The HYDROLYSIS a SALT DERIVED from a WEAK ACID and a WEAK BASE* S. JAMES O'BRIEN
AND
CHRISTOPHER L. KENNY
The Creighton University, Omaha, Nebraska
This paper attempts to answer two questions concerning zhe hydrolysis of a salt derived from a weak acid and a week base which are greatly emphasized by a treatment of salt hydrolysis i n t e r n of the modern theory of acids and bases. The questions are: (1) To what are the values cited i n the literaturefor the degree of hydrolysis of salts of this kind referred; and (2) should not the degree of hydrolysis be stated separately for each ion? It is shown
that the degree of hydrolysis need not be determined se@rately for each ion except for very low salt concentrations; that it is possible to determine the degree of hydrolysis for the ions individually by methods employing measurements of hydronium-ion activities or of distribution ratios. The available data in the literature for the hydrolysis of salts derived from weak acids and bases at room temperatures i s compiled.
T
and hydroxyl ions produced in the two above reactions according to the equation,
WO questions concerning the hydrolysis of a salt derived from a weak acid and a weak base, not explicitly answered in textbooks on physical chemistry, are: To what are the values in the literature for the degree of hydrolysis of salts of this kind referred? Should not the degree of hydrolysis be stated separately for each ion (I)? These questions are very much emphasized when hydrolysis is considered in terms of the Br@nstedconcept of acids and bases (2). This is due to the fact that when hydrolysis is treated from this point of view, the reaction is considered separately for each ion. Thus the hydrolysis of a uniunivalent salt derived from a weak base and a strong acid is represented by an equation of the type BH+
+ K O = HaO+ + B.
(1)
and the hydrolysis of a salt from a weak acid and a strong base is represented by the type equation, H90
+ A-
=
HA
+ OH-
(11)
When, then, a salt from an acid and a base both of which are weak is hydrolyzed, it might be expected that the reactions involved should be represented by both of these equations. Then, naturally, the questions which have been mentioned arise. However, the hydrolysis of a salt derived from two weak protolytes involves not only reactions of the type represented by equations (I) and (11), but also by a third reaction (3), namely, that between the hydronium
-
* Presented before the Divisions of Chemical Education and History of Chemistry at the fourteenth Midwest Regional Meeting of the A. C. S., Omaha. Nebraska, April 30, 1937.
HaOf
+ OH-
=
2H30
(111)
This reaction, incidentally, provides the explanation for the fact that salts derived from protolytes, both of which are weak, are much more hydrolyzed than salts derived from acids and bases, only one of which is weak. That is, the reactions represented by (I) and (11) proceed further to the right when they occur together, as in the case of salts derived from two weak protolytes, than when they occur separately, as in the case of salts derived from protolytes, only one of which is weak. This, of course, is due to the removal of the hydronium and hydroxylions produced when reactions (I) and (11) occur simultaneously. Now, it will also be seen that the sum of equations (I), (II), and (111) is BH++A-=HA+B.
(IV) . .
and it can be readily shown that the equilibrium constant for the reaction represented by (IV) is identical with the classical hydrolysis constant for a salt derived from a weak acid and a weak base, given by the eqnation, Kn = K, in which K, is the classical ion nroduct constant for water, a n d & and Ks are the classical dissociation Constants of the weak acid and weak This indicates that equation (IV) corresponds to that
which would be written for the hydrolysis of a salt of this kind in accordance with the Arrhenian theory of acids and bases. In fact, i t diEers from the classical equation only in the exclusion of a molecule of water from both sides of the equation. Therefore, when hydrolysis is considered from the point of view of the modem acid-base theory, it is to the reaction corresponding to equation (IV) that the values in the literature for the degree of hydrolysis of salts derived from two weak protolytes are referred. It is an interesting fact that the hydrolysis of a salt of this kind, in terms of the Br6nsted theory of acids and bases, is a reaction similar to thermal dissociation (4). In this respect the term, hydrolytic dissociation, common in the older literature, seems to be quite significant. That solutions of salts of this kind are in many cases not neutral, but are either acid or alkaline depending upon the relative strength of the acid and base from which the salt is derived, is a factor that may make i t seem desirable to state the degree of hydrolysis separately for each ion, since the acidity or the alkalinity of the solution is due to the unequal hydrolysis of the
Conc.
