n Y JVILIJS
w.F L O Y D
Introductory The nsual stoichioiiirtric cqnntion forthe inversion of sucrose indicates that the hydrolysis is n lmioleculsr rc:icticin ))etwren sucrose and water, thus,
+
( ' i y l T ~ ~ O i 1 EI.0 ?('c€I12Oti Studies of the col1ig:ilive propclrt ic? of :Iqncous sucrose solutions1however, show that the sucrose ex :IS :i Iiydr:~it,in solution. The most probable mechanism, therefore, is t the tii,+solvtd -1icrose first fornix a hydrate with the water, and that it is this hytllaie Lvliicli is cut:ilytic:illy hydrolyzed by the hydrogen ion. Thr equation for tlict 1iydr:ition of the sucrose may Le written, ('liH22Oli
-2
XI€?() ---i ( ' ~ ~ 1 I z ? ( J ~ l . S I € z O ,
(1)
where x is a variable number, usunlly of thc order of 6 k 2 . The sucrose hydrate may then conihine n.ith the hydrogen ion t o form :in intcrmediste complex which rapidly decomposes to produce th!. products of the inversion, according to the equation,
.sH*C)
c~12€122011
-+ I%' + (x-
+ ((12H22011
I)H?C)
.SH*O 1-1-
+ I$-.
'
+
2('6€I12O0 (2)
Or, the sucrose hydrate may be hydrolyzed by the hydrogen ion directly into the reaction products, :ts represented by the equation,
+ fI+
C11zH220ii.~H20
+ ( x - I ) H ~ O + H-.
-+~ ( ' t i l J l ? O e
(2')
Since the inversion velocity is iricrc d liy increasing the proportion either of the sucrose or of the hgdrogrn ion, but is not increased by increasing the proportion of the water, it fo1loTvs that vither reaction ( 2 ) or reaction ( 2 ' ) ) rnther than reaction ( I ) , m u a t be thr mrmured rwction. That is, the hydration of the sucrose is ininirnsur:ibl~ r:ipitl in comparison with the catalytic decomposition of the siicrosc 1iytir:ite into glucose and fructose. If this is true, the inversion of s u c ~ s cproceeds cwntially 2s a unimoleeular reaction. There has been much diu:igrtem!,nt :iIiionjL' the investigators! as t o the unimolecularity of the inversion process. The results obtained ljy the in'Bousfield: Trans. Fnrnday Soc., 13, 141 U y 1 7 ; FraLer :ind Myrick: J. . h i . Chern. SOC.,38, 1907 ( 1 ~ 1 6 1Scatchard: ; 43, 2406 ~ I ~ z I ) . a . Armstrong and Coldwell: Proc. Roy. Soc., 74, ~ y (1904); j Cnldwell: 78.-1, 272 (1906); Colin and Chaudun: .J. Chim. phys., 2 4 , 507 I 1 ~ 2 7 1 . b. S l e y r : Z. physik. Chem., 62, 59 !1g08!; \Vorley: Proc. Roy. Soc., 87.1, j ~ [51 y 1 2 ) ; Fales and RIorrell: J. Am. Chem. Yoc., 44, zo;r 1922 . e . Hudson: J. Am. Chem. Soc., 30, 1160 [,Igo8,; Ros:,noff, Clark, and Sihley: 3 3 , 1911 ( 1 9 1 1 ) ; Jonesand 1.ewis: .J. Chem. Soc., 117, 1 1 2 0 ~ y z o ) .
