T H E E F F E C T OF SALTS ON WEAK ELECTROLYTES* I. Dissociation of Weak Electrolytes in the Presence of Salts BY HENRY S. SIhIhlS
I. Notation and Definitions The notation used in this article is the same as in a previous paper on the relation of dissociation constants to titration data’ and a paper on the relation of dissociation constants to chemical structure,* with the exception of the elimination of the “corrected” titration constants (GI, G2, Ga, etc.) which are not true constants under the present assumptions, and a redefinition of T , which is now defined by the equation log r = a d T where
a
=
p =
a constant = 0,495a t 25°C ionic strength = b Z z Y Z
where i is the concentration of a given ion, Y is its valence, and z is a number between 2 and I defined by Equation (9). The term INDEXis introduced to refer to the negative logarithm of a number or variable. -log X = P x = “Index oi x”. \Then X is a type of constant the word “const ant” may be omitted: PK = Dissociation index PG’ = Titration index PH = H- ion (activity) index Ph = H’ ion (concentration) index. .In “index unit” (which we formerly called
PH unit) is the logarithm of
IO.
Thus if
Pc,’ = 4.0 and Pc*‘= 5 . 5 , the two titration indices are 1.5 index units apart.
The following symbols are repeated for convenience: KI‘, Kz’, Ks‘, etc. = Dissociation constants not corrected for activity. K,,K 2 , K?,etc. = Dissociation constants corrected for activity. Gl’, Gn’, Gal, etc. = Titration constants (uncorrected). = Probabilities of dissociation according to GI’, Gz’, and Gz’, respectively. al, OLZ: u , m, d , and t = Fractions of a substance in the undissociated, mono-ion di-ion and tri-ion forms, respectively. c , a , b , h , and oh = Molal concentrations of substance, strong acid, strong base, hydrogen ion and hydroxyl ion, respectively. H and OH = Acticities of hydrogen ion and hydroxyl ion, respectively. “Dissociation” refers to the effect of ionization oi acid groups and hydrolysis of the salts of basic (amino) groups. Dissociation indices arc designated in order of numerical value. regardless of type of group. f,, f i ,f?,etc. = Activity coefficients when 0 , I , 2 , etc. groups have “dissociated”.
* From the Department of Animal Pathology of The Rockefeller Institute for Medical Research, Princeton, K, J. Simms: J. Am. Chem. SOC.,48, 1239 (1926). To be consistent with the present notation and assumptions, section VI1 of that paper should be omitted; also omit the fifth s t e p in section VIII, the last sentence in the sisth step and the last clause in the seventh step. I n Table I, 0.03 should be subtracted from the values in column 5 , thus slightly altering the rest of the table. Simms: J. Am. Chem. SOC.,48, 1251 (1926).
HEXRY S. SIMMS
I122
The following notation is added: after the number of an equation signifies that t h e equation refers only to substances with “ieolated” constants ( 2 .j or more index units apart). A after the number of an equation indicates that it refers only to acids. B only to tmsr:s. and M only to ampholytes. I or I1 before the number of an equation in the text refers to an equation in paper I or 11. respectively.1,Z Molar concentration refers to mols per 1000 cc. of solution. I
II. Introduction The Debye-Hiickel equation has been found to apply fairly accurately to inorganic (strong) electrolytes, although less has been done in extending it to weak electrolytes. It would be expected that those molecules of a weak electrolyte which are ionized should obey this equation, On this assumption Sherrill and Noyes, and also P\lacInnes3have successfully applied an actiyity correction to conductivity data on monovalent weak acids and obtain consistent dissociation constants. Harnedl has studied formic acid by catalysis. Hastings and Sendroyj have studied carbonic and phosphoric acids. C’ohn6 has studied PK!’of phosphoric acid. Attempts have been made by Cohn, by Sorensen, and by Htadie’ to extend the Debye-Huckel equation to proteins. However, no systematic study has been made of the activity coefficients of monovalent and polyvalent organic acids, bases and ampholytes. This paper deals with the effect of ionic strength of various salts on the activity coefficients of weak electrolytes as shown by the effect on the dissociation indices. 111. Theory
A . Monovalent substances. The mass action expression for a monovalent acid such as acetic acid is:
where a (which equals X - / c ) is measured as concentration and H is observed as activity. The true constant ( K ) must be expressed entirely in terms of activity, hence :
I n dilute solution we may assume that the ions of the weak acid obey the limiting Debye-Hiickel equation -logf=
au2d\/
=
au2d/ziiz
(3)
3 Sherrill and Iioyes: J. Am. Chem. SOC.,48, 1861; McInnes: 2068 (1926). 4Harned: J. Am. Chem. SOC.,49, I (1927). 5Hastings and Sendroy: J. Biol. Chem., 65, 445 (1925); Sendroy and Hastings: 71, 783 (1927). 5Cohn: J. Am. Chem. SOC.,49, 173 (1927). 7 Cohn: Physiol. Rev.. 5, 349 (1925); SBrensen, Linderstrom-Lang and Lund: J. Gen Physiol., 8, 547 (1927); Stadie and Hawes: J. Biol. Chem., 74, xxxi (1927;.
