34 7.95 0.09 4a 0.00155 0.00650 0.02107 0.145 7.59 -0.34 7.93 0.11 4b 0.00155 0.00650 0.02107 0.145 7.60 -0.32 7.92 0.12 4c 0.00224 0.00580 0.01964 0.140 7.43 -0.53 7.96 0.08

5 0.00232 0.00976 0.03159 0.178 7.58 -0.34 7.92 5a 0.00232 0.00976 0.03159 0.178 7.58 -0.33 7.91 5b 0.00232 0.00976 0.03159 0.178 7.59 -0.34 7.93 5c 0.00336 0.00870 0.02944 0.172 7.39 -0.54 7.93

6 0.00402 0.01690 0.05474 0.234 7.55 -0.35 7.90 6a 0.00348 0.01464 0.04740 0.218 7.55 -0.34 7.89 6b 0.00348 0.01464 0.04740 0.218 7.56 -0.34 7.90 6c 0.00504 0.01304 0.04416 0.210 7.37 -0.55 7.92

7 0.00502 0.02113 0.06842 0.261 7.54 -0.36 7a 0.00464 0.01957 0.06333 0.252 7.52 -0.35 7b 0.00464 0.01957 0.06333 0.252 7.52 -0.35 7c 0.00464 0.01957 0.06333 0.252 7.54 -0.35 7d 0.00672 0.01740 0.05888 0.243 7.33 -Q.56

7.90 7.87 7.87 7.89 7.89

0.12 0.13 0.11 0.11

0.14 0.15 0.14 0.12

0.14 0.17 0.17 0.15 0.15

I- C ompcsition:

I I

P 4 KHzPOa N~sHPOI

Electro- metric PaHf.

- I Colori-

metric color ratio: log R.

PK’ indica-

tor. ApK

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XVII-concluded.

Composition.

(r 4 KHzPOa NazHPO4 ___~~-

Electro- metric PaH+.

Colori- metric color ratio: log R.

8 0.00579 0.02439 0.07895 0.281 8a 0.00579 0.02439 0.07895 0.281 8b 0.00579 0.02439 0.07895 0.281 8c 0.00579 0.02439 0.07895 0.281 8d 0.00840 0.02175 0.07360 0.271

7.51 -0.36 7.87 0.17 7.50 -0.36 7.86 0.18 7.51 -0.35 7.86 0.18 7.52 -0.36 7.88 0.16 7.31 -0.56 7.87 0.17

9 0.00696 0.02927 0.09475 0.308 9a 0.00696 0.02927 0.09475 0.308 9b 0.00696 0.02927 0.09475 0.308 9c 0.00696 0.02927 0.09475 0.308 9d 0.01008 0.02610 0.08832 0.297

7.50 -0.37 7.87 0.17 7.48 -0.37 7.85 0.19 7.49 -0.36 7.85 0.19 7.48 -0.37 7.85 0.19 7.26 -0.57 7.83 0.21

10 0.00804 0.03380 0.10946 0.331 10 a 0.00850 0.03577 0.11579 0.340 10b 0.00850 0.03577 0.11579 0.340 10 c 0.00850 0.03577 0.11579 0.340 10d 0.01232 0.03190 0.10802 0.329

7.47 -0.37 7.84 0.20 7.46 -0.38 7.84 0.20 7.47 -0.36 7.83 0.21 7.47 -0.37 7.84 0.20 7.26 -0.57 7.83 0.21

11 0.01004 0.04227 0.13683 0.370 11 a 0.01004 0.04227 0.13683 0.370 lib 0.01004 0.04227 0.13683 0.370 11 c 0.01004 0.04227 0.13683 0.370

7.45 -0.38 7.83 0.21 7.43 -0.39 7.82 0.22 7.44 -0.37 7.81 0.23 7.44 -0.37 7.81 0.23

12 0.01159 0.04877 0.15790 0.397 12 a 0.01159 0.04877 0.15790 0.397 12 b 0.01159 0.04877 0.15790 0.397 12 c 0.01159 0.04877 0.15790 0.397 12 d 0.01159 0.04877 0.15790 0.397 12 e 0.01690 0.04346 0.14728 0.384

7.42 -0.38 7.80 0.24 7.42 -0.39 7.81 0.23 7.43 -0.35 7.78 0.26 7.43 -0.37 7.80 0.24 7.43 -0.37 7.80 0.24 7.22 -0.58 7.80 0.24

PK’ ndicator.

L pK’

in the electronic environment. Thus all salts are reduced to the same basis of number and charges of the ions. Where the ionic strength principle holds, individual differences in salt effects vanish.

If we follow out the curves for brom-cresol purple (Fig. 6) when the diluting salts are KC1 and NazS04, all of the ions being different in kind, and the salts in valence type, it is apparent that the

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XVIII.

Phenol Red pK’ Change at 20” with Increase of Ionic Strength by Means of Sodium Chloride. Calorimetric Readings with


1 la lb

Cy;pai- phospdate

as in Sample 3, ‘able XVII, + N&l.

per kg.H,O

0.00000

0.00000

0.00000

2 2a

0.00905 0.00905

3 0.01810 3a 0.01810 3b 0.01810

4 4a

0.02716 0.02716

5 5a

0.04528 0.04528

6 0.06343 6a 0.06343

7 7a

0.08159 0.08159

8 8a

9 0.13617 9a 0.13617

10 0.16352 10 a 0.16352

-

P

Electro- metric PaH+.

COlOri- metric

ulor ratio: log R.


0.01575 0.125 7.61 -0.32 7.93 0.11 0.01575 0.125 7.64 -0.33 7.97 0.07 0.01575 0.125 7.59 -0.34 7.93 0.11

0.02480 0.02480

0.157 0.157

7.59 7.57

-0.33 -0.34

7.92 7.91

0.12 0.13

0.03386 0.184 7.54 -0.34 7.88 0.16 0.03386 0.184 7.56 -0.34 7.90 0.14 0.03386 0.184 7.54 -0.35 7.89 0.15

0.04292 0.207 7.51 -0.35 7.86 0.18 0.04292 0.207 7.52 -0.36 7.88 0.16

0.06106 0.247 7.47 -0.37 7.84 0.20 0.06106 0.247 7.48 -0.38 7.86 0.18

0.07922 0.281 7.43 -0.40 7.83 0.21 0.07922 0.281 7.43 -0.40 7.83 0.21

0.09738 0.312 7.40 -0.42 7.82 0.22 0.09738 0.312 7.40 -0.41 7.81 0.23

0.12466 0.353 7.36 -0.43 7.79 0.25 0.12466 0.353 7.35 -0.43 7.78 0.26

0.15197 0.15197

0.17934 0.17934

0.390 7.32 -0.46 7.78 0.26 0.390 7.32 -0.45 7.77 0.27

0.423 7.29 -0.47 7.76 0.28 0.423 7.27 -0.48 7.75 0.29

variation in pK’ mainly depends on the concentration in terms of &. The two curves are very close together for the two different salts. However, if the molal unit of concentration is taken a

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XIX.