EFFECT OF STROSG ELECTROLYTES ON INVERSION OF SUCROSE
2969
genious method of Pennycuick3 show that there is a slight but st,eady increase in the unimolecular velocity constant as the inversion proceeds. This increase, however, is of the same order of magnitude as the common experimental error and so is usually overshadowed by the latter. Hence, for practical purposes the velocity coefficients determined by the ordinary polarimetric method may be considered constant throughout the entire course of the inversion. It has long been known that certain neutral salts increase the rate of inversion of sucrose by acids. Considerable experimental work has been done on this neutral salt effect, and an extensive, widely varied theoretical literature has been produced in the attempt to explain it. Several of these better known theories are summarized in a recent article by B0we.l Of particular interest in connection with modern theories of reaction kinetics in general are the efforts on the part of some to correlate the velocity of sucrose inversion with the thermodynamic concept of the activities of the reactants. As defined by Lewis,; the activity of a constituent of a system is the true measure of its thermodynamic concentration. Hence, the velocity of a given reaction is proportional to the product of the activities of the reactants, each raised to a power equal to the coefficient of the reactant in the equation which represents the given reaction. IV. C. M. Lewis and his associates6 have used the hydrogen electrode to determine the activity of the hydrogen ion in acid solutions containing sucrose. The electromotive force measurements of Taylor and Bornford' show that the activity of the hydrogen ion in such solutions increases during the inversion process. ScatchardRhas shown that the hydrogen electrode does not give reliable values of the hydrogen ion activity in sucrose solutions. The hydrogen gas hydrogenates the sucrose, producing an inconstant hydrogen pressure, and the sucrose produces an unknown change in the liquid junction potential of the cell. Bronstedg represents the inversion of sucrose by acids as occurring in two steps. The first step consists of the formation of an intermediate complex from a sucrose molecule and a hydrogen ion,
CizHzzOii
+ H+
+
CizHzzOii .H+.
(3)
This is followed by the hydrolysis of the intermediate complex to form glucose and fructose, with the re-liberation of the hydrogen ion, CizHzzOii.H+
+ HzO
+
+
C G H ~ ~ O Ci"2O6 B
+ H-.
(1)
Pennycuick: J. Am. Chem. SOC., 48, 6 (1926). Bowe: J. Phys. Chem. 31, 291 (19271. Lewis: Proc. Am. Acad., 37,49 (1901); J. Am. Chem. Soc., 35, 16 (1913); 45, 16 (1923). Cf. also Lewis and Randall: 43, 11x2 (1921). Jonesand Lewis: J. Chem. SOC.,117, 1 1 2 0 (1920); Rforan and Lewis: 121, 1613 (1922); Corran and Lewis: J. .4m. Chem. Soc., 44, 1673 (1922). Taylor and Bomford: J. Chem. Soc., 125, 2016 11924). Scatchard: J. Am. Chem. Soc., 48, 2026 (1926). Bronsted: Z. physik. Chem., 102, 169 (1922).
2970
WILLIS W. FLOTD
He assumes that reaction (4) is exceedingly rapid as compared with reaction (3). Accordingly, he represents the velocity of inversion of sucrose by the expression,
Here c, f , and a indicate the concentrations, the activity coefficients, and the activities of the components, respectively. The subscripts (s), (h), and (x) refer respectively to the sucrose, the hydrogen ion, and the intermediate fugitive complex. The present investigation was undertaken with the view of studying the influence of strong electrolytes upon the rate of inversion of sucrose by acids. From the results obtained we have hoped to gain further information concerning the inversion process and to test the applicability of the modern theories of solution. To this end we have employed four typical salts of different valence types. To emphasize the specific influence of the salts upon the velocity of inversion we have arbitrarily chosen to employ constant concentrations of sucrose and of acid, and to vary only the concentration of the salt. Materials and Apparatus
Sucrose. The sucrose used in this research was the purest crystalline rock candy available. It was first pulverized and preserved in a desiccator over anhydrous calcium chloride. Duplicate determinations showed an ash content of less than 0.001percent. Hydrochloric A c i d . Constant boiling hydrochloric acidla was taken as the source of the standard acid. From this a 0.j X acid was prepared by dilution. Salts. The salts used in preparing the ionic solvents were of the “Analyzed” quality. They were further purified by at least two crystallizations from pure distilled water. After heating to constant weight, the solutions of sodium chloride and potassium sulphate were made up by direct weighing. The barium chloride was allowed to stand over anhydrous calcium chloride until analysis showed it to be the pure dihydrate, BaC12.2H20. It was weighed directly as such. .A concentrated “mother” solution of magnesium sulphate was prepared and then standardized on a weight molal basis by precipitation as barium sulphate. The various concentrations of this salt were made by the proper dilution of the mother solution. A p p a r a t u s . The polarimeter was a high precision, triplefield Schmidt and Haensch instrument, readable by two verniers to 0.01’. The 40 cm. inversion tubes were encased in metal jackets through which water was circulated under pressure from a constant-temperature water-bath. This bath was electrically heated and electrically controlled to within i 0.02’ of a temperature such that the water passing through the inversion tube was exactly 25’ 0.02, or 30’ 0 . 0 2 , depending on the temperature chosen. The temperature of the water bath was read on a standard thermometer, graduated in ‘“Foulk and Holiinsglvorth: J. Am. Chem. SOC.,46, 1 2 2 0 (1923).
