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Primary salt effects with some paraffin-chain salt solutions
P R I M A R Y SALT EFFECTS W I T H S O M E P A R A F F I N - C H A I N SALT S O L U T I O N S 1, 2. 3 J. A. Erikson 4 and E. C. Lingafelter
The Department of Chemistry, University of Washington, Seattle, Washington Received August 24, 1954 ABSTRACT The primary salt effect of tetramethylammonium dodecanesulfonate, tetramethylammonium tetradecanesulfonate, and sodium decanesulfonate all at 25°C. and sodium dodecanesulfonate and tetramethylammonium tetradecanesulfonate at 40°C. on the displacement reaction between thiosulfate and bromoacetate ions has been studied. It was found that the measured rate constant from a paraffin-chain salt solution containing micelles had nearly the same value that it had in a solution containing an equivalent amount of simple, completely dissociated electrolyte. Since it is well established that a considerable number of gegenions are attached to the micelle, the above result indicates that the micelle has a rather large ionic effect. This effect compensates for the decrease in ionic effect brought about by the decrease in simple ion concentration due to the aggregation of the simple ions to form micelles. INTRODUCTION
This paper is concerned with the ionic catalysis of an ionic reaction, the thiosulfate-bromoacetate displacement reaction, by some paraffin-chain salts, the sodium and tetramethylammonium salts of decane-, dodecane-, and tetradecanesulfonates. A previous experiment (1) indicated that the rate constant at 40°C. was increased as reactants were replaced by sodium dodecanesulfonate. This was found to be true here, but to a much smaller magnitude. The previous results are in error mainly owing to the use of an inadequate calculation method. This will be discussed later. Paraffin-chain salts are ionic compounds which have paraffin chains incorporated in one or both ions. Because of the hydrophobic nature of the paraffin-chain part there exists a threshold concentration of paraffin-chain 1 Taken from a thesis submitted by J. A. Erikson to the University of Washington in partial fulfillment of the requirements for the Ph.D. degree, June, 1954. Presented before the Division of Physical and Inorganic Chemistry at the Northwest Regional American Chemical Society Meeting, Riehland, Washington, June, 1954. a A part of this work was carried out under United States Army Ordnance Corps Basic Research Contract No. DA-04-200-ORD-236. 4 Procter and Gamble research fellow 1950-1951. Present address: Department of Petroleum Refining, Colorado School of Mines, Golden, Colorado. 71
72
J.A.
ERIKSON AND E. C. LINGAFELTER
ions in aqueous solution, called the critical micelle concentration, above which the excess paraffin-chain ions associate to form aggregates of colloidal dimensions. The electrical charge of this aggregate is partially neutralized by an "atmosphere" of simple ions whose charge is of the opposite sign to the charge of the micelle. These simple ions are called gegenions and the resulting aggregate of paraffin-chain ions and gegenions is called a micelle. One of the many questions concerning micelles is the question concerning the effect of the micelle charge on the activity coefficients of simple ions. An analysis of the values of the activity coefficients of gegenion and micelle has been given by Hartley (2). Activity coefficients which may behave more rationally and therefore may be simpler to discuss are those of simple ions whose charges are of the same sign as the micelle charge. No method exists to determine such activity coefficients individually, but a value for a group of some of these coefficients may be determined by studying the primary salt effect. The rate constant of the thiosulfate-bromoacetate reaction, $203- + B r C H 2 C O O - --~ ( A c t i v a t e d C o m p l e x ) ~ --* B r - + S~O~CH2COO-
[1]
is related to the activity coefficients vr, vB and v* of the thiosulfate, bromoacetate, and activated complex ions, respectively, by 7rTB
koxp = k0 ~,.