Phenol Red pK’ Change at 20’ with Increase of Ionic Strength by Means of Potassium Chloride. Calorimetric Readings with


Ir

Eleotxo- metric PaH+.

Colori- metric

:olor ratio: log R.


1 la

Cotgyi-

phosphate a8 in

rF$Y@1

f per kg.HxO

0.00000

0.00000

0.01575 0.125 7.59 -0.36 7.95 0.09 0.01575 0.12.i 7.60 -0.34 7.94 0.10

2 0.00905 0.02480 0.157 7.57 -0.34 7.91 0.13

3 0.01810 0.03386 0.184 7.54 -0.38 7.92 0.12 3a 0.01810 0.03386 0.184 7.55 -0.36 7.91 0.13

4 0.02716 0.04292 0.207 7.52 -0.39 7.91 0.13 4a 0.02716 0.04292 0.207 7.51 -0.37 7.88 0.16

5 0.04528 0.06106 0.247 7.48 -0.39 7.87 0.17 5a 0.04528 0.06106 0.247 7.48 -0.39 7.87 0.17

6 0.06343 0.07922 0.281 7.44 -0.39 7.83 0.21 6a 0.06343 0.07922 0.281 7.44 -0.40 7.84 0.20

7 0.08159 0.09738 0.312 7.41 -0.41 7.82 0.22 7a 0.08159 0.09738 0.312 7.42 -0.42 7.84 0.20

8 0.10886 0.12466 0.353 7.39 8a 0.10886 0.12466 0.353 7.39

7.82 0.22 7.82 0.22

9 0.13617 9a 0.13617

0.15197 0.15197

0.17934 0.17934

0.390 0.390

7.33 7.35

-0.43 -0.43

-0.44 -0.44

-0.45 -0.44

7.77 0.27 7.79 0.25

10 0.16352 10 a 0.16352

0.423 7.31 0.423 7.32

7.76 0.28 7.76 0.28

-

-

great discrepancy arises. An apparent difference due to the kind of salt used is obtained almost in the very beginning of the curves at great dilutions.

-c

-

It is clear that ionic strength is as closely correlated to variation in the activity coefficients of these indicators as it is to variations

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

TABLE XX.

Phenol Red pK’ Change at 20” with Increase of Ionic Strength by Means of Sodium Sulfate. Calorimetric Readings with


1 la lb 1C

2 2a

3 3a 3b 3c

5 5a 5b

6 6a

7 7a 7b 7c

8 8a 8b 8C

9 9a 9b SC

10 10 a

Camposi- tion:

phosphate as in

Sample 3 or 3b.

‘able XVII t NaaS0~

. per kg.HzC

0.00000

0.00000

0.00000

0.00000

Electrc- metric PaH+.

Colori- metric

olorratio: log R.

PK’ ldicator. A pK’

0.01579 0.126 7.62 -0.32 7.94 0.10 0.01579 0.126 7.59 -0.33 7.92 0.12 0.01579 0.126 7.62 -0.32 7.94 0.10 0.01472 0.121 7.62 -0.53 7.95 0.09

0.00302 0.02485 0.158 7.60 -0.32 7.92 0.12 0.00302 0.02379 0.154 7.40 -0.54 7.94 0.10

0.00537 0.03190 0.179 7.56 -0.32 7.88 0.16 0.00604 0.03389 0.184 7.53 -0.35 7.88 0.16 0.00604 0.03389 0.184 7.56 -0.35 7.91 0.13 0.00604 0.03283 0.181 7.36 -0.35 7.91 0.13

0.00906 0.04295 0.207 7.54 -0.36 7.90 0.14

0.01343 0.05606 0.237 7.50 -0.35 7.85 0.19 0.01509 0.06106 0.247 7.50 -0.36 7.86 0.18 0.01509 0.05999 0.245 7.31 -0.56 7.87 0.17

0.01880 0.07219 0.269 7.45 -0.37 7.82 0.22 0.02113 0.07916 0.281 7.48 -0.37 7.85 0.19

0.02417 0.08830 0.297 7.44 -0.38 7.82 0.22 0.02717 0.09728 0.312 7.42 -0.38 7.80 0.24 0.02717 0.09728 0.312 7.44 -0.37 7.81 0.23 0.02717 0.09622 0.310 7.44 -0.57 7.81 0.23

0.03223 0.11247 0.335 7.42 -0.38 7.80 0.24 0.03622 0.12445 0.353 7.39 -0.39 7.78 0.26 0.03622 0.12445 0.353 7.42 -0.38 7.80 0.24 0.03622 0.12339 0.351 7.22 -0.58 7.80 0.24

0.04028 0.13663 0.369 7.38 -0.39 7.77 0.27 0.04528 0.15161 0.389 7.35 -0.40 7.75 0.29 0.04528 0.15161 0.389 7.38 -0.40 7.78 0.26 0.04528 0.15055 0.388 7.18 -0.60 7.78 0.26

0.04834 0.16079 0.401 7.36 -0.41 7.77 0.27 0.05433 0.17878 0.423 7.32 -0.42 7.74 0.30

225

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XXI.

Phenol Red pK’ Change at 20’ with Increase of Ionic Strength by Means of Potassium Sulfate. Calorimetric Readings with


SXllple No.

1 la lb

r per kg.HnO

0.00000

0.00000

0.00000

0.01579 0.126 7.62 -0.34 7.96 0.08 0.01579 0.126 7.59 -0.34 7.93 0.11 0.01472 0.121 7.42 -0.53 7.95 0.09

2 0.00227 0.02259 0.150 7.60 -0.35 7.95 0.09 2a 0.00227 0.02259 0.150 7.61 -0.34 7.95 0.09 2b 0.00227 0.02259 0.150 7.57 -0.34 7.91 0.13 2c 0.00227 0.02152 0.147 7.40 -0.54 7.94 0.10

3 0.00453 0.02938 0.172 7.57 -0.37 7.94 0.10 3a 0.00453 0.02938 0.172 7.59 -0.35 7.94 0.10 3b 0.00453 0.02938 0.172 7.55 -0.35 7.90 0.14 3c 0.00453 0.02832 0.168 7.38 -0.55 7.93 0.11