*
*
EFFECT O F STRONG ELECTROLYTES ON INVERSION O F SCCROSE
2 9j I
and readable to rt 0.01'. A short stem thermometer graduated in 0.2' was immersed in the inversion solution. An intense sodium light was used for illumination. All flasks, burettes, and pipettes were accurately calibrated by weight at 25' and at 30'. Each polarimetric reading recorded is the mean of at least two independent readings, and each is accurate to f 0.01'. 0.1'
Experimental Procedure For each experiment exactly 1.7109 grams of sucrose (air weight) and the desired quantity of salt, weighed to one-tenth of a milligram, were transferred to a 50 cc. calibrated flask. The sucrose and salt were then dissolved in a minimum amount of distilled water, exactly I O cc. of the 0.5 K hydrochloric acid were added, and the whole was made up to volume at the temperature of the experiment. The solution was thoroughly shaken, quickly weighed to the nearest centigram, and then transferred as quickly as possible to the inversion tube. Care was taken to have the temperature of the component solutions at the temperature of the bath before mixing. The instant of adding the acid to the sucrose solution was taken as zero time. Polarimetric readings were taken at definite time intervals. From six to ten readings were taken in the early period of the inversion and an equal number near completion. Each reading recorded is the mean of two or more readings taken about 30 seconds apart. For every solution duplicate series of measurements were made. When these did not agree other series were made until satisfactory agreement was obtained.
Calculation of the Coe5cients To calculate the values of the inversion constants we have made use of an algebraic modification of a method first used by Guggenheim." His relation is, kti 2.3026 log (vi' - vi) = A.
+
On transposing this reduces to, 2.3026 log (vi' - vi) = -kti
+ A.
Here vi is the ith reading of the series taken in the early period of the inversion, vi' is the ith reading of the series taken near completion, and A is a constant. The reading v, is taken at time ti measured from the instant of starting the T measured from the instant of starting inversion; vi' is taken a t time t i the inversion. The constant time interval T is at least, twice the half period of the inversion. Since in sucrose inversion the polarimetric reading decreases with the time, vi > vi', hence the signs of vi and vi' must be interchanged in the relation derived by Guggenheim to give a usable expression. The relation then obtained is
+
"Guggenheim: Phil. Mag., ( 7 ) 2, 538 (1926).
WILLIS W. FLOYD
2972
2.3026 log
vi-^,')
=
-kti
+ A.
(6)
The mean value of the velocity coefficient k is found by use of this relation without determination of the initial and final inversion readings. An example will serve to illustrate the method employed. For the solution with respect t o sucrose, 0.1molar with respect to hydrochloric acid, and 2 molar with respect to sodium chloride a t 2 j” the following d a t a were obtained: 0.1 molar
ti
t,
VI
= 60
= I20
v2 =
6.81
t 3
= 180
= j.83
4.94
= 4.14
min.