EFFECT OF SALTS ON WEAK ELECTROLYTES
1123
and that the undissociated molecules have unit activity coefficients,* hence fo/f1
(4)
= 7
and we obtain the following equation for a monovalent weak acid:
Determination of the PHof solutions of a weak electrolyte in the presence of known amounts of strong acid or base gives us its "potentiometric titration data" from which we may calculate the dissociation constants as previously described.' I t is evident from Equation 5 t'hat if we plot p , for the various points, against calculated dissociation indices ( PK') we should obtain in dilute solutions a straight line curve with a slope equal to -a, for a weak acid, and equal to +a for a weak base.g The intercept of this curve with the P K ' axis should equal PK(the true dissociation index). B . Polyvalent substances.-In the second paper,? Equations I1 2 2 , I1 2 3 , and 11 2 4 gave the relation between the observed dissociation constants, the intrinsic constants, the internal electrostatic work and the activity coefficients. The corresponding equations for a divalent substance are (we include also the relation to the titration constants) :
Ki' Ks' K1'
=
KO' KO1' L'
=
KO' 12' ( f 0 / f ~ ) ' + KO" L"
I'
(fO/f2)'
I'
= GI' =
(72'
(folfi)"
GI'
+ Gq'
(6)
(7)
K2' = Equation 6 divided by Equation 7 where L,a function of electrostatic work, is defined by Equation I1 z j. Any observed deviation from these exact expressions should be due to error in the assumptions made in their application. I t will be seen that these dissociation constants are dependent upon the The Debye-Huckel equation activity coefficient ratios (fo If2) and (f0/f1). is satisfactory for determining the activity coefficient ratio of monovalent acids; but we must modify the equm5on before we can deal ufith the polyvalent acids. C. ModiJcation of the Debye-Hiickel equation to a p p l y to long ions,The Debye-Huckel equation is derived on the assumption that the charge on an ion is located at a point or on the surface of a sphere. If we should 3 I n spite of the evidence offered by Randall (Chem. Rev., 4 , 291 (1927) ) that the activity coefficients of non-ionized molecules differ from unity by a few per cent, we make the working assumption that j, = I . We also assume that the coefficients for ions are given by Equations 8 and 9. The error in these ideal assumptions appears as a discrepancy between experimental and calculated values of S. These discrepancies when converted into differences in activity coefficient ratios in 0 . 9 solutions ~ amount to less than 3 per cent in the presence of NaCl; but in the presence of MgC12 represent a lowering of 3 to I O per cent in f i / f o ; 13 to 90 per cent inj*/j,; and 95 per cent in j3/f2.The effect of K 8 0 n is to increasef,/.f, IO per cent above the calculated value. I t is unwise to assign these deviations to particulai ionic species until we have more data on weak electrolytes. Randall's assumption that the weak ions have activities identical with HC1 mitigates the accuracy of his resulting calculations. See definition of ''dissociation" a t beginning of article.
HESRP S . SIMMS
I124
have a dianion with charges so far separated that the distance between them is comparable to that between individual ions, it is evident that each should behave like a separate univalent ion. To correct for this distance we may write the limiting equation (3) as fo1lows:'O -1ogf
=
vz a
zi
2/
yz
=
log
(8)
;.Yl
where z is a number between I and z such that for a point charge vz = v? and for an ion with a very longodistance between charges v z = v. For acids with a maximum distance of r, Angstrom units between the charges we may write as an appr0ximation:ll
vz
= v2-
(v? - v) r,/18
(9)
where the probable mean dist>nce between ions is about 18 A. ( T , must never be assumed greater than 18 A in this equation.) The agreement o€ the data with these equations is shown in Fig. I .
D. Application of modified equation. Let us assume that the ions of a divalent acid obey the modified equations (8 and 9) and that the non-ionized molecules have unit activity coefficients ( y o z = o), then (jO/jI)I=
=
7v!z-YoZ
=
7vlz
11 =
7Y'z-Yoz
=
7u'c
(f0/,j,)II (fo,!f2)I
(For ions with a point charge v; =
=
7
(IDA) (IIA)
z 2 = 4)
From the general equations (6 and 7) we get:
+
10 The contribution of a weak acid ( p , = 4 Z i u z ) to the total ionic strength ( p = p o pB where ps is the contribution of salts) is calculated as described in the following paper. The Debye-Huckel equation was derived t o apply to such ions as could be considered to have either a point charge, or a multiple charge distributed with spherical symmetry. In other words the equation applies to ions with a spherical field of force. By no stretch of the imagination can the diion of azelaic acid be 80 considered. I t s field of force is dumbbell shaped (resulting from the fusion of two spherical fields). Prof. Debve was kind enough (in 1925) to calculate the result of an ellipsoidal field of force (as an ap"proximation to the dumb-bell field) and arrived a t equations which in the extreme case of a sphere give the usual limiting equation (u' = 9 ) ;and in the opposite extreme case of a very long ellipsoid agree with Equation 8 where uz = Y . This agreed with Equation 8 which I had postulated a t that time. However, as Prof. Debye pointed out, it is unlikely that a simple relation between Y Z and the distance can be derived on theoretical grounds since the equations are too complex. I t therefore seems justifiable to find a n empirical relation. The simplest and most likely assumption is that within a given range Y Z varies from u2 to Y as a linear function of the distance between charges, reaching Y a t the effective mean distance between ions. This proved to be so in the entire range of substances studied. The effective mean distance being 18 A with an ionic strength from 0.01 to 0.1 p and a weak acid concentration of 0.01 molar. (The average distances between like charges in 0.01 and 0.1 molar solution would be 55 t o 25 A,) This mean effective distance should be higher than 18 in more dilute solution and lower in more concentrated solution. However we are not justified in introducing a correction for concentration until we have obtained supporting data. It should vary as a function of and should not affect the data much with small changes in concentration. above I 5 A &e.. the curves of Fig. I Equation 9 probably gives too low values of probably deviate from the straight lines). However it is seen to agree with those data up to 12 A. The data for sebacic acid (14 A) were poor and are not published, but they appeared to agree within the experimental error.
+=
EFFECT O F SALTS ON WEAK ELECTROLYTES
(where v; - vIz = 4-
Azelaic
I
= 3 for
a point charge).
-
FIG I Plot of values of Y Z (from data with SaC1) aga nst the d stance ( r a ) between the negative charges in polyan,ons The curves are calculated from equat on 9 The small squares are V I Z values. Large squares u p values. The solid square is v a t for HsP04 (data of Sendroy and Hastings),
Similarly for = K 3 of a trivalent acid we get:
K1 =
K3
‘
(equal t o
Ks’
K1’ F~ = - for a point TS
charge)
In the case that the constants are “isolated” (more than apart) these simplify t o : Kl = K1’/ T Gl’j‘ ‘T K21/u:’=vt‘ = G2‘/ r ~ > e - u t z K1 =
K3
-
-
Kat/ r ~ ~ z - v ~ z= GS’ / T ~ ~ z - u . s
2.j
(1 4 4
index units ( I jdI) (16dI)
(17x1)
For a divalent base we must substitute r’2z-u~z for I i ’ T in Equations ~ 13A and 16ilI. 12A and I j A I ; and r for I / T ” ~ ~ - ”in~ Equations For a trivalent base we must substitute for I ’T in Equations ~ ~ Equations 14.l and 1 7 M ; while 12A and I S M ; and r for I / T ” ~ * - in r y ~ z -must y ~ z be substituted for I / T ~ ? ~in- Equations ~ ~ ~ 13hand 16hI. ~
~
j
’
-
~
‘
~
1126
HENRY S. S I M M S
For a divalent (simple) ampholyte we may write = I/T
(.f0/j1)I
also
(fOlS2)
and
(fo/.fl)ll
= T
(I
81f)
(I9W
= 1
This gives us unusable equations for overlapping constants, but we may apply the following equations when the constants are “isolated.”