4 0.00679 0.03618 0.190 7.55 -0.38 7.93 0.11 4a 0.00679 0.03618 0.190 7.62 -0.27 7.89 0.15 4b 0.00679 0.03618 0.190 7.54 -0.36 7.90 0.14 4c 0.00755 0.03738 0.193 7.37 -0.56 7.93 0.11

5 0.01133 0.04976 0.223 7.52 -0.38 7.90 0.14 5a 0.01133 0.04976 0.223 7.59 -0.28 7.87 0.17 5b 0.01133 0.04976 0.223 7.52 -0.36 7.88 0.16 5c 0.01133 0.04976 0.223 7.51 -0.36 7.87 0.17 5d 0.01133 0.04870 0.221 7.33 -0.57 7.90 0.14

6 0.01586 0.06335 0.251 7.49 -0.39 7.88 0.16 6a 0.01660 0.06559 0.253 7.56 -4j.29 7.85 0.19 6b 0.01660 0.06559 0.253 7.50 -0.36 7.86 0.18 6c 0.01586 0.06335 0.251 7.50 -0.37 7.87 0.17

7 0.02039 0.07695 0.277 7.46 -0.40 7.86 0.18 7a 0.02265 0.08374 0.286 7.44 -0.39 7.83 0.21 7b 0.02265 0.08374 0.286 7.54 -0.30 7.84 0.20 7c 0.02265 0.08374 0.286 7.48 -0.37 7.85 0.19 7d 0.02039 0.07695 0.277 7.47 -0.37 7.84 0.20

-

.-

M

-

Cotyoyi-

phosphate 8,s in

“;,“3”b” 3

rable X+11 + KzS04.

CL

Electro- metric P=H+.

c&g olor ratio:

log R.

-

i

_-

-

PK’ ndioatm. A pK’

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


Sample No.

8 8a

8b 8C

9 9a 9b 9c

10 10 a 10 b 10 c

11 11 a

‘1

M

-

COtgP$

phosphate a3 in

sgyt 3 .‘able X+11 + IMOP.

P

Electro- metric PmH+.

COlOri- metric

olor ratio log R.

PK’ ldioator. : il A pK’

w- kq.HgO

0.03019 0.03019 0.03019 0.02718

0.10636 0.323 7.41 -0.39 7.80 0.24 0.10636 0.323 7.50 -0.31 7.81 0.23 0.10636 0.323 7.45 -0.37 7.82 0.22 0.09733 0.312 7.46 -0.37 7.83 0.21

0.03398 0.11771 0.343 7.39 -0.43 7.82 0.22 0.03776 0.12907 0.355 7.39 -0.40 7.79 0.25 0.03776 0.12907 0.355 7.47 -0.33 7.80 0.24 0.03398 0.11771 0.343 7.43 -0.38 7.81 0.23

0.04077 0.13810 0.371 7.36 -0.44 7.80 0.24 0.04682 0.15625 0.391 7.37 -0.41 7.78 0.26 0.04682 0.15625 0.391 7.44 -0.34 7.78 0.26 0.04077 0.13810 0.371 7.42 -0.38 7.80 0.24

0.05588 0.18343 0.423 7.35 -0.42 7.77 0.27 0.05588 0.18343 0.423 7.40 -0.37 7.77 0.27

TABLE XXI-Concluded. -

in the activity coefficients of the salts of simple organic and in- organic acids. Whatever differences exist in the “salt errors” caused by different salts at equal ionic strengths may or may not be attributable to individual specific ion or molecule effects.

Individual Xpecijic Ion Effect.-To what extent specific ion effects are present in these systems is not clear, nor may one decide the question from these experiments alone. In Fig. 2, for brom- cresol green, NaCl and KC1 follow along practically the same curve as does the pair NazSOl and KzS04, and the pair MgC12 and CaClz; and this latter, in spite of the fact that MgCL has an enormous effect, through hydrolysis, on the pan+ of buffer soutions as compared with the other salts. The acetate mixture curve is of a slightly different shape. The curves for the various salts seem to show an indicator activity coefficient variation due to valence type differences in the salts of the surrounding medium. As the solution is more concentrated, the effects become more pronounced. The glucose experiment (Table VIII), indicates a

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XXII.

Phenol Red pK’ Change at 20’ with Increase of Ionic Strength by Means of Magnesium Chloride. Calorimetric Readings with

Indicator Concentration = O.OOOO$ M.

“%?

Composi- tion:

phosphate a8 in

Sample 3, ‘able XVII + M&is.

0.121 0.121

0.157 0.157

0.185 0.185

0.218 0.218

0.252 0.252

0.289 0.289

per kg.HzG

1 0.00000 0.01472 7.63 -0.31 7.94 0.10

la 0.00000 0.01472 7.61 -0.32 7.93 0.11

2 0.00327 0.02452 7.49 -0.43 7.92 0.12 2a 0.00327 0.02452 7.47 -0.45 7.92 0.12

3 0.00653 0.03432 7.37 -0.54 7.91 0.13 3a 0.00653 0.03432 7.36 -0.56 7.92 0.12

4 0.01089 0.04738 7.25 -0.64 7.89 0.15 4a 0.01089 0.04738 7.23 -0.66 7.89 0.15

5 0.01633 0.06370 7.15 -0.71 7.86 0.18 5a 0.01633 0.06370 7.14 -0.73 7.87 0.17

6 0.02286 0.08329 7.05 -0.77 7.82 0.22 6a 0.02286 0.08329 7.03 -0.77 7.80 0.24

7 0.02939 0.10288 6.99 -0.82 7.81 0.23 7a 0.02939 0.10288 6.97 -0.84 7.81 0.23

8 0.03918 0.13227 6.91 -0.88 7.79 0.25 8a 0.03918 0.13227 6.89 -0.89 7.78 0.26

9 0.04898 0.16165 6.85 -0.92 7.77 0.27 9a 0.04898 0.16165 6.83 -0.92 7.75 0.29

10 0.05877 0.19104 6.79 -0.96 7.75 0.29 10 a 0.05877 0.19104 6.77 -0.96 7.73 0.31

constant level of pK at constant salt concentration unaffected by variation in sugar concentration.

Fig. 3~, for brom-cresol purple, is very much like that for brom- cresol green; the relationships, however, are a little different.

0.321 0.321

0.364 0.364

0.402 0.402

0.437 0.437

-

P

Electro- C&Ii- metric metric PK’

olor ratio: Idicatm. A pK’

P&H+. log R.

-

.-

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XXIII.

Phenol Red pK’ Change at $0’ with Increase of Ionic Strength by Means of Magnesium Sulfate. Calorimetric Readings with

Indicator Concentration = 0.00002 di. -

?