Tcmg. Sot1 Ammoniumacetnte Ammoniumaeetate Ammonium acetate Ammonium borate Ammooiumdiketotetrahydrothiazoiafe Ammonium phenolate Aniiinium acetate Anilinium seefate Anilinium acetate ~vridinivmaectate
'C. 20 20 20 25
range 0.05 -0.1 0.5 -1.0 1.0 0.005-0.02
Per cml. of ,¶ydroly$is 0.35 0.39 0.45 46.3
finMethod 7.07 7.15 7.08 6.87
A
B C
D
Rcfcrrnu (8) (8) (8) (9)
ions. However, i t may easily he shown that this difference in the extent of the hydrolysis of the ions of such salts is, for practical purposes, negligible, and that i t is unnecessary, therefore, to consider the degree of hydrolysis of each ion separately. When a solution of a salt of a weak acid and a weak base has come to equilibrium, electrical neutrality demands that the number of cations and anions in the solution be equal, or (BH+)
+ ( H a O f )= ( A - ) + ( O H - )
(1)
where the quantities in parentheses represent concentrations. If the degree of hydrolysis of the cation is represented by x, that of the anion by y, and the original salt concentration by C, then a t equilibrium
When these values are substituted into equation (I), the equation, x = y +
is obtained.
( H 8 0 C )- (OH -)
C
(2)
Equation (2) indicates that the difference
betweeu cation hydrolysis and anion hydrolysis is negligible, except in cases where the pH of the resulting salt solution is very high, or very low, or where the concentration of the salt is low. For those salts for which data a t room temperatures are available (Tables 1and 2), the pH of the salt solutions lie betweeu 4 and 9, and for such salts the hydrolyses of the ions are very nearly equal except in very dilute solutions. With anilinium acetate, for example, solutions of which give a pH of 4.64, i t may be shown by the above equation that a t concentrations greater than 0.002 molar the hydrolysis of each of the ions is practically the same. For those salts like ammonium borate which are greatly hydrolyzed, and solutions of which give a pH of approximately 7, the diierence in the degree of hydrolysis of the two ions is negligible down to concentrations as low as 5 X lo-= molar. It is to be emphasized, then, that the factor which controls the acidity or alkalinity of solutions of salts derived from weak acids and bases may be considered negligible in the determination of the extent of hydrolysis. Since this is true, the statements in the literature concerning the degree of hydrolysis of salts of this kind will be satisfactory for most purposes. It should be remembered, however, that the term, salt-hydrolysis, is to be interpreted to mean ion-hydrolysis, which, of course, is nothing more than what is already being done in the case of salts derived from acids and bases only one of which is weak. Incideutally, the fact that the hydrolysis of the ions of asaltof this kind is essentially equal is one of considerable importance as may be realized when it is considered that some of the "best" values for the ion product constant of water in "International Critical Tables" (7) have been derived from measurements of the degree of hydrolysis of salts derived from weak acids and bases (9,10,14). THE SEPARATE DETERMINATION OF THE DEGREE OF HYDROLYSIS OF THE IONS
While, as has been shown, it is not necessary to state the degree of hydrolysis for each ion separately, i t is interesting to note that methods of determining the degree of hydrolysis of salts involving measurements of hydronium activity or of the distribution of a weak acid, or base, between two phases permit a determination for each ion individually. This may be illustrated for hydronium-activity measurements as follows. If the original salt concentration is represented by C, the degree of hydrolysis of the anion by y, and if activity coefficients are assumed to be equal to unity, then a t equilibrium ( A -) = C ( l - y ) ( H A ) = Cy
(3) (4)
where the symbols in parentheses represent activities. Also, the relationship,
in which K. is the thermodynamic dissociation constant of the weak acid, and the quantities in parentheses represent activities, is valid. Substitution of (3) and (4) into (5), and rearrangement gives
in the activities of the ions with concentration is disreTABLE 2 METALLIC ACBTATBS AT
(&O+) Y= 1-Y Ka
conc. Salt
Aluminum acctate
which demonstrates that the degree of hydrolysis of $ $ the anion may be determined from a measurement of Chmmie acetate acetate the hydronium-ion activity of the salt solution and the Cobalt cuprie value of the dissociation constant of the weak acid. +: :;2:;: The equation relating the extent of cation hydrolysis,,,CP to the hydronium-ion activity of the solution, namely,
2::;:;:
X K, -1 -x Ks(H80+)
in which xis the degree of cation hydrolysis, K6 the dissociation constant of the weak base and K.. the ionproduct constant of water, is derived in a similar manner. From this i t will also be obvious that the degree of hydrolysis determined from distribution measurements is that of but one ion, since only the distribution of the weak acid, or of the weak base, between the two phases is measured. It should be mentioned, however, that the accuracy of measurements by these two methods recorded in the literature is not sufficient to warrant the calculation of values for the degree of ion hydrolysis.