[2]
Equation [2] has been tested many times (3) and shown to be correct. Where anomalies were found, these anomalies were shown to be due to side reactions between associated ions (4), orientation effects (5), or anomalies in the activity coefficients (6). If the activity coefficients in Eq. [2] depend upon the charge of the corresponding ions and on the common environment in a manner no more complicated than the Debye-Hfickel dependence, then a study of the variation of the experimental rate constant may yield an effective ionic strength for this environment. EXPERIMENTAL
Materials
Sodium dodecanesulfonate was prepared by refluxing a Halogen Chemical Co. dodecyl bromide, an analytical-grade sodium sulfite, and water for several days until the bromide layer disappeared. A weighed amount of the recrystallized material was diluted to the mark of a liter volumetric flask and the concentration computed, taking into account the water content of the material, which was determined by drying a sample in a vacuum oven. The tetramethylammonium alkanesulfonates were made from the corresponding sodium alkanesulfonates by first converting them to the silver alkanesulfonates and then reacting these with tetramethylammonium chloride. Solutions were made in the same manner as the sodium dodecane-
PRIMARY SALT EFFECTS W I T H PARAF F IN -C H A IN SALTS
73
sulfonate solutions and also by preparing a solution of the approximate concentration and then drying a sample of this solution to constant weight in a vacuum oven. Sodium decanesulfonate was already in stock and was recrystallized before being used. A reagent-grade potassium hydrogen phthalate was dried at 100°C. in a vacuum oven, without any previous purification. A weighed amount was diluted to volume in a volumetric flask. Carbonate free sodium hydroxide was prepared by filtering a 50 % solution into a liter of cooled, boiled, distilled water. The solution was protected as completely as possible from the air by two drying tubes filled with Ascarite, one on a piece of tubing through a rubber stopper on the bottle, and the other on the end of the pipet, which also went through the stopper of the bottle. The pipet was used to transfer the solution. An Eastman 10% solution of tetramethylammonium hydroxide was diluted to an approximate concentration with cooled, boiled, distilled water. The hydroxide solutions were standardized against the standard acid phthalate solutions, with a Beckman pH meter used to detect the end point. A reagent-grade bromoacetic acid was recrystallized three times from benzene, and then once from acetone. It was stored in a desiccator over phosphorus pentoxide. An approximate amount was quickly transferred to a weighed weighing bottle, and weighed. The bromoacetic acid was rinsed into a beaker and transferred to a liter volumetric flask. The solution was standardized against the hydroxide with the pH meter to detect the end point. The normality obtained from the initial weight of the bromoacetic acid was used as a check on the experimental technique and on the purity of the compound. The bromoacetic acid solution and the appropriate hydroxide solution were mixed to form the corresponding bromoacetate solution by adjusting the pH of the mixture to the standardization end point pH. A reagent-grade potassium iodate was dried at 150°C., weighed, and diluted to volume in a 2-liter volumetric flask. The solutions were approximately 0.005 N. An approximate amount of reagent-grade sodium thiosulfate was placed in a liter pyrex bottle, which had just been rinsed with boiling, distilled water. A liter of boiling, distilled water was added, and the bottle was stored to permit the solution to cool. The solution was standardized by the potassium iodate solution; the dead-stop technique was used to detect the end point. Tetramethylammonium thiosulfate was prepared from tetramethylammonium sulfate and barium thiosulfate. The tetramethylammonium sulfate was prepared from silver sulfate and tetramethylammonium chloride, and the barium thiosulfate was prepared from sodium thiosulfate and barium
74
J. A. ERIKSON AND E. C. L I N G A F E L T E R
chloride. Solutions were prepared and standardized in the manner described above for solutions of sodium thiosulfate. A reagent-grade sodium nitrate was dried at 110°C., and a weighed amount was diluted to volume in a liter volumetric flask. Sometimes, as a check, the solution was standardized by evaporating a known volume to constant weight. Tetramethylammonium nitrate was prepared from tetramethylammonium chloride and silver nitrate. Iodine solutions containing 4 % potassium iodide were prepared in the usual manner. They were filtered through a sintered glass filter to remove any small crystals of iodine. Concentrations varied, but most solutions were approximately 0.005 N. Iodine solutions containing 5 % tetramethylammonium iodide were prepared by dissolving the iodine in a hot solution of the required amount of the iodide and then allowing the solution to cool. Any tetramethylammonium iodide or tetramethylammonium tri-iodide was removed by filtration. The concentration of iodine was limited to less than 0.002 N because of the insolubility of the tetramethylammonium tri-iodide (7). Iodine would not dissolve in the cold solution of tetramethylammonium iodide because the crystals of iodine became coated with the insoluble tri-iodide. Both iodine solutions were standardized against the calculated initial concentrations of thiosulfate salt present in the kinetic solutions. Sometimes the iodine solutions were checked against the potassium iodate solution by employing a thiosulfate solution of a comparable concentration as an intermediate standard.