.-

M

cotyop-

phosph’ate as in

Sample 3, ible XVII t M&304.

per k,,.HtO

0.00000

0.00000

C&Xi- Electro- P 4 metric metric PK’ A pR’

PUH+. olor ratio: Idicatm. log R.

0.00226 0.00226

0.00453 0.00453

0.00754 0.00754

0.01131

0.01659 0.01659

0.02263

1 0.01472 0.121 7.61 -0.32 7.93 0.11 la 0.01472 0.121 7.60 -0.32 7.92 0.12

2 0.02378 0.154 7.53 -0.41 7.94 0.10 2a 0.02378 0.154 7.52 -0.41 7.93 0.11

3 0.03283 0.181 7.45 -0.48 7.93 0.11 3a 0.03283 0.181 7.46 -0.48 7.94 0.10

4 0.04489 0.212 7.37 -0.55 7.92 0.12 4a 0.04489 0.212 7.36 -0.55 7.91 0.13

5 0.05998 0.245 7.28 -0.61 7.89 0.15

6 0.08110 0.285 7.21 -0.67 7.88 0.16 6a 0.08110 0.285 7.22 -0.68 7.90 0.14

7 0.10524 0.324 7.13 -0.71 7.85 0.19

8 0.13540 0.368 7.07 -0.76 7.83 0.21 8a 0.13540 0.368 7.07 -0.76 7.83 0.21

9 0.16558 0.407 7.01 -0.81 7.82 0.22 9a 0.16558 0.407 7.01 -0.80 7.81 0.23

10 0.20178 0.449 6.96 -0.84 7.80 0.24 10 a 0.20178 0.449 6.96 -0.84 7.80 0.24

11 0.23798 0.488 6.91 -0.88 7.79 0.25 11 a 0.23798 0.488 6.90 -0.87 7.77 0.27

MgS04 shows a tendency (more pronounced in the case of phenol red), to lower the pK’ curve. The glucose experiment (Table XVI) showed no effect of the non-electrolyte, at least, in these concentrations. More concentrated sugar solutions would probably

0.03017 0.03017

0.03771 0.03771

0.04676 0.04676

0.05582 0.05582

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

230 indicator Activity Coefficients

TABLE XXIV.

Value of pK’ Indicator Extrapolated to p = 0.

Salt.

N&l KC1 NazSOa KzS04 NaGHzOz MgClz CaCL

Average.. .

PK Salt. PK Salt.

4.90 4.92 4.92 4.91 4.93 4.94 4.95

4.92

NaCl 6.46 NaCl KC1 6.47 KC1 Na2S04 6.47 NazSOI K,SOa 6.46 KzSOd PO4 6.47 PO4 MgCl, 6.45 M&L MgS04 6.45 MgSCh

6.46 8.04

Broom-cresol purple T Phenol red. -

--

PK

8.05 8.05 8.05 8.05 8.02 8.04 8.00

I I I I I 0 k+/

FIG. 2. The effect of varying concentrations of different salts on pK’ of brom-cresol green.

affect the pK’ as found by the methods used in this work, by causing a change in light absorption through the medium, and by altering the dielectric constant of the solution, the non-electrolyte exerting a salting-out effect.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


p”‘I I I I I I.4 I I I I 6.1

0 005 0.2 0.15 02 025 03 03.5 04 0% 0.5

VF

FIG. 3. The effect of varying concentrations of different salts on pK’ of brom-cresol purple.

I I I I i/

FIG. 4. The effect of varying concentrations of different salts on pKE of phenol red.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XXV.

Data of Lepper and Martin ($6) Calculated to Show Phenol Red pK’ Change at 18” with Increase of Ionic Strength.

Lwr

Martin table NO.

I

II

III

IV

V

-7-

.-

1

I

I

1

_-

-

_-

-

Composition. Eleotro Ir G metric

Bllffer. salt. PaH+.

pm--

Phosphate. ~/lOOO 0.002710.052 7.83 M/400 0.006800.082 7.81 M/150 0.018110.135 7.74

M/M 0.067910.260 7.65 M/15 0.181060.425 7.55

~-_-- Phosphate. NaCl

M/loo0 0.012870.113 7.76 M/l00 0.021430.148 7.74 ~/32 0.043310.208 7.70 ~/16 0.075760.275 7.61 48 0.137630.371 7.53 ~-

Phosphate. NaCl MC0 0.0256 0.160 7.51 M/loo0 0.026640.163 7.50

~/128 0.033500.183 7.45 ~/32 0.05709 0.239 7.38 M/16 0.089540.299 7.31 703 0.151400.389 7.22

Bicarbonate. NaCl M/loo0 0.021120.145 7.50 M/50 0.040220.20: 7.48 M/16.6 0.0807 0.284 7.44 M/6.9 0.1660 0.4Oi 7.42

--~ Bicarbonate. NaCl

0.040300.20 7.51 M/30 0.07019 0.26 7.47 M/lo 0.1409. 0.37., 7.44

c!olori- metric PaH+.

Salt error” PaH+ (C)

- PaH+ k’).

1 pK’ ndica-

tar. i

_

7.65 7.66 7.66 7.61 7.55

- #.

--

.-

-0.18 7.96 -0.15 7.93 -0.08 7.86 -0.04 7.82 *o.oo 7.78

7.62 -0.14 7.92 7.61 -0.13 7.91 7.58 -0.12 7.90 7.56 -0.0, 7.83 7.53 ~0.00 7.78

7.36 -0.15 7.93 7.36 -0.14 7.92 ‘7.33 -0.12 7.90 7.31 -0.07 7.85 7.27 -0.04 7.82 7.22 zto.00 7.78

7.37 7.38 7.38 7.41

--

_-

-0.13 7.91 -0.10 7.88 -0.06 7.84 -0.01 7.79

--

7.41 -0.10 7.88 7.43 -0.04 7.82 7.43 -0.01 7.79

Phenol red curves (Fig. 4) present a slightly different picture. The average slope is somewhat lower than for the brominated methyl compounds, and all of the salts are much more closely grouped. MgSO+ however, particularly at the lower concentrations, seems out of line. La Mer and coworkers (27) have found the same diihculty in working with salts of tri-trivalent type.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

0 a05 a2 aI5 a2 a25 w o.35 a4 a45 as

c-

FIG. 5. Comparison of data of Lepper and Martin with those of present paper on change in pK’ of phenol red.

t;ir 0 am a2 0~5 0.2 025 03 a35 a4 a45 05

FIG. 6. The change in pK’ of brom-cresol purple with KC1 and NatSOl plotted against concentrations on molal basis and on ionic strength basis.