Ki
=
Ki’7
= G~T’
(ZOMI)
All the types of substances discussed in this paper are included in the above discussion except for aspartic acid. P K ~and ’ P K ~ of ‘ this substance should approximately obey the last two equations (above). There will be some error, however, since these constants are not sufficiently isolated. P K 3 ’should follow Equation 16A1. I n all these equations oh t o Z I M I ) vIz = I , but the values of v?z and v3’ are t o be obtained from Equation 9. Only in the hypothetical (and impossible) case of point charges can the original Debye-Huckel equation be obeyed by di- and trivalent organic ions (giving values of 4 and 9 respectively). IV. Experimental TT’e have obtained potentiometric titration data on a number of organic substances, first in the absence of other electrolytes (except the strong acid or base required for titration), second in the presence of two different concentrations of NaCl (0.07 j molar and 0.037 j molar), and third in the presence of two different concentrations of MgC12 ( 0 . 0 2 j molar and 0.0125 molar) having the same respective ionic strengths as the XaC1 solutions. The following general procedure was used: A 0 . 0 2 molar solution of the substance (sometimes with I or 2 equivalents of S a O H or HC1, depending on conditions) mas made up in a z j o cc. volumetric flask. j cc. samples were placed in I O ee. volumetric flasks with the requisite quantities of 0.10or 0 . 0 2 molar Il-aOH or HC1 and with I cc. of 0.7 j o or 0 , 3 7 j molar XaC1, or I cc. of 0 . 2 5 0 or 0.125 molar LlgC12, or with no salt. The samples mere then made up to I O ce. with distilled water. The 1 ’ ~ values of these solutions were obtained in water-jacketed hydrogen elertrotle cells’* a t z5.0°C. The cells were used alternately with the different types of solutions, thus eliminating errors in the comparative values. Except where otherwise indicated the final concentration of substance was 0.01 molar. The cells were calibrated against O . I O O O molar HC1 ( P H1.075) a t the beginning and end of each day. The liquid junction potential with saturated KCl was assumed constant. The dissociation index of water was taken as 13.890 a t 25.ooC. A11 alkaline solutions containing JlgCl? which were in the least cloudy were rejected. Simms: J. .Im Chem. SOC.,45,
2503 (1923)
I127
E F F E C T O F SALTS ON WEAK ELECTROLYTES
The “dilution experiments” consisted of a series of PH measurements on half neutralized ( ( b - a ) / c = 0. j) solutions a t the various concentrations indicated, all samples being obtained by dilution of the most concentrated solution. The data are given in Tables I1 to V. To save space the steps incalculation are omitted from these tables. The method of calculation has been fully described.’ The data on substances with overlapping constants are given and calculated in the succeeding article. The results, however, are discussed in this paper. The expressions ‘IC. - NaC1” and “D. -l;aCl” in these tables refer to data in the presence of 0.075 molar and 0.0375 molar NaC1, respectively. “C. -MgCl,” and D. -MgC12” refer to 0 . 0 2 j molar and o 0 1 2 5 molar MgC12, respectively; C, and D, being abreviations for concentrated ( 0 . 0 7 5 ~ )and dilute (0.037jp).
V. Results The above data give us dissociation indices ( P K ’values) in the absence of salts, in the presence of two concentrations of YaC1, and in the presence of two concentrations of MgCh (with the same respective ionic strengths). We have calculated the dissociation index from each observation and have plotted 4; against PK‘ for each constant of each substance (Figures I to 5 , where circles represent no salt, squares SaC1, diamonds MgCh and triangles dilution data). The slopes of the curves (Sa)are indicated in each case in the presence of NaCl and in the presence of MgCl?. Thesr are given in the fifth and sixth columns of Table I. The third column gives the slopes predicted if the ions obey the Debye-Huckel equation. The fourth column gives the slopes calculated from equation 9. Xote that these agree with the esperimental data with NaC1 in column j. The true constant is given in column 2 . The observed constant may be expressed in each case by the equation: PK’ = pK Sa d F (22)
+
The results may be discussed as follows: The rnonomlent acids. Acetic acid and succinimide have slopes approsimately equal to --a, indicating that their ions obey the Debye-Huckel equation. The equations for their dissociation indices may be expressed as in Equation zz : Acetic acid: Succinimide:
P K ’= 4.740 - 0.9 n dF PK’= 4.740 - 1 . 1 a PK’= 9.560 - 1 . 1 a v’? PK’ = 9.560 - 1 . 3 a diF
(with XaC1) (with hlgCI?) (with SaCC (with MgCI,)
(z3a) (23bj (24a)
(24b)
Similar equations may be written for all the other subst>anceslisted in Table I, but we will not take the space t o present them. The value of 4.740 for the true dissociation index of acetic acid agrees well with the extrapolated value (4.748) from MacInnes’ calculation of Kendall’s conductivity data
HES’RY S. SIMMS
1128
TABLE 1 Summary of results presented in this and the following paper. Slope = Sa
with SaCl .-,-
PK
Substance
DebyeHuckel
YZ
Equntion g
’ -
Found
Founds
Acetic Acid
4.740
-a
-a
-0.9s
-1.1a
Succinimide
9.560
-a
-a
-1.1a
-1.3a
-a
-a
P K ~1 . 1 9 Oxalic Acid ( T d = 4 . 5 A ) P x ? 4.22
-3a
-a - ~ j a -2.ja
hlalonicAcid* PK, 2.89 ( r d = j.7A) PK: 5 . 7 4
-a -3a
-a -2.4a
-a
- 1 . 1 ~
-2.4a
-5. ja
-a
-a
-a
-2.3a
-2.8a
-1.m
-9a
Succinic Acid PI;, 4 195 -a (rd=7.OW) P K ? 5 . 5 7 0 -3a
-2.28
AzelaicAcido P K ~4 . j z j (Td = I2.1A) PK? 5,395
-a -3a
-a -0.9a -1.6ja - 1 . 7 a
-2.oa
-a
-a -2.3a -3.3a
-0.6s. -5.h -11.2a
Citric Acid (meanrd = 7.4A) Aminoethanol Glycine
PKI 3.08 PK? 4 . 7 4 PKZ6 . 2 6
-3a
-5a
9.470
+a
+a
PK, 2.365
+a
+a
PI 6.040 o P K * 9.715 -a
o
AsparticAcid P K ~2.05 (Td = 7.01) P I 2.96 P K ~3.87
P K ~10.00
+a o -a -3a
-a +a
o
Calm- Debye- Equa- F o u n d t latedt Hlickel tion ’? (NaCI)
-6a
4.0 3 . 5
3.5
-7a
4.0 3 . 4
3.4
(-6a)
4.0
3.3
(-a)
4.0 2.65 2.6
3.2
-a
-6a -14a
4
-6a
4.0 3.2
0 3,3 9.0 6 . 6
+o,47a + o . o j a -0.08s. -0.o8a (-0,ja)(-1,6a\ -a -3.2a
-0.6a - 0 9a
-a
- 1 . m
-2.za
-2.3a
-0.6a - 0 9a -1.2a -5.9a
3.5
* Malonic acid was also titrated with 112S0, (Sa equal +o.za for PK,‘and - z I a for P n z ’ ) and with hIgSO4 ( S a equal -0.m and -4.5a respectively).