The Dead-S~p Titration The end point of the iodine-thiosulfate reaction was determined by a dead-stop technique (8). A potential difference of about 10 my. was used. A 10-cm. deflection of the galvanometer indicated an iodine concentration 3 X 10-~ N. The end point was almost always noted before the deflection attained 1 cm., but in a number of titrations the variation of the galvanometer deflection was measured and graphed versus the volume of iodine solution so that all the readings could be extrapolated back to zero deflection.
Apparatus The 500-ml. Erlenmeyers in which the runs were performed were thermostated in a 20-liter water bath, regulated by a Sargent zero current relay. The temperature was regulated to -+-0.1°C. All the temperatures were adjusted with the same 0 ° to 50°C. thermometer. The sampling pipets were left in the Erlenmeyers according to an arrangement described by Hahn (9). Volumetric glassware was calibrated at 25°C. and computed correc-
PRIMARY SALT EFFECTS WITH PARAFFIN-CHAIN SALTS
75
tions were applied when the glassware was used at 40°C. Time was measured with a stop watch.
Experimental Procedure The solutions used in the kinetic experiments were assembled by various methods by adding stock solutions to volumetric flasks by means of burets and pipets. Usually solutions of thiosulfate salt and other electrolytes were made and thermostated. To these were added aliquots of the stock solution of the bromoacetate salt. The time at the addition was observed, Samples of 50 ml. each were titrated with standard iodine. The reaction was stopped by adding the sample to an amount of iodine solution, delivered from a buret, which was insufficient to react with all of the thiosulfate in the sample. The titration was completed using the dead-stop technique to detect the end point. The time was recorded when the 50-ml. sample was released from the pipet. Two drops of 0.1 N acetic acid were added initially to the iodine solution to suppress the formation of hypoiodite.
CALCULATIONS Three methods were used in the calculations of the rate constants. The magnitude of the difference between the reactant concentrations in a run determined which method was to be employed for that run. If the reactant concentrations were equal, the equation kt -
1 a -- x
1 a
[3]
was used with the following modification. Since
[41
[I~lU = (a - x) V ,
where M is the volume of iodine required for a sample of volume V, Eq. [3] became 1
M-
[I~]k
1
V t -F M-~o
[5]
so that the rate constant, k, could be obtained from the slope, [I,] k/V, of the graph of 1/M versus t. The intercept 1/Mo was used together with the initial concentration of the thiosulfate to calculate the normality of the iodine. A normality of the iodine solution was calculated from each intercept and an average value was found from all the runs using the same iodine solution, and this average was used to calculate the rate constants. The equation for the unequal reactant concentration case
( a - b)kt_ l o g a - - x 2.303
b -- x
loga b
[6]
76
J. A. ERIKSON AND E. C. LINGAFI~LTER
was modified using Eq. [4] and V (a - b)
[7]
to give M log M - D -
[I~]Dk °-~ 2.303~ t + log M
D"
[8]
I t was thought t h a t D could be chosen to give the straightest line for a M graph of log M - - - ~ versus t. Roughly this was true, but usually there was a range of D where the curvature was obscured by the experimental deviations. D was calculated from the initial concentrations of the reactants and the normality of the iodine solution; the latter value was obtained from runs having equal reactant concentrations. When D was small, but not zero, it was found that Eq. [5] was not accurate, and Eq. [8] was too cumbersome. Equation [8] was therefore rearM ranged by expanding log M - D' that is,
-
-
D - 2,303M
and simplified to
2
+ ~
+ ~
+ .--
1 (o)
F
--- - i f - t + Mo
= 1 +-~
+3\M]
Moo
[9]
[10]
where
F
+4
+ ...