v1
= i.92‘
ta
= 240
va v4
tj
=
300
v5
t6 = 360 ti = 4 2 0 ta = 450
ve
=
v;
= 2.73
=
- 960
+ 960 = min. + 960 = 1080 t a + 960 = 1140 t , + 960 = t 5 + 960 = 1260 t a + 960 = 1320 ti + 960 = 1280 tg + 960 = 1410 tl tz
tl t*
3.41
vy = 2.44
1020
1200
VI’
VI’ - - 1.0; V Z ’ = - 1.26 pf -1.44 vt’
=
v5’
= - 1,;j
\,,it
=
v; = vy’ =
-1.60
-1.90 -2.03 -2.08
Substituting these values in the relations,
(vi - Vi’) = -ktl (v? - VZ’) = - k t ? log (v3 - v3’j = - k t 3
2.3026 log 2.3026 log 2.3026
+ -1,
+ -1, + A, etc.,
we obtain the following equations: 2.3026
log 8.97 =
+ .I, + A, -18ok + A, - - z ~ o l i + -1)
-
60k
2.3026 log 8 . o j = -12ok 2.3026 log 7.27 = 2.3026 log 6 . j = ~
2.3026 log 5.89 = - 3 0 0 k 2.3026 log 5.31 = -360k 2.3026 log 4 , j 6 = - q o k 2
3026 log 3.53 = -4:ok
- A,
+ -1, + A, + A.
ii) (ii) (iii) (iy) (v) (vi) (vii) (viii)
The velocity coefficient, k, may be evaluated by eliminating the constant
X from any two of these equations. I n order to Tveight each reading equnlly we eliminate A from equations (i) and (iii), (ij and (v), (i) and (rii), (iii) and (v), [iii) and (vii), (vj and (vii), (ii) and (iv), (ii) and (vi), (ii) and (viii), (iv) and (vi), (iv) and (viii), and (vi) and (viii), respectively. Thus, we obtain t d v e independent values of k. The mean of these twelve values is the value taken for k for this deterniination. The subtractions are indicated beloiv:
EFFECT O F STROSG ELECTROLYTES ON INVERSIOS' OF SCCROSE
(i) - (iii) gives, Izok
2(j j J
(log 8.97 - log 7 . 2 7 ) ; 0.OoIijII.
= 2.3026
k Sim i1a r 1y ,
-
= 0.001ij2j,
(iv) - (vi) gives, (iv) - (viii) gives, (vi) - (viii) givts,
k k k k k k k k k k k
Average :
k
= o.ooIij44.
ii)
(v) gives,
(i) - (vii) gives, (iii) - (v) gives, (iii) - (vii) gives, (v) - (vii) gives, (ii) - (iv) gives, (ii) - (vi) gives, (ii) - (viii) gives,
= 0.031j601, = 0.001; j l o , = 0.0017646, = 0.0017T~2, = O.CCI;~I~, = o.cori++c, =
0.0017498,
= 0.0017363, = c.oc1i486, = c.cc1i6jo.
All of the values found for the velocity coefficient, k , are average values obtained in this manner.
Experimental Results The experimental results of this investigation are given in Tables I-V. Table I shows the velocity coefficients of inversion of sucrose found at z j o for the ionic solvents listed. Tables I1 to V list the velocity coefficients of inversion of sucrose in aqueous solutions, respectively, of sodium chloride, barium chloride, potassium sulphate, and magnesium sulphate at 30'. Here m is the molality, S the normality, and IJ the total ionic ctrength as defined by Lewis and Randall.I2
TABLE I The Yelocity ('onstants of Inversion of Sucrose in .Icid Solutions at 2 j o
Salt-free acid I S SaCl 2 S SaCl 0 . 9 8 j 3 N BaCL 1.9705 S BaCL I 1; hlgSO4 2 N lIgS0, l2
0.1
Molar Hydrochloric
79.65
79.05
79.35
115.94
IIj.10
IIj.j 2
175.89
Iij.44 108. j o
175.67
IjO.9j 29.20
150.93 28.91
26.17
25.94
107. 78
1jo.88 28 63 2j.72
Lewis and Randall: "Thermodynamics," 6th Impr., 3;3 (1923).