233

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


The foregoing experiments were performed with dilute solutions of acetate and phosphate mixtures. Although Lepper and Martin (26) make a distinction between results obtained with bicarbonate and phosphate buffers, their own data with NaCl (Fig. 5) in phenol red solutions show very good agreement between solutions of these two buffers. We did no experiments with bicarbonate buffer our- selves, but there is little reason to believe that the results would have been very different, provided the salt concentrations were calculated on the ionic strength basis. In physiological solutions the maximum concentration of about 30 mM bicarbonate would be di = 0.16, where apparent individual salt or ion effects only begin to come into play. However, if further work indicates a real difference in effect of bicarbonate and phosphate, correction figures would have to take into account the nature of the buffer. Lepper and Martin’s curve for phosphate effect is quite different from ours. Ours was established on the basis of 52 different points, and fits in well with the curves for other salts.

The whole series of experiments shows no very consistent specific ion or salt effects. For example, we find no common effect of Mg++ ion in MgCI, and MgS04, or of SOh ion in KzS04, Na2S04, and MgSO4.

Activity Coeficient Variation and Interionic Force E$ects.--We have attempted to apply the equation of Debye and Hiickel (Equation 8) to the curves of Figs. 2 to 4, but have not been completely successful in obtaining equations which would describe the curves throughout their entire course. The whole of the ionic dissociation and interionic attraction theory at the present time is in such a state of flux (29,30) that we have attempted no modi- fication such as would enable us to fit the data to the theory, or vice versa. Nernst (31) and his coworkers (32, 33), on the basis of the anomalous heats of dilution obtained with uni-univalent strong electrolytes, advocate a return to the old Arrhenius in- complete or partial dissociation theory, at the same time retaining the Debye-Hiickel explanation for such effects as are due to interionic forces. Bjerrum (34) also has put forward a slightly different “association” explanation, and more recently (35) the idea that the effective dielectric decreases in the immediate neighborhood of the ions, thereby causing anomalous results. Gronwall, La Mer, and Sandved (36) have expanded the Debye-

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


Hiickel formula in the form of an infinite series. They thereby eliminate negative ion sizes and obtain positive values even in the case of ions of small size. Simms (18), working with polyvalent weak electrolytes, has attempted to correct for deviations from the theory by taking into account a variable distance between the two charges of a di-anion.

In general, the curves obtained in Figs. 2 to 4 conform approximately to the equation of Debye and Hiickel. Also, the correspondence between these curves and some of those obtained with weak acid buffer systems is very good. For example, the calculated curve of Cohn (16) based on the data of Sorensen, for the second dissociation constant of phosphoric acid, and the curve for the effect of NaCl on brom-cresol purple coincide almost exactly,

and have the equation pK’ = pK - 1.5&

l+ 1.654; Also, there is here added proof of the dibasic character of these

indicators. The equation for a monobasic indicator, with the assumption of a constant thickness of the ionic atmosphere = 0.33 X lo8 &, cm., would yield negative ion sizes. It is fairly certain that such a result is not due to the same factors which caused La Mer and his associates to expand the Debye-Htickel equation, for here the ion sizes are quite large.

Gtintelberg and Schiodt (37) have recently published some work in which they state that the behavior of the activity coeficient of brom-phenol blue, the tetrabrom compound of the sulfonphthalein series, is that of a monobasic acid. However, if we calculate from their single result at low concentrations, where KC Ii’ ho corresponding to our z is given as 2.12 for a concentration of

KC1 = 0.1 N, pK’ = pK - 0.33, which corresponds almost exactly to our results for brom-cresol purple and brom-cresol green. The treatment of these indicators as dibasic is consistent with their structure and known behavior.

Phenol red presents curves of a type somewhat different from those of brom-cresol purple and brom-cresol green. For this, we have no good explanation at the present time. Whether the difference is due to large ion size, or the absence of the methyl and bromide groups, we cannot say. Perhaps the results are due to the same reason which caused the evaluation of 1.6 4; instead of 2.0 4; for - log yoo; (15).

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


On the assumption of a constant value for the thickness of the ionic atmosphere, 0.33 X lo* &J cm., we can make approximate calculations for ion size at di = 0.4, this value changing with different types of salt present, with the ratio of alkaline to acid forms of the indicator, and with the concentration: from 5 to 8.7 X lo+ cm. for brom-cresol green and brom-cresol purple, and from 8.7 to 13.0 X 10d8 cm. for phenol red. These values are merely speculative. Further developments in the theory of solutions, and particularly those concerned with buffers and weak electrolytes, may make it necessary to revise our treatment of these indicator anions, which, in structure at least, are so different from the simpler substances on which the modern theories are based. Furthermore, it must be remembered that not only ionization but tautomerism equilibria are here involved. The latter may not be affected to the same degree by electrostatic forces.

Activity Coeficient Variation and Indicator Color.-The recent work of Cohn and his collaborators on the phosphate and acetate buffer system activity coefficients indicates that the mol fraction

&A partition of the two members of the system, i.e. the ratio BA or

BA --, may also enter in as a factor governing the magnitude of the HA activity coefficient at any one given ionic strength. This variation would be in accord with Briinsted’s specific ionic interaction theory, Applied to these indicator studies, this would mean that at any one given ionic strength, the pK’ of the indicator would not be a constant, but would show some variation, depending on the color, i.e. the ratio of alkaline to acid form of the indicator, of the solution. Instead of one curve describing the variation of pK’ of the indicator with changing ionic strength, one should obtain, for each salt studied (see Figs. 2 to 4), a family or narrow sheaf of curves. The width of such a sheaf of curves would be approximately the same for all salts, at the same ionic strength, Each one of these curves of any one family of curves would describe the pK’ variation with ionic strength change, for the particular salt studied, at a constant ratio of alkaline to acid form of the indicator; i.e., the curves would be isochromatic.

To obtain such isochromatic curves at varying values of log R

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


(the logarithm of the ratio of alkaline to acid form of the indicator), the actual pan+ and the ionic strength of the particular salt solution used would progressively have to be so altered that the indicator color remained constant. In otherwords, the change in p&u+ of the solution would have to be equal to, and of the same algebraic sign as the change in pK’ of the indicator. Such a nice ad- justment is impossible for these studies, since the two variables

to.02 to.9 a.6

to.01 to.4

CpK’ I I I I I 0.0

-0.02

-0.03

-0.04

-0.05

-0.06 c -0.07gL

-0.2 -0.3

-0.4 -0.5

-0.6

-0.7 -0.8 -0.9 :5

\\\

0.05 0.10 0.15 0.20 0.2

FIG 7. Correction chart for values of pK’ of the indicators at different ionic strengths, when the ratio (R) alkaline to acid form of the indicator varies. Adapted from Cohn’s (16) data on phosphate buffer mixtures.

are not known, but are to be observed or calculated. Hence the curves given in Figs. 2 to 4 are not isochromatic nor do they cover the possible variation of pK’ with ionic strength change between the two extremes of color within which the indicators may be used.