5 Since the substances in the presence of MgCIz were titrated with SaOH the solutions contained both M g + - ions and NaT ions. The curve which gives the slope corresponding to only hIg-+ cations would be drawn through a set of points for hIgClz and through t h e points without salt. The values S, thus obtained for the polyvalent ions with 0 . 0 3 7 5 ~of MgCI2 are: oxalic, (-1.9); malonic -10.7; succinic, -3.6; azelaic, -2.5; citric, - 1 1 and -32’ and aspartic, - 1 1 . 7 . These korrespond roughly t o the empirical equation S , = 32 S (where So is the value with SaC1). t T i e “calculated” values of Sa in Column 7 are obtained from the empirical equation S, = 12.j 8 So (applying only to polyvalent ions). Note that these values agree roughly with those in Column 6. $ The values of uZ in the last column equal -SI-SZ.
+ 16
+
The MONOVALEST BASE aminoethanol has a slope of +o.47a in the presence of XaC1 and +o.oga with MgCln, whereas a slope of +a is required by the Debye-Huckel equation. If the true dissociation index is constant this deviation must be due either to an increased activity of the ions in the presence of salt (which is improbable) or to a decreased activity of the undissociated molecule. The SIMPLE AMPHOLYTE glycine is represented in Fig. j . PK,‘ shows a similarity to aminoethanol except that the deviation is even greater than in the case of the base, but is about the same with both NaCl and M&L.
EFFECT O F SALTS ON WEAK ELECTROLYTES
1129
The difference in action of the two salts is manifested in the P K ~curves ‘ where it behaves like acetic acid in the presence of NaC1, but shows a n anomaly with M g C L The DIVALENT ACIDS are represented by four au-dicarboxylic acids, namely, oxalic, malonic, succinic, and azelaic acids. The data are presented in Tables I to IT’ and Figures 2 to 5 of the subsequent paper. The first dissociation index (PK,’) in each case behaves similarly to acetic acid in the presence of either XaC1 or MgC12.
The second dissociation index (PP,’) has a slope in the presence of NaCl less than required by the Debye-Huckel equation, while the slope with MgC1, is greater than with XaC1 in each case. Sebacic acid behaves similarly to azelaic acid, but its data are not satisfactory for publication. Curves I , 2 , and 3 of Figure I represent the values of vZ calculated from Equation 9. The observed values (of data with NaC1) are seen to agree within experimental error for ions with I , 2 , or 3 charges. This proves that Equations 8 and 9 may be used as a reasonable approximation of the relation between activity and the distance between charges. The long divalent acids (succinic, azelaic and sebacic) show a small but definite deviation in the presence of ;IlgC12, while the short acids (oxalic and
I 130
HENRY S. SIMMS
malonic) show a very large deviation, as indicated by the large diamonds in Fig. I which would fall on the curve of YZ. if there were no deviation. The data with MgS04 and K2S04 show that the sulfate ion has an effect on both indices of malonic acid which is opposite in direction to the effect of magnesium ions.
FIG.3 Succinimide
A TRIVALENT acid, namely citric acid, was studied in the presence of LIgCl? only. P K , ' , like the first indices of monovalent and divalent acids, obeys the Debye-Huckel equation with MgC12. PK2' (like that of oxalic and malonic acids) shows a large deviation, while PK,'shows a still larger deviation, having a slope of -11.2a (not shoivn in Fig. I ) . The slope predicted by equation 9 is -3.3a. A TRIVALENT AMPHOLYTE was studied, namely aspartic acid, which is both an ampholyte and a divalent acid. The first dissociation index (PK,') behaves like that of glycine. The second ( P K ~ behaves ') like acetic acid and is unlike P K z ' of glycine in that the data with ;\IgC12 are normal. The abnormality is not found until we reach the third index (PKJ') where the effects of hIgC12 and NaC1 differ much more than for succinic acid.
EFFECT O F SALTS O S WEAK ELECTROLYTES
1131
VI. Discussion of Anomalies From the above section and from Table I it will be seen that monovalent acids as well as the monoions of polyvalent acids obey the Debye-Huckel equation either in the presence of ?IlgC12or of XaC1 (altho not with sulfates). Furthermore, divalent anions obey a modified equation (Equations 8 and 9) in the presence of XaC1. (This modified equation involves the distance between charges.)
93 94 95
46 97 9.8
PK/ FIG.