108.14
29i4
WILLIS W. FLOYD T.4BLE
11
The Velocity Constants of Inversion of Sucrose in 0.1Nolar Hydrochloric Acid Solutions containing Sodium Chloride at 30' HCI
rn
sac1
XaCl
s
k.10'
rn
0.1026 0.1028
0
0
o r
o
0.I O 4 8
I
I 0480
0,1069 0.109j
2
2
3
0.1123
4
0.1156
5
3 2852 4 4924 5 ii90
1028
1386
il
(2,
0.1026 0.20j6 I . I j28 2.24jj 3.3947
4.6047 5 8946 '
Mean
163.03 169.62 236.24
163 2 1 j 168 840 236 9 2 0
34i.2 0 523.69 79:. 48 11g1.98
348 275 523 joo 802.04; I 148.31 j
TABLE I11 The Velocity Constants of Inversion of Sucrose in 0 .I Molar Hydrochloric Acid Solutions containing Barium Chloride at 30' HCI m
P
3.1026
o 1026 0.866,I . 6422
3.1033
0.1041 I049 0 . I058 0.1068 0.I081 0.
2.4305 3,2330 4 0524 4 9003
(1)
163.40 191.09 225.60 267.IO
k.105 (2)
163.03 189.09 225.09
309.98 367,12
265.57 309.04 368.38
435.41
43i . 6 2
TABLE IV The Velocity Constants of Inversion of Sucrose in 0.1Molar Hydrochloric Acid Solutions containing Potassium Sulphate at 30' HCI m
K290r N
K,SO, rn
k.105
P
0.1026
o
0
0.1026
0.1028
0.1
o.ojr4
o.zjjo
0.1032
0.3
0.1037
0.5
0.1j48 0.2592 0.3616
0 . j676 0.8814 1.1980 1.5199
0.104~ 0.1048 0.9 0 .j
o.4;17
(1)
iZ!
163.40 110.gjo 62.962
163.03 109.860 62.271
48.900
4j.j21
40.390
38.896 36.175
35.683
Mean
163.215 110.415 62.617 48.211 39.643 35.929
EFFECT O F STRONG ELECTROLYTES O S INVERSION O F SUCROSE
297j
TABLE T The Velocity Constants of Inversion of Sucrose in 0 . I Xolar Hydrochloric Acid Solutions containing Magnesium Sulphate at 30' HCI m
hlgS0r S
JlgSO;
m
P
163.03 115.380
163.215 11j.47j
79.329 67.574 56.023 51.957
79.326 67.212 j6.810
I ,0358
0.1026 0.3083 0.7196 I , I313 2,1651 3.2017 4.2468
j1.007
5 0 . j86
1.2999 1.6;36 2.1088
5.3036 6.7990 8,5407
50.612 51.709 55.097
j o . 485
0.1026
0
0
0.IOZj
0 .I
0.0514
0.1028 0.1029 0.1031 0.I033 0.1036
0.3
0 ,I
0.j
0.2571
I .u
0.5I55
1.5
0.
2.0
0.I040
2 . 5
0.1046
3.2
0.10;;
4.0
j42
7746
52.084
jz ,064
54.975
Discussion of the Experimental Results The data recorded in Tables I1 to T are shown graphically in Fig. I . Here the velocity coefficients of inversion at 30' are plotted against the total ionic strength of the solution. Since the molal concentration of the hydrochloric acid remains very nearly constant, the ionic strength is essentially a measure of the Concentration of the added salt. It is to be noted that the chlorides increase the velocity of inversion at a rate which increases rapidly with the salt concentration. In solutions of equal ionic strength the uniunivalent chloride has a greater accelerating effect than biunivalent chloride. This same order holds if equivalent normal concentrations are employed. The reverse order holds, however, if molar or molal concentrations are employed. These differences indicate that the cation of the salt is not entirely without effect upon the inversion velocity. Harned and HawkinsI3 have studied the acid hydrolysis of certain esters in solutioins containing alkali chlorides and nitrates. They find that the velocity coefEcient of hydrolysis increases with the salt concentration, passes through a maximum, and then decreases with further increase in the salt concentration. )Ye find in the present work no indication of such a maximum value either for sodium chloride or for barium chloride. On the contrary, the rate of hydrolysis increases a t a rate which increases more and more rapidly with increasing ionic strength. Especially is this true for the sodium chloride solutions. The sulphates markedly decrease the inversion velocity. Potassium sulphate has a greater retarding effect than the bibivalent magnesium sulphate, regardless of the basis of concentration taken. The values of the velocity l 3 Harned
and Hawkins: J. Am. Chem. SOC.. 50, 85 (1928).