The indicator, in its acid and alkaline form, constitutes a buffer pair, and must so be treated. On the assumption that the BAZ: BA or BA:HA ratio of an indicator affects the pK’ in the same way that the mol fraction partition of phosphate and acetate

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


buffers influences their respective pK’ values, even when the indicator concentration is as low as in our experiments, one may correct for this factor in the following manner. Fig. 7 is inter- polated from Cohn’s data on the second dissociation constant of phosphoric acid, and applied to the indicators, which are also regarded here as dibasic. The figure shows the correction cPxl, to be applied to the pK’ value of the indicator at any ionic strength, as the logarithm of the ratio of the alkaline to acid form of the indicator varies. The experimentally determined pK’ values at different ionic strengths, with different salts, have all been cor- rected to the value at log R = 0, and are given in Tables XXVI to

TABLE XXVI.

Values of pK’ of Brom-Cresol Green at 20’ in Various Salts at Different Ionic Strengths, When Log R = 0. Extrapolated pK at M = 0 Is 4.92.

B N&l

0.025 4.77 0.050 4.72 0.075 4.68 0.100 4.65 0.125 4.63 0.150 4.61 0.175 4.59 0.200 4.57 0.225 4.56 0.250 4.55

KC1 N&O4 KG304 C&12 M&h

4.77 4.78 4.79 4.75 4.73 4.71 4.74 4.74 4.69 4.67 4.67 4.70 4.70 4.65 4.63 4.65 4.68 4.68 4.62 4.60 4.63 4.66 4.66 4.59 4.58 4.62 4.64 4.64 4.57 4.56 4.61 4.62 4.63 4.56 4.55 4.59 4.60 4.61 4.53 4.52 4.59 4.59 4.60 4.52 4.50 4.58 4.57 4.59 4.51 4.49

XXVIII. These are the pK’ values to P

Acetate mixture.

4.78 4.73 4.71 4.69 4.67

ich cPKl is to be added when the indicator color is such that log R is different from zero. At the physiological ionic strength, p = 0.16, the corrections for the indicator pK’ values given in these tables, would vary throughout the useful range of the indicators, in the following manner: for brom-cresol green, from +O.Ol to -0.03, for brom- cresol purple, from +O.Ol to -0.02, for phenol red, from +O.Ol to - 0.04, depending on the value of log R. At lower ionic strengths, the corrections would, of course, be less. It is apparent from Fig. 7 that this factor of the mol fraction partition is of much less importance when the predominating color is that of the alkaline form of the indicator.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


The impossibility of systematically testing this effect for indicators has already been mentioned. However, the probable validity of such an effect for these substances also is indicated by the table given by Hastings and Sendroy (24) in which such consistency of pK’ for phenol red in ~/15 phosphate solutions

TABLE XXVII.

Values of pK’ of Brom-Cresol Purple at 20’ in Various Salts at Different Ionic Strengths, When Log R = 0. Extrapolated pK at p = 0 Is 6.46.

B NaCl KC1 N&30, KzSOa M&h Phosphate MgSo4 mixture.

_______~ ~_________

0.025 6.28 6.29 6.30 6.31 6.30 6 32 6.30 0.050 6.22 6.23 6.24 6.26 6.23 6.28 6.25 0.075 6.18 6.19 6.20 6.23 6.19 6.25 6.22 0.100 6.15 6.17 6.18 6.21 6.16 6.23 6.20 0.125 6.14 6.15 6.16 6.19 6.14 6.21 6.19 0.150 6.13 6.14 6.14 6.17 6.12 6.19 6.18 0.175 6.12 6.13 6.13 6.16 6.11 6.18 0.200 6.11 6.12 6.12 6.15 6.11 6.17

TABLE XXVIII.

Values of pK’of Phenol Red at .PO”in Various Salts at Different Ionic Strengths, When Log R = 0. Extrapolated pK at p = 0 Is 8.04.

P

0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225

N&l KC1 N&O, KG301

7.91 7.86 7.84 7.82 7.80 7.79 7.78 7.78

7.93 7.87 7.86 7.84 7.81 7.79 7.78 7.77 7.76

7.92 7.87 7.85 7.82 7.80 7.78 7.77 7.76

7.93 7.93 7.94 7.88 7.89 7.91 7.85 7.86 7.89 7.83 7.84 7.88 7.81 7.82 7.87 7.79 7.81 7.86 7.78 7.79 7.85 7.78 7.77 7.84 7.77 7.77 7.84

-

.- M&12 MgSOa P

1

.-

hocphate mixture.

7.93 7.90 7.87 7.86 7184 7.81 7.80 7.79

through the range of PCY n+ from 6.84 to 7.98 was obtained. From Table XXVIII one would expect the increase in P from 0.1200 to 0.1740 in their experiments, at constant color, to cause a progres- sive decrease in pK’ indicator of about 0.04 unit. However, the pan+ of the M/15 phosphates varied with the ionic strength, and the consequent color change was such that log R varied from -0.94 at P = 0.120 to to.20 at p = 0.174. Fig. 7 indicates that between these limits the pK’ will progressively increase by the same

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


amount; namely, 0.04 unit. The resultant of the two effects would be the constant pK’ for phenol red obtained throughout the whole range.

Results Applied to Calorimetric Estimation of p(~~+ of Salt Solutions.-It is apparent that these indicators possess definite physical characteristics which are much like those of other weak acids or alkali buffer systems with their salts, and are affected in approximately the same way by changes in the medium by which they are surrounded. Hence it is no longer necessary to refer to the “salt error,” when all that is meant is that the activity coefficients of the colored anions, for the same general class of salts, are different at different ionic strengths, and at different proportions of the alkaline to acid form of the indicator.

In salt solutions of known ionic strength, one should be able to estimate the pK’ of these indicators to within ho.02 unit, and to determine pan+ with nearly the same accuracy. The “salt error,” pcUn+(c) - pan+(e), has been a source of discrepancy, owing to failure to allow for a predictable effect of interionic forces on the apparent dissociation constants of the indicators in standard and unknown solutions.

Practically, one may calculate, when using bicolor standards at 2U”,

(9) pcuH+ = pK’ of indicator at p + cPx, at log R of indicator + log R of sample of sample at p of sample

where log R is the logarithm of the ratio of the alkaline to acid form of the indicator, and $Kl is the correction in pK’ when log R is not zero. The values pK’, in salt solutions of varying p, when log R = 0, are found in Tables XXVI to XXVIII. The values of crx’ when log R # 0 are found by referring to Fig. 7.