-
Manganous acetate Mangaoouo acetate Mercuric acetate Nickel acetate et",,;z;;:g ;;
m"ge
..
200 (8)
PETL c " ~ . of K~dralrris
9H
0.01 -0.2
45.0
4.82
0.25 -0.5 0.04 - 0 . 2
50.0 0.85 46.0
4.71 6.81 4.81
0.1 0.03 -0.25 0.5 0.02 0.25 -0.5 0.06 -0.25 0.05 -0.1 0.05 0.125-0.25 0.1 0.05 -0.25 0.025-0.5 0.125-0.5
0.15 6.81 32.0 75.0 1.73 1.2 1.34 0.29 0.34 20.0 0.36 0.25 1.16
7.56 5.88
~
~
~
Mdhod B A B
B B
B B
B 8.40 6.06 6.50 7.16 7.21 5.34 7.20 7.35 6.66
B
B
A
A B B B A B
garded. The pH values given in the fifth column are either averaged experimental values or values calculated from theper cent. of hydrolysis given in the fourth column by means of the equation (6), (H$o+) = -21 - 2 K.,
or
(L)"'
(HIO+) = K* K d a
The various methods employed in making the determinations are listed in the sixth column as follows: A, colorimetric pH measurements; B, measurements of the distribution of acetic acid between the salt solutions and ether; C, measurements of the partial pressure of ammonia from the salt solutions (distribution of ammonia between the salt solutions and a gas); D, measurements of the conductance of the salt solutions. Partington (6) gives a general outline of these methods, but for details the reader is referred to the original literature.
THE HYDROLYSIS OF SALTS DERIVED FROM WEAK ACIDS AND WEAK BASES AT ROOM TEMPERATURES
The data in these tables have been taken from the literature. The values for the per cent. of hydrolysis in the fourth column are averazes of several determinations made a t concentrations within the ranges indicated in the third column. It is assumed, therefore, that the degree of hydrolysis of salts of this kind is independent of the concentration of the salt. That is, changes in the extent of hydrolysis due to the changes
~~
~
LITERATURE CITED
(1) WUDW, E. A,, J. CDM. Eouc., 12, 15 (1935). ' (2) BR$NSTED, J. N., Chem. R&s, 5, 231-338 (1928); Z. phyrik. Chem., 169,52-74 (1934); HALL,N. F.,J. CHEM. EDUC., 782-93 (1930); ~ P A T ~ I M., C Kibid., , 12, . .. .. .7, ... . . lUlt-11(lWd5).
I' M' W' FURMAN' "Indieators," John Wiley and Sons, Inc., New York City, 1926, pp. 16-9. (4) C f . LOWRY,T. M., Trans. Far. Soc., 23, 514 (1927). , O., ibid., 17, 52&7 (1922). 5) C f . G m ~ mR. 6) TAYLOR, H. S., editor, PARTINGTON, J . R., "A treatise on physical chemistry," D. Van Nostrand Co., Inc., New York City, 2nd ed., 1931, Vol. I, pp. 6984. KoLTHopp'
*
(7) B J E R R ~ M N., . "International Critical Tables," McGrawHill Book Co., Inc., New York City, 1929, Vol. VI, p. 152. (8) L~PMAN, N., Z. enora. Cham., 107, 24144 (1919). - aUaem. . . (9) LUNDEN, H., 3. chirn. phys.. 5, 574-6138 (1907). (10) KANOLT,E. W., J. A m . Chem. Soc., 29, 1402-16 (1907). (11) Bum, K., Z. physik. C h . ,70, 6 6 8 7 (1910); Ber., 41, 692-5 (1908). (12) TIURD,H. T.9 J. C h m . Soc.8 979 490-5 (1910). (13) LUNDEN,H., J. chim. phys., 5, 155 (1907). S., Z. physik. Chem., 5, 1-22 (1890). (14) ARREEN~S,
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