2976
WILLIS W. FLOYD
G
FIG.I
coefficient for the magnesium sulphate solutions pass through a slight minimum a t an ionic strength of about 4.5. Those for the potassium sulphate solutions decrease still more rapidy with increase in p , to practical saturation. Here, as in the case of the chlorides, the cation evidently exerts some influence.
The Neutral Salt Effects The data showing the influence of the neutral salts upon the rate of the inversion are collected in Tables TI t o IX. Here 31 signifies the molar, S the equivalent concentration of the salt, k the inversion coefficient in the ealt solution, and ko the coefficient in salt-free acid. The salt effect is given as the percentage increase or decrease in ko. The salt effects, measured as percentage change in ko, are plotted against the equivalent concentrations of the added salts. These are shown in Fig. 2 . The two chlorides produce positive, the two sulphates produce negative salt effects on the inversion of sucrose. The effects are very pronounced, especially
EFFECT O F STRONG ELECTROLYTES O N INVERSIOS OF SUCROSE
2977
TABLE VI The Effect of Sodium Chloride on the Irelocity of Inversion of Sucrose by Hydrochloric Acid at 30' NaCl Sac1 k loo(-k - I ) r = I l o g kM s K ko M k, 0
0
I
0 .I
0.I
1.03lj 1.4j16 2.1338 3.20j.t 4.9140 7.0356
1.0
1.0
2 . 0
2 . 0
3.0
3.0
4.0
4.0
5.0
j.0
__
0
3,4j% 4j.16 113.38 2 2 0 . 74 391.40 603.j 6
0 .I473
0.1619 0,1646 0.1687 0.1729 0.1695
TABLE VI1 The Effect of Barium Chloride on the Velocity of Inversion of Sucrose by Hydrochloric Acid at 30' BaClz h.1
BaC12 N
k
ka
0
0
I
loo( kko
- I)
0,2463
0,4926
I . 1647
0.9853 I.4i79 2.4632
3807 1.6318 I .8963 2.2532
125.32
1.4779
2.9558
2.6745
I67,45
1.9705
k,
?VI
__
0
0.4927 0.i390 0.9853 1.2316
1
r = L ~ o kg
16.477~ 38.07 63,18 89.63
0.2689 0,2844
0.2878 0.2821 0.2865 0.2891
TABLE VI11 The Effect of Potassium Sulphate on the Velocity of Inversion of Sucrose by Hydrochloric Acid at 30' KsSOa M
K2S04 N
k
k,
0
0
I
0.05
0.I
0.I 5
0.35
0.3 0.5 0.7
0.6j6j 0.3836 0.2954 0.2429
0.45
0.9
0.2201
0.25
Ioo(k-
k,
-
I)
0
r
~
rVl
~
k- o k,
__
-32.35'3 -61.64 - 70.46
-3.3946 - 2 .I 184
-75.71 -77.99
-1,7559 - I.4608
- 2 . 7 741
g
2978
WILLIS W. FLOYD
FIG.2
TABLE 1); The Effect of hlagnesium Sulphate on the 1-elocity of Inversion of Sucrose by Hydrochloric Acid at 30'
0
J
0.05
0.iOij
0.Ij
0.4860 0 . 4 1I8
0 . 2 5
0.50
0.i5 1.00
1.25 I . 60 2
.oo
0.3483 0.3'9' 0.3112 0.3093 0.3190 0.3368
0
- 2 9 . 2 5 5, -jI .40
-3
0054
-2
-j8.82
-1
0891 5412 9161 6614 5070
-6j.17
-0
-68.09 -68.88 -69.07 -68.10 -66.32
-0
-0 -0
-0 -0
4077 3101 2363
EFFECT O F STRONG ELECTROLYTES ON INVERSION O F SUCROSE
2979
those of sodium chloride and of potassium sulphate. The inversion coefficient for the z normal sodium chloride solution, for example, is more than double that for the salt-free solution, and for the 5 normal solution the increase is over 600% of the constant for the salt-free acid. The negative effect of potassium sulphate is even more striking. The addition of this salt in an amount sufficient to make a 0.2 normal salt solution decreases ko by j o y 0 of its value, and the inversion coefficient for the 0.7 normal solution is only one-fourth that for the solution containing no salt. Schmid and O1senl*have proposed the empirical relation,