If instead of bicolor standards, standards with buffer and indicator in the same solution are used, the assumed or electrometrically determined pCXu+ value of the standard buffer-indicator solution also enters in :

(10) pcuH+ of = p”H+ of + pK’ of indicator + cpK, at log R of

sample standard at p of sample indicator at p of sample

- pK’ of indicat.or - cpK, at log R of indicator

at P of standard at p of standard

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


For most purposes, the cpxt corrections of Equation 10 may be neglected. Nevertheless, it is obvious that calorimetric readings of salt solutions may be simplified and made more accurate by using bicolor standards made up and marked in even color ratio (log R) series, and calculating pan+ according to Equation 9. Table XXIX is given to facilitate the preparation of such a series of standards for any indicator.

Although these indicator dissociation constants have been obtained at 20”, the results may also be applied to determinations at 38” or at any intermediate temperature. In previous work (24, 25), brom-cresol green was found to have practically no temperature coefficient for pK’. Brom-cresol purple changed -0.10 unit and phenol red -0.13 unit in pK’ when the temperature was increased from 20” to 38”. These temperature coefficients should be the same throughout the ionic strength range from zero to p = 0.2.

On the basis of these results, we may examine some previous results in the field of calorimetric pan+ determinations. The pK’ for phenol red in ~/15 phosphate solutions at 20’ was found by Hastings and Sendroy to be 7.78. For the same phosphate solutions we obtain here a revised value of 7.80. This correction is probably due to the actual change in pQn+ of the phosphates (about +0.02 to i-0.01) when diluted 10 per cent, a refinement in technique not used in previous determinations. In like manner, the pK’ at 20” for brom-cresol purple previously found for the same phosphate solutions would be changed from 6.19 to the value 6.21 found in the present work.

The acetates are not affected by dilution to the extent that phosphates are. In fact, the results of the present determinations show pK’ of brom-cresol green at 20” to be 4.67 for acetate solution instead of 4.72 for the ionic strength of 0.140. What this discrepancy may be due to is not known. This indicator, as was previously noted, is not always of constant purity.

In the development of a pan+ method for body fluids (24) we previously noted that the ionic strength of the bicolor standards (aside from the effect of salt on optical absorption) was of no moment. This we can now better understand. If the acidity and alkalinity of the two tubes are sufficient to keep the color of the indicator in total acid and total alkaline form respectively,

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


TABLE XXIX.

Rounded Values of Log Alkaline Form

Acid ForrrL at Intervals of 0.05 or 0.1 pa H+ Unit

for Use in Preparing Bicolor Standards.

Alkali tube.

Indicator. Alkali. Indicator. Acid.

cc. cc. cc. cc.

0.18 24.82 2.32 22.68 .20 .80 .30 .70 .23 .77 .27 .73 .25 .75 .25 .75 .28 .72 .22 .78 .31 .69 .19 .81 .34 .66 .16 .84 .38 .62 .12 .88 .42 .58 .08 .92 .46 .54 .04 .96 .50 .50 2.09 23.00 .55 .45 1.95 .05 .60 .40 .90 .lO .66 .34 .84 .16 .71 .29 .79 .21 .77 .23 .73 .27 .83 .17 .67 .33 .90 .lO .60 .40 .97 .03 .53 .47

-1.10 -1.05 -1.00 -0.95 -0.90 -0.85 -0.80 -0.75 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20

1.04 23.96 .46 .54 -0.15 .ll .89 .39 .61 -0.10 .18 .82 .32 .68 -0.05 .25 .75 .25 .75 0.00 .32 .68 .18 .82 +0.05 .39 .61 .ll .89 +0.10 .46 .54 .04 .96 +0.15 .53 .47 0.97 24.03 $0.20 .67 .33 .83 .17 $0.30 .79 .21 .71 .29 +0.40 .90 ..lO .60 .40 +0.50

2.00 23.00 .50 .50 $0.60 .08 22.92 .42 .58 $0.70 .16 .84 .34 .66 +0.80 .22 .78 .28 .72 +0.90 .27 .73 .23 .77 t-1.00 .32 .68 .18 .82 +1.10

- I Acid tube.

- I Log R.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


regardless of how the indicator dissociation curve may be shifted by some change in ionic strength or temperature, the bicolor standards will always have the same color ratio. The conclusion from our previous results on addition of salt to bicolor standards, namely that the pK’ of phenol red would be 0.02 unit lower at zero ionic strength than in ~/15 phosphate solution, is, of course, erroneous.

The difference of -0.05 between calorimetric determinations of dilute bicarbonate solutions at 20’ and 38”, given in the same paper (24), was to be expected. The carbonic acid pK’, and hence the actual pffn+ would be decreased 0.18 unit at the higher temperature, while the indicator pK’ would decrease only 0.13 unit. The color reading would therefore be 0.05 unit lower.

CONCLUSIONS.

The data given in this paper represent, we believe, an advance in the systematic tabulation of the experimental effect of salts on the colors of three indicators widely used in biological work. The practical application of these findings holds regardless of the degree of validity of the theory involved.2

Until there is an extension, to other types of indicators, of this method of studying the effect of salt concentration on indicator color, it would be premature to advocate the application of these theories to every indicator. All that may be stated at the present time is that there are three indicators of the sulfonphthalein series, which, on the basis of extensive experimental work, seem to behave as do other typical weak electrolytes. The results are well in accord with recent studies involving electrolyte behavior, and also with Ostwald’s dissociation theory of indicator color.

2 As this paper is about to to go to press, we find that Kolthoff reports (J. Physic. Chem., 32, 1820, December (1928)) the result of a study of the “salt error” of several indicators, from which he concludes that the salt correction of indicators cannot be adequately calculated from the equation of Debye and Htickel. That the ionic strength of solutions alone is inade- quate to account for the activity coefficients of ions in general is well recognized. It seems from his results as well as those presented in this paper that the treatment of “salt errors” as a problem of activity coefficients of weak electrolytes provides the best explanation for their existence and magnitude.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


We are indebted to Mr. Gilbert Stone for his careful determination of the electrometric pan+ values in this paper.

SUMMARY.

1. By means of electrometric pan+ estimations, and color readings against bicolor standards, the effect of NaCl, KCl, NazSO1, KzS04, MgCL, CaCL, MgSO+ acetate and phosphate buffer mixtures, and glucose, on the activity coefficients of the sulfonphthalein indicators, brom-cresol green, brom-cresol purple, and phenol red, has been studied.

2. With the indicators, as with other weak acids in the presence of their salts, the value of pK’ is dependent upon the total electrolyte content of the solution. It is because of this fact that addition of neutral salts alters the color of an indicator solution.