1
Aminoethanol
However, there are four anomalies to be found in the data. The first is the anoniaiozts behmior o j cations. Cations from either amines or ampholytes do not obey the Debye-Huckel equation. Khereas the slopes of the dissociation index of aminoethanol and the first indices of glycine and of aspartic acid should each be + a , we find that they are, respectively, +o.47a, -oo.08a, and -0.6a in the presence of SaC1; and - 0 . 0 5 0 , +o.o8a, and - 0 . 6 ~ in the presence of IIgC'l?. These deviations involve a shift in the dissociation indices toward the acid side which might signify either that the activity of the ions (liKH3+) is too large, or that the non-ionized fraction (KXH,) has a low activity. In this connection we may refer to the work of Pfeifferl3 who isolated complex salts between amino acids, peptides, etc., and inorganic salts and obtained evidence that these exist in solution. Xorthrup and KunitzI4 find indication of combinations of ions n i t h proteins. l3PEeiffcr and K i t t h a : Ber., 48. 1289; Pfeiffer, Wdrgler and Kittha: 1938
Z.physik. Chem.. 133, 2 2 ; 134. 180; 135, 16; 143, 265 (1924). l'
Sorthrop and I i u n i t z : J . Gen. Physiol.. 9, 3 j 1 (1926) and unpublished data.
(1915);
1132
HESRY S. SIMMS
The second anomaly is in the efecl of MgCZz on ampholytes, namely on the second dissociation index ( P K 1 ' ) of glycine and also on the third index ( P K ~ ' ) of aspartic acid. Both these indices behave normally with XaC1. The index of glycine represents the change from a neutral molecule to an anion. That of aspartic acid represents a change from monoanion to dianion. They have one thing in Common, namely, that they represent a change from an amphion (zwitherion) form in neutral solution to a normal form in alkaline solution.
FIG. 5 Glycine The isoelectric point ( P I = 6.040) has a slope of -o.ja with XaCl and - 1 . 6 ~ with AIgC12
The third anomaly is in the e$ect of M g C l , on the second and third indices ( P K ~and ' P K ~ of ' ) divalent and trivalent acids, as shown by the difference between the slopes with XaC1 and XgClz (see Figures 2 to 6 in the following article, and Table I and Fig. I of this paper). The effect is small with long chain acids (succinic, azelaic and sebacic) but is large for oxalic, malonic and citric acids. I n this connection we may refer to the deviations observed by Bronsted and LaMer'j with salts of higher valence type, which Bjerrum and also LaMer and attribute in more recent studies to neglect of higher terms in deriving the Debye-Huckel equation. \Ve may refer also to the high solubility of C a C 0 3 in phosphate and citrate solutions observed by Hastings, Murray and Sendroy." The high concentration of calcium in the blood was thought by Holt, LaMer and Chownl8 to be due to supersaturation Bronsted and LaMer: J. -1m. Chern. Soc., 46, j j j (1924). '6LahIer and Mason: J. Am. Chem. Soc., 49, 410 (1927). liHastings, l l u r r a y and Yendroy: J. Biol. Chem., 71, 7 2 3 (1927). Is Holt, La Mer and Chown: J. Biol. Chem., 64, j o g , 567 (192j).
1'33
EFFECT OF SALTS O S WEAK ELECTROLYTES
but Hastings and SendroyIgexplain it as a combination with other constituents in the serum. The fourth anomaly is the e j e c t of sulphate ion. The data on malonic acid in the presence of M g S 0 4 and &So4 indicate an effect different from the corresponding chlorides but opposite in direction from the effect of the magnesium ion. This deviation is shown by both mono- and dianions. K e will not attempt to explain any of the anomalies. More data are being obtained which have a bearing on this question. The direction of all the deviations observed in this paper (with the exception of the effect of S6,ions) is to render the solutions more acid than expected. It is interesting to note that the curves for P K , ' )P K ~ and ' , P K ~of' polyvalent acids and ampholytes approach each other a t higher ionic strengths particularly in the presence of MgC12. Should the same laws hold a t higher concentrations we would have K3' > Kp' > K1' which is the reverse of the usual relation. This would mean for a polyvalent acid that the ions of higher charge would form more readily. Such a condition may be experimentally possible with oxalic or citric acid. For an ampholyte i t would mean that the zwitherions would be supplanted by nonionized molecules. TABLE I1 A Acetic Acid (o.oro0 molar) Salt
c. -hlgCln
PH
b- a
b'
3,332 3.350 3,394 3.352 3.342
0 0 0
o.oj1
0
,051
0
,054
3.742 3.766 3.864 3.780 3.761
0 .I o 0
.I o 0 . IO0 .Io0 .IO0
. I20
4.238 4.276 4.372 4,293 4.260
D. -MgC12 S o salt D. -NaC1 C. - S a c 1
4.601 4.631 4.715 4.631 4.609
C.-MgC12 D. - 3fgCln No salt D. - S a c 1 C. - XaCl
4.944 4.983 j.063 j.008 4.971
KOsalt
6,768
D. -hfgC11 Xo salt D. -KaC1 C. -NaCl
c.-3IgC12
D. - hlgC1, S o salt D. - S a c 1 C. - NaCl
c.-MgClz
D. -MgClz Xo salt
D. -?;aC1 C. - S a c 1
c.-JlgC11
19
P R I
dZ
C
,051 ,041
0.274 , '94 ,020
I94 ,274 '
,114 ,119
. I20
4.597 4.629 4,751 4.645 4.624
276 ,196 '034 ,196 ,276
.3m ,300 ,300 ,300 ,300
,307 ,306 ,304 ,306 ,306
4.588 4,629 4.729 4.646 4.613
,279
,500
,503 .SO3 ,502 ,503 ,503
4.594 4.624 4.709 4.624 4.602
,283 ,206
,701 ,701 ,701 ,701 .70 I
(4.571) (4.610) 4.690 4.635 4.598
,122
,500
,500 500
,500
,700
Z"
. /oo ,700 ,700 I
4.594 (4.612) 4.756 (4.614) (4,566)
.ooo
.
1.000
Hastings and Sendroy: J. Biol. Chem., 71, 723 (1927).