as describing generally the influence of neutral salts on the velocity of hydrolytic reactions. Here k is the velocity coefficient measured for the salt solution, ko is the coefficient in the absence of the salt, r a constant specific for each salt, and bl the molar concentration of the salt. A test of the applicability of this relation to sucrose inversion may be made by writing the equation in the logarithmic form, ~k r = -log--, M ko and then determining the actual constancy of r by substitution of the measured values of M, k, and ko. The values of r thus determined are given in column 5 of Tables VI to IX. Judging by the constancy of r, we see that the SchmidOlsen equation describes reasonably well the positive salt effects produced in the inversion of sucrose by the chlorides in concentrations above 0 . j molar. This conclusion agrees with the results obtained by Kautz and Robinsonlj in their study of the influence of the alkali and alkaline earth chlorides on the rate of hydrolysis of sucrose by hydrochloric acid. The equation of Schmid and Olsen is totally inapplicable, however, in describing the negative salt effects produced by the sulphates. When the salt effects are negative, the values of r, of course, are also negative, and are not constant for any range of salt concentration. Bronsted and his co-workersL6distinguish between two types of neutral salt effect,s. The one, the primary salt effect, is produced when the added salt changes the activity coefficients of any of the reactants of the system as given by equation ( 5 ) ; the other, the secondary salt effect, consists of a change in the actual concentrations of any or all of the reactants, due to the addition of the salt. Bronsted" characterizes the primary salt effect in hydrogen ion catalysis as being at all dilutions an exponential function of the salt concentration. This postulate may be deduced, in the case of sucrose inversion, by evaluatSchmid and Olsen: Z. physik. Chem., 124, 97 (1926). Kautz and Robinson: J. Am. Chem. SOC., 50, 1022 (1928). '6Bronsted: 2. physik. Chem., 102, 169 (1922);115, 337, (192.5);Bronsted and Pedersen: 108, 185 ( I 241, Bronsted and Teeter: J. Phys. Chem., 28, 579 ( 1 9 2 4 ) ;Bronsted and King: J. Am. C4em.'Soc., 47, 2523 (1925). 1' Bronsted: Trans. FaradaySoc., 24,-630 (1928). l4
WILLIS W. FLOYD
2980
fsfh ing the "kinetic activity factor," of equation
(j),
from the expression,'Y
fx
- In f
=
+O.jz'v'/L
- Bp.
(7)
Here f is the activity coefficient and I , the valence of the molecule, while p is the ionic strength and B a characteristic constant of the solution. Substitution in equation ( j j of the value of f obtained from equation ( 7 ) gives,
v
=
kC,Chefl!Bs+Bh-Bx)
(8)
where R,, R h , and B, are comtants of the solution due t o the influence of the sucrose, the hydrogen ion, and the critical complex, respectively. Obviously, equation (8) requires that the primary salt effect in sucrose inversion, as measured by the velocity of the reaction, shall vary exponentially with the salt concentration. Furthermore, since for very small values of j i we may write, ,r!Bs +I