3. When the effects of salts on indicators are correlated with ionic strengths, salts of different valence types show at the same ionic strengths approximately like effects on the pK’ of the indicator.

4. Quantitatively the relation between ionic strength and pK’ is expressed by the equation of Debye and Hiickel, based on the assumption that all the salts are completely dissociated and that the combined effect of their ions on the log of an activity coefficient (in this case on the change they produce in pK’) is proportional, as a first approximation, to the square root of the ionic strength.

5. Our results indicate that other, lesser, factors than ionic strength influence the relationship between pan+ and indicator color. Among such factors may be varying specific interionic effects of individual ions or groups of ions. Such effects are, however, in most cases, relatively slight compared with the main, non-specific effect indicated by the ionic strength.

6. Tables and equations are given for the determination of pan+ calorimetrically, which take into account possible variations in the salt content either of the sample or of the standards, or of both. A correction is also applied for the ratio in which the alkaline and acid forms of the indicator are present in solution.

7. The results are applied to a discussion of various phases of recent work in calorimetric pan+ estimations.

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

J. Sendroy, Jr., and A. B. Hastings

BIBLIOGRAPHY.

1. Kiister, F. W., 2. anorg. Chem., 13,144 (1897). 2. VanCleeff, G. D., Rec. tram. chim. Pays-Bus, 20,198 (1901). 3. Acree, S. F., Am. Chem. J., 36,120 (1906). 4. von Szyszkowski, B., 2. physik. Chem., 68, 420 (1907); 63, 421 (1908). 5. Michaelis, L., and Rona, P., 2. Elektrochem., 14, 349 (1908); Biochem.

Z., 23, 61 (1909). 6. Sorensen, S. P. L., and Palitzsch, S., Compt. rend. Lab. Cadsberg., 9,

8 (1910). 7. Bjerrum, N., Die Theorie der alkalimetrischen und azidimetrischen

Titrierungen, Stuttgart, 1914. 8. Thiel, A., Sammlung chemischer und chemisch-technischer Vortrilge,

Stuttgart, 16, 307 (1911); 2. anorg. Chem., 132, 159 (1924). 9. Prideaux, E. B. R., The theory and use of indicators, London, 1917.

10. Michaelis, L., Hydrogen ion concentration, translated by Perlzweig, W. A., Baltimore, 1926.

11. Kolthoff, I. M., Indicators, translated by Furman, N. H., New York, 1926.

12. Clark, W. M., The determination of hydrogen ions, Baltimore, 3rd edition, 1928.

13. Bronsted, J. N., J. Chem. Sot., 119,574 (1921). 14. Stieglitz, J., J. Am. Chem. Sot., 26,1112 (1903). 15. Hastings, A. B., and Sendroy, J., Jr., J. Biol. Chem., 66,445 (1925). 16. Cohn, E. J., J. Am. Chem. Sot., 49,173 (1927). 17. Cohn, E. J., Heyroth, F. F., andMenkin, M. F., J. Am. Chem. Sot., 60,

696 (1928). 18. Simms, H. S., J. Physic. Chem., 32,112l (1928). 19. Debye, P., and Htickel, E., Physik. Z., 24,185 (1923). 20. Bronsted, J. N., and La Mer, V. K., J. Am. Chem. Sot., 46,555 (1924). 21. Lewis, G. N., and Randall, M., Thermodynamics and the free energy

of chemical substances, New York and London, 1923. 22. von Halban, H. V., and Ebert, L., Z. physik. Chem., 112,321 (1924). 23. Hastings, A. B., Murray, C. D., and Sendroy, J., Jr., J. Biol. Chem.,

71, 723 (1926-27). 24. Hastings, A. B., and Sendroy, J., Jr., J. Biol. Chem., 61,695 (1924). 25. Hastings, A. B., Sendroy, J., Jr., and Robson, W., J. Biol. Chem., 66,

381 (1925). 26. Lepper, E. H., andMartin, C. J., Biochem. J., 20,45 (1926). 27. La Mer, V. K., King, C. V., and Mason, C. F., J. Am. Chem. Sot., 49,

363 (1927). 28. La Mer, V. K., and Mason, C. F., J. Am. Chem. Sot., 49,410 (1927). 29. Tr. Far&y Sot., 23,334-544 (1927). The theory of strong electrolytes. 30. La Mer, V. K., Tr. Am. Electrochem. Sot., 61,631 (1927). 31. Nernst, W., Z. physik. Chem., 136,237 (1928). 32. Nernst, W., and Orthmann, W., Z. physik. Chem., 136,199 (1928).

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/


33. Naudo, S. M., 2. physik. Chem., 136,209 (1928). 34. Bjerrum, N., Kgl. Dan&e. Vidensk. Selskab., Math.-jysisk. Medtl., 7,

No. 9 (1926). 35. Bjerrum, N., Tr. Farady Sot., 23,445 (1927). 36. Gronwall, T. H., La Mer, V. K., and Sandved, K., Physik. Z., 29, 358

(1928). 37. Giintelberg, E., and Schiijdt, E., 2. physik. Chem., 136,393 (1928).

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/

Julius Sendroy, Jr. and A. Baird HastingsCERTAIN ACID-BASE INDICATORSTHE ACTIVITY COEFFICIENTS OF

1929, 82:197-246.J. Biol. Chem.

http://www.jbc.org/content/82/1/197.citation

Access the most updated version of this article at

Alerts:

When a correction for this article is posted•

When this article is cited•

alerts to choose from all of JBC's e-mailClick here

ml#ref-list-1

http://www.jbc.org/content/82/1/197.citation.full.htaccessed free atThis article cites 0 references, 0 of which can be

by guest on Decem


ww

.jbc.org/D

ownloaded from

http://www.jbc.org/content/82/1/197.citation

http://www.jbc.org/cgi/alerts?alertType=citedby&addAlert=cited_by&cited_by_criteria_resid=jbc;82/1/197&saveAlert=no&return-type=article&return_url=http://www.jbc.org/content/82/1/197.citation

http://www.jbc.org/cgi/alerts?alertType=correction&addAlert=correction&correction_criteria_value=82/1/197&saveAlert=no&return-type=article&return_url=http://www.jbc.org/content/82/1/197.citation

http://www.jbc.org/cgi/alerts/etoc

http://www.jbc.org/content/82/1/197.citation.full.html#ref-list-1

http://www.jbc.org/content/82/1/197.citation.full.html#ref-list-1

http://www.jbc.org/

the activity coefficients of certain acid-base … · j. sendroy, jr., and a. b. hastings 199 the...

Documents