,201
'055 ,201
,279
071
206 ,283 ,286 ,211
,084 ,211
286
1 I34
HEKRY S. S I Y N S
It will be observed that the isoelectric point is dependent upon ionic strength. More information as to the cause of this deviation must be obtained before we can accept the theory of Sorensen' that a constant "isoionic" point exists. This theory necessitates that the deviation is due to the substitution of H+ ion by another cation producing a weakly ionized salt. This is not consistent with some of our (unpublished) data. TABLE II B Acetic Acid a t Various Dilutions-Half Seutralized C
b'
P K
0.160
.I o 0
,075 ,050
.02j ,010
,005
PK
0,joo
4 619 4 636 4 644 4 660 4 680 4.705 4 717
b-n = o j '
d7
4.619 4.636 4.644 4,660 4.678 4.701 4 . 709
,500 500 500
,501
. 502 ,504
0.283 224 194 , I 58 ,112
,071 ,050
TABLEI11 Succinimide (0.0112 and 0.0123 molar*) The data plotted in Figure 3 were lost. These data are less accurate. Salt c.-3lgClt D. -hlgClz S o salt D. -NaCl C. -KaC1
PS
b- a C
b'
8.695 8.756 (8.83) 8.751 8.724
0.178 I 78
0.178
I78
Po' 9,358 9.419 (9.49) 9.413 i9.487)
8 911
,267 ,267 267 267 ,267
9.349 9.404 9 537 19.40) 9.370
. ,
I78
,178 ,178
,178 . I78 ,178
\G 0.277 . '99 045 '199 ,277
C. -MgClt D. - MgCli No salt D. -NaCl C. - S a c 1
8.966 9.097 (8 96) 8,930
,268 ,268 ,268 ,268 ,268
No salt D. -N&1 C. - NaCl
9 260 9 175 9 137
,357 ,357 ,357
356 ,356 356
9 518 9.433 9.393
,063 204 ,281
No salt D. - S a c 1 C. -NaCl
9,426 9.323 9,290
446 ,446 ,446
445 ,445 445
9.525 9.42' 9.388
. 07 I ,206 283
No salt D. -NaCl C. - NaCl
9,509 9.423 9,380
,488 * ,488' .488*
,485 ,485 ,485
9 535 9.449 9.406
,077 208 .285
c.--hIgClz
9.529 9,578 9,625 9.585 9.539
,569; ,569 .569* 569: ,569
,564 564 564 564 564
9.417 9.466 9 513 9 473 9.427
,286
9.679 9.737 9.776 9.752 9.708
. 650' ,650'
'
,644 644 ,644 ,644 ' 644
9.421 (9.479) 9.518 (9 494) 9.450
,288 ,213 089 ,213 ,288
D. -M@ No salt D. -KaCl C. - S a c 1
c.-MgclP
D. - MgCL No salt D. -NaC1 C. - NaCl
'
'
,650'
,650' 650'
'
'
,279 ,201
,055 ,201
279
,211
,084 ,211
,286
* The concentration of solutions marked with an asterisk was 0.0123 molar. The other solutions were 0.0112 molar.
E F F E C T O F SALTS O S WEAK ELECTROLYTES
TABLE IVA Xminoethanol (o.010o molar) Experiment VI1 b - a Salt
b'
~
C
P H
P K I
KOsalt
3 032
-1.100
--I
S o salt
4 82
--I
- ,998
c -3IgC12
8j I j 8 519
-
8 53 8 536
,900 900 - ,900 - ,900 - ,900
-
-3IgCL D -3lgClr
8 714 8 i46
- ,850 - ,850
- ,851 - ,851
9 502 9 504
C -MgC12 D -3IgCI2 90salt
8 876 8 872
-
- ,801 - ,801 - ,801 - ,801 - ,801
9 9 9 9 9
D -LlgCl? S o salt D -Sac1 C -Sac1
c
8 482
D -Sac1 C -Sac1
8 874 8 893 8 909
c
000
,800 ,800
,800
,800 ,800
,007
,900 .9m ,900 ,900 ,900
-3IgC12
8 984 8 984
- ,750 - ,750
-
.ijl
D -1IgC12
c
-3lgClz D -SlgCl2 Yo salt D -Sac1 C -Sac1
9 IO1 9 099 9 103 9 I21 9 I35
- ,700 - ,700 - 700 - 700 - ,700
-
,702
-
702
c. - 31gc12
9 9 9 9 9
306 283 290 323 323
-
-
602
9 473 9 497 9 519
-
500
- '504
-
j00
- ,504
500
D -Sac1 C. -XaCl
9 652 9 679 9 693
-
400 400 ,400
So salt D. -NaCl C. - S a C l
9 820 9 844 9 863
- ,300 - 300
D. -3IgClz S o salt D. - S a c 1 C. - S a C l
S o salt D -Sac1 C. - S a C l S o salt
,600 ,600 ,600 600 - ,600
-
,300
,751
702
,702 702
9 9 (9 (9 19
470
474 437) 54) 491)
o 290 216 09 5 216 290 289 214
481 477 479 498
288 213 090 213
514
288
9 464 9 464
287
9 9 9 9
474 472 476 494 9 508
212
286 211
084 211
286
9 486 9.463 9 472 9 505 9 505
285 208 078
- ,504
9 480 9 504 9 526
074 206 283
- ,406 - ,406 - ,406
9 486 9 513 9 527
063
- '309 - ,309
9 47@ 9 494
055
9 513
279
- ,602 - ,603 -
,603
- ,603
-
,309
208
285
204 281
201
1136
H E S R Y S . SIMMS
TABLE IV B Aminoethanol (o.oroz molar) Experiment I11
Salt
PH
Iio salt
10.633
No salt D. -NaCl C. -NaCl
10.264 10.302 I O .302
No salt D.-NaC1 C. -NaCl
10.066 10.075 10.088
b- a
\'7
b'
PK'
-0.054
(9.5)
-0.098 - ,098 - ,098
- . I21 - ,124 - ,124
(9,399) (9.452) (9.452)