[11]
To facilitate the computations, a large graph of F(D/M) versus DIM was drawn. D was computed from Eq. [7] as before, and the rate constant was computed from the slope of a graph of (1/M)F(D/M) versus t. For all runs, the method of averages was used to calculate all slopes and intercepts directly from the co-ordinates of the points. Deviations of the points from this average straight line were calculated and compared. Points with too large a deviation were investigated for mistakes, and if an error could not be found, the point was discarded from the data. ACCURACY A N n P R E C I S I O N OF THE R E S U L T S
If the required volumes of iodine solutions were calculated for a hypothetical run using reactant concentrations which differed slightly, and a
PRIMARY SALT EFFECTS W I T H PARAFFIN-CHAIN SALTS
77
rate constant were calculated from these data on the assumption that the reactants had equal concentrations, two results were apparent. First, the usual reciprocal volume of iodine solution versus time graph was a slightly curved line, and, therefore, the average deviation from the best average line was no longer zero and, second, the calculated rate constant from the slope of this best average line no longer agreed with the assumed rate constant. The curvature of the data or the average deviation of the data from a straight line, the difference in the reactant concentrations, and the change in the rate constant were all related. Thus it was found b y calculation that a 2.8, 5.5, and 11% decrease in the bromoacetate concentration gave curves concave downwards, whose average deviations were 0.052, 0.11, and 0.30 %, respectively, and whose "slopes" yielded rate constants which were too small by 4.5, 10, and 20 %, respectively. I t should be emphasized that these curves all appeared approximately straight. The actual magnitude of the per cent average deviation in an actual run does not mean too much, since any curvature probably would be obscured by the random scatter of the titration values. Thus a small average deviation, although desirable, did not necessarily mean that the rate constant was accurate. T h e errors in the rate constants are primarily due to the errors in the concentrations of the solutions employed, and secondarily due to the error in setting the temperature of the water bath. The change in the rate constant with temperature, dk/dt, at 25°C. and an ionic strength of 0.014 M is 0.034 min. -1 degree -1. A tenth of a degree temperature change corresponds to a 1% error in the rate constant. However, the effect on the rate constant due to the variation in temperature during a 3000-minute run will be averaged to a smaller value than this, and the relative error of the rate constants from runs produced at the same time will likewise be smaller than this, but rate constants compared from runs produced at different times or compared to literature values will be influenced proportionally b y any error in the temperature. I t is reasonable to assume that the thiosulfate concentration is known to 0.5 %, while the bromoacetate is known to 1%, twice as much because two standard solutions had to be made to make the one bromoacetate solution. The error in the rate constants is accordingly about 3 %. The precision of the rate constant values in an experiment where the same stock solutions were used and the same temperature setting of the bath was used for all the runs, is much better, and the agreement and reproducibility are about 1%. Errors due to other causes are negligible. RESULTS
The results are tabulated in Table I. The concentrations are expressed in millimoles per liter. The concentration sum, used here and on some of
78
J. A. ERIKSON AND E. C. LINGAFELTER TABLE I
Experimental R~sults
I
Paraffm-ehain salt Run number [ concentration I (mm./l.)
Nitrate salt Thiomlfate Bromoace- l Concentra- Square root I Experimental concentration salt con- concentsaof the [rate constant tate salt [ tion sum [ Centration (roll° concentration[ (L/mole (ram./1.) (mm./l.) tion limoles/l.) I sum minute) (nun./1.)
Experiment 2. 25°C. (CHs)~N CI~-I~SO~, Fig. 8 1 2 3 8 5 6 4 U 9 10 7 13
0.0 0.20 0.41 0.61 0.81 1.02 2.03 4.05 5.06 6.07 8.09 10.12
10.12 9.92 9.72 9.51 9.31 9.11 8.10 6.07 5.06 4.04 2.03 0.0
0.854
1:19
too 20.3
c¢ C~ C~
o 0.0 o 21.61 17.86 II.07 II.06 8.94 6.81 4.65 2.16 0.0
o o l o o0.428 oo 22.2
0.92 0.!9 i
Experiment 5.40°C. Na 0.0 0.0 6.25 i i .92 17.90 19.59
0.0 C~ cc
cc ~C
olo
0.149
5.38 5.38 3.84 2.44 0.98 0.46
• These data are illustrated on Fig. 1. b These data are illustrated on Fig. 2.