035 ,196 ,275
- ,196
-
,196 - ,196
- ,211
-
,212
9.491 9,499 9.51.5
'047 . I99 ,277
- .303 - ,304 - '304
9.483 9.516 9.528
,056
C
0
-
,211
0.023
No salt D. -NaCl C. - NaCl
9.847 9.876 9.888
- '294 - '294 - '294
No salt D. -NaCl C. - NaCl
9,673 9.708 9.722
- ,392 - ,392 - ,392
-
'398 ,399 ,399
9.492 9.529 9.543
,064 ,204 ,281
No salt
9.517 9.534 9.554
- ,490 ,490 - '490
- ,494 - ,494
9.507 9.524 9.545
,071 ,206 ,283
C. -KaCl
9,331 9,368 9.381
- ,588 - ,588 - ,588
- ,591 - '591
9.487 9.524 9.537
,078 ,208 ,285
No salt D. -NaCl C. -NaCl
9.162 9.187 9.199
- ,686 - .686 - ,686
- ,688 - ,688 - ,688
9.505 9.530 9.542
,211
No salt D. -NaC1 C. -NaCl
8.939 8,964 8.981
-
-
,785
9,501 9.526 9,543
,089 ,213 288
No salt
8.600 8.632 8.629
- ,882 - ,882
-
,883
D. -iYaCl C. --NaCl
,882
- ,883 - ,883
(9.472) 9.506 9.503
.290
No salt No salt
7.615 3.198
- ,980
- ,980
-1.016
-I
D. -NaC1 C. - NaCl No salt
D. -NaCl
-
,784
- ,784 - .784
-
-
,495 '59'
- ,785 - ,785
016
,201 '
279
,083 ,286
,095 ,215
E F F E C T O F SALTS ON WEAK ELECTROLYTES
TABLE IV C Aminoethanol Hydrochloride (0.0100molar) Experiment VI ( PH
b of mother ~ solution =
-1.00)
b'
b__ - a
PK'
\5
C
871
8 9 9 9 9
321 485 835
- ,600 - ,500 - ,300
9 9 9 9 9
113 317 485 670 840
- ,700 - ,600
I20
8 551
-0.801 - ,702 - ,603 - '504 - '309
-0.800 - ,700
-
-
- ,400 - ,300
-
-
,291
- ,600 - ,600
- ,603 - ,603
9 515 9 533
,218 ,291
- ,500 - ,500
- , 504 - ,504
9 518 9 54'
,218 ,291
-
- ,407 - ,408 - .31I
9 519 9 536
,218
9 518 9 538
,218
,312
- ,217 - ,218
9 504 9 532
,218 291
- ,700 - 700
-
D -Sac1 C . -XaCl
9 333 9 353
D. - S a c 1 C. - S a c 1
9 511 9 534
D. - S a c 1
9 683 9 698
C. - S a c 1
IO IO
061 086
100 100 100
9 530 9 553
9 155 9 I80
D. -NaCl
100
100
,702
c -sac1
9 864 9 881
486 498 491 504 490
100
,218 ,291
- ,800 - ,800
D. - S a c 1 C. -XaC1
9 9 9 9 9
i00
. IO0 . IO0
9 518 9 544
8 939
C -Sac1
491 485
502
,218 ,291
8 913
D -Sac1
476 493
9 510 9 530
,900
- ,900
C. - S a c 1
,406
- ,309
8 571
D. - S a c 1
,702
- ,603 - '504
,500
9 9 9 9 9
0.100
-
,400
- ,400 - ,300 - ,300 - ,200 - ,200
-
,901
,901 ,801
,801 ,702
,218
,291 ,291
c. -?rlgCln
8.471 8.488
-
- ,900
-
,900
,900
(9 426) (9 443)
,218 ,291
D. -hlgClz
8 702
-
,850 ,850
-
,850 ,850
9 456 9 467
,218
-
,800 ,800
-
,800 ,800
9 486 9 483
,218 ,291
- ,751 - ,751 - ,702 - ,702
9 451
D -l\lgClz
c. -MgC12 D. -l\lgClz c. -1lgClz D. -XlgCI2 c. - MgClz D. -hIgClr
c. -hIgCl,
8 713 8 884
8 881
8 971
9
001
9 I08 9.111
Average values Salt S o salt D -Sac1 C. - S a c 1 D. -MgCIz C. - hlgCli
,900
- ,750 - ,750 - ,700 - ,700
PP' 9.492 9.517 9.538 9.469 9.479
291
,218
9 481
,291
9 481 9 484
,218 ,291
VT 0,100
,218
,291 ,218
,291
1138
HESRY S. SIMMS
TABLEI\' D .Iminoethanol (3.0488 molar) Experiment VIII. (Higher Concentration!
h - a
P H
b'
__
PO'
C
10.93 10.045 9.834 9,636 9.471 9.280 9 . IO1 8.823
0
-0.022
zoj
- -717 - ,820
-
-1.025
- I ,000
-0
- ..lo7 - ,410 ,514 - ,615 -
2.88
,208
9 9 9 9 9 9
,309 '414 ,515
,615 ,717
0 .IO0
465 484 484
,
141 I 58 173
496 502
188
507 9 483
,820
I22
200
TABLE IV E Arninoethanol a t various concentrations-half C
0.200
.I00 ,040
Exp. I1 a
,020 ,010
004 ,002
,180
Exp. I1 b with C. -?JaCI
,089 ,036 ,018
009 ,200 ,150 ,
Exp. V
I00
075 ,040 ,020 ,010
,004
neutralized (*+
P H
b'
9.467 9.497 9.504 9.486 9.486 9.424 9.407
-0,500
9.483 9.512 9.521 9,512 9.491
- ,500
-
50 I
- ,502 - ,503
-
,507 ,504
-
,504
-
'504 ,504 ,504 .504
- ,500
-
,500
,500 ,501
,501
- ,502 - ,504 - ,510
= PK
-0.5)
'
(9.467) 9,497 9.506 9,490 9.492 (9.437) (9.440)
47 0,316 ,223 ,141 100
,071
045 ,032
9.489 9.518 9.527 9.518 9.497
,505 ,415 ,333 ,305 ,288
(9.500) 9.489 9 491 9 509 9,509 9.511 9.498 9.483
,316 ,274 ,223
194 ,141 , IO0
.07 I ,045
1'39
EFFECT O F SALTS OX WEAK ELECTROLTTES
TABLE V .1 Glycine Ealt
c
Pn
(0.0100 molar)
.,Acid titration -
b'
b- n
PK,'
\!J
C
35; 35i 350
- I ,000 - I ,000 - I ,000
2 2
357
-1
000
- 510 - .
2
S o salt D -Sac1 C -Sac1
2 2
47s 469 477
-
2
484
2
550
2
546
2
541
-\IgCL
D -1IgC1, s o snit D -1aCl C -YaCl
c
-1lgCln
D -1IgC12 S o salt D -Sac1 C -Sac1
c
-11IgC12
D -1lgCln S o salt
D -Sac1 C -Sac1
c.- MgCln D. -1lgClz
2 2 2
2 jj0
2 553
36;
IO0
2
3il
218
500
2 360
292
420 429
2
288
43i
2
338 350 359
,429 420
2
352
089 213
2
344
288
2 324
286
-
- io0 - io0 - 700 - 700 - 700
- .3i3
-
-
-
211
2
350
084
2 2
337 326
286
343 ,343
2
,349 ,343
2 2
,333
2
(2
- ,600 - ,600
2 2
729 714
- jO0 - j00 - 500 - . j00 - 500
- ,285 - ,280 - ,302
- ,400 - ,400 - ,400 - 400
- -238 - ,241 - ,249 - 245 - ,241
2
c.-11IIgc12
2
854
D. -1lgCIz
2
853
2
843 856 861
2 2
3 007 32 996 3 012 3 022
c.-MgCI2
3 198
D. -1lgCln
3 186
S o salt
3 178
D -Sac1 C. - S a c 1
3 I96
3
210
7.1
-
,400
-
,300
-
300
-
3043 ,300
- ,300
-
-
200 200
200 200 ,200 0
- ,294
- 290
-
213
333
-
C. - S a c 1
218
2
628 640 640
,600
2
o 292
,380 ,391 380 373
2 2 2
726 736 739
s o salt
2
- ,600 - ,600
2
D. -lIgCl? S o salt D. - S a c 1 C. -XaC1
357 374
643
2
c.- MgCln
2
jI0
643
salt
S o salt D. - S a c 1 C. - S a c 1
2
-
2 2
D. - NaCl
$0
- 800 - do0 - ,800 - ,800
-0 j00
,188
188 ,198 ,191 ,191
- ,128 - I28 - I 32 - ,129 - ,129
211
360
285
z 380
208
357
077
357 346
208 28j
329 303) z 361
283 206
2
355
2
349
206 283
2
348 353 363 366 362
2
2 2 2 2
071
281 204
063 204
281
37' 365 ( 2 389) 2 386 (2.396)
,279
2 . ,365
,277 I99
2
2
353 2.369 2.366 2.380 2
201
,055 ,201
279
,045
. I99 ,277
1140
HENRY S. SIMMS
TABLE VB Glycine Salt
c.-MgClz
PH
(0.0100 molar)
Alkaline titration
b-a -
b'
PKz'
dF
9 9 9 9 9
276 435 694 584 547
0.277 "99
299 298 297 297 297
9 9 9 9 9
301
,279
393 701 615 584
,201
398 398 396 396 396
9 9 9 9
9 593
,281
497 497 494 494 494
9 2.53 9 323 9 663 9 593 9 588
,283
9 079 9 166 9 671 9 612 9 581
,285
9 671 9 585 9 568
,084
089
C
0.200
D. -XaC1 C. -NaCl
8 671 8 830 9 087 8 979 8 942
,200 ,200 ,200 ,200
0.199 I99 198 I99 199
C. -MgClz D. -MgC12 No ealt D.-PiaC1 C. -NaCl
8 930 9 020 9 326 9 240 9 209
,300 ,300 ,300 ,300 ,300
C. -MgC12 D. -MgC12 No salt D. -NaCl C. - NaCl
9 9 9 9 9
065 I28 494 427 409
,400 ,400
9 9 9 9 9
248 316 653 583 578
,530
9 9 9 9 9
240 337
D. -MpClz No salt
c.-MgClz
D. -MgC12 No salt D. - S a c 1 C. -NaCl
C. -MgC12
,400 400 ,400 ,500 500
,
goo
,500
,600
245
308 678 611
832
,600
773 742
,600
,600
597 597 591 591 591
N o salt D. -NaCl C. -NaCl
I O 011
,700 ,700 700
686 687 687
No salt D. - S a C l C. -NaC1
I O 178 I O I02 10 077
800
773 78 1 78 I
9 631 9 550 9 525
S o salt D. -NaCl C.-SaCl
IO
622 525 513
1.000 I ,000 1.030
94 I 949 948
9 416 9 355 9 252
D. -MgClz S o salt D. - S & l C. -?JaCl
9 927 9 910
IO 10
,600
800 800
04.5 199 ,277
,055 ,201 '
279
,281 ,204 ,063 ,204
206 ,071
,206 ,283 208
,077 ,208 ,285 ,211
286 ,213
,289 ,
IO0
,218 292
vu. summary Titration data of 0.01molar solutions of various organic acids, bases and ampholytes were obtained, in the absence of salt, in the presence of two concentrations of XaC1, and in the presence of two concentrations of MgC12. (K2S04and MgSO, were also used with malonic acid.) From each observawas calculated and plotted against the tion a dissociation index value (PK') square root of the ionic strength ( d i ) .The slopes of these curves show the extent of agreement of the activity of the ions with the activities predicted by the Debye-Huckel equation. The true dissociation indices and the slopes are given in Table I. Singly charged anions from monovalent or divalent acids obey the DebyeHuckel equation in the presence of either KaC1 or MgC12, or the salt of the weak acid, but not with K 8 0 1 or MgSO1.
EFFECT OF SALTS ON WEAR ELECTROLYTES
I141
Polyvalent anions in the presence of NaC1 obey a modified form of this equation which includes a correction for the distance between the charges (Equations 8 and 9). Polyvalent anions behave anomalously with MgC12. This effect is much greater for oxalic, malonic, and citric acids than for succinic, azelaic and sebacic acids. Sulfate ions produce an effect on both mono- and dianions which is opposite to the effect of magnesium ions. Cations from amines or amino acids do not obey the Debye-Huckel equation but show a deviation with both NaCl and MgCls, which varies with the substance. P K i ’ of glycine and P K ~of ‘ aspartic acid are anomalous in the presence of hlgCl2 (but normal with NaCl). Isoelectric points drop with increase in ionic strength. (The term “index” signifies the negative logarithm of any constant or variable.)