1.60
C12H~6S0~,Fig. 7
0.91 0.88,,
25.3 21.4 ~c ~C
0.159 0.146 l~
"Cc ~
0.408° 0.410 0.408 0.411 0.411 0.410 0.408 0.397 0.394 0.394 0.397 0.385
C1~H25SO~
0.488
Experiment 4.25°C. (CH,)~N 0.0 0.0 6.77 6.77 8.91 II.07 13.21 15.71 17.83
0.118 4¢
Experiment 3, 40°C. Na
1
13,.,9
cc
c¢
0.480~ 0.458" 0.462 0.451 0.449 0.454 0.445 0.442 0.433
C,2Hs5SO3, Fig. 4 5.37 5.37 3.84 2.44 0.98 0.46
21.5 21.5 21.6 21.7 21.8 21.4
0.147 CC
O. 146
1.53 b 1.52b 1.54 1.55 1.57 1.58
TABLE number Run
I--Continu¢d
l f a t e ] B rr oa tme o "a -cIetN i t r a t e s a l t I T shai•l°ts uconconcentration c e n t r a t i.o n c o n ct ie n t r a (mm./L) (mm./L) (n~.~L)
Paraffin-chain salt c o n(cmem n t.r/ al .t)i o n
Experiment 6.25°C. (CH,)~N 7
0.0
{
11.73
I 0.99
0.99
Experiment 7.25°C. (CH~)~N 7 5 8 10 4 4' 2 3 8' 5'
0.0 0.81 4.05 6.08 8.11 0.0 0.81 4.05 16.21 11.05
8.13 7.32 4.05 2.02 0.0 16.22 15.38 12.17 0.0 36.78
6 4 3
2 6 8 4 10
0.0 0.85 1.70 2.54 4.24 7.04 25.44 50.88
0.0
0.0
1.23
o.o 2.33 5.80 11.61 0.0 2.32 11.61 23.22 46.43 68.49
13.0
0.114
21.1
0.145
c¢ " c~ "
gc
¢¢ " "
c~
~c "
1.11
I.II
1.08
1.'
c~
19.2
4.35 5.19 • 6.04 6.89 8.59 11.38 29.79 55.2
Experiment 9.25°C. (CH,)~N
None
0.0
1.21
1.21
cc
2.22 2.22 2.66 3.80
2.21 2.21 2.65 3.80
4.83 8.87 8.86 10.62 15.~
1.65
O. 139
c~
0.066 0.072 0.078 0.083 0.093 0.107 0.173 0.235
0.361" O. 373 O. 379 0.382 O. 396 0.404 0.471 0.548
0.0695 0.0942 0.0941 0.1031 0.1233
0.378 ~ O. 378" O. 389~ 0.415 ~
18.2
O. 135
~c
cc cc
4c
¢c ¢c
cc ~c
c¢
79
0.346"
1.59 a
1.56
cc ¢c
0.418 • 0.422 0.410 0.404 0.398 0.476 ~ 0.472 0.464 0.434 0.433
C u H 2 ~ O , , Fig. 10
1.65
~c
0.434"
C,~H~,S08, Fig. 6
~c
11.59 9.26 5.79 0.0 23.17 20.94 11.59 0.0 0.0 0.0
0.125
"
¢c
~c
I
c¢
"
Experiment 11.40°C. (CH3)~N 5 1 6 3 7 8 2 10 9 4
15.7
~c
c~
~c ~c
None
"
~c
cc
Square root Experimental of t h e rate constant c o n c esum ntration[ m ( Li n/ m u toel)e
C~H2~SO~, Fig. 9
Experiment 8.25°C. (CHs)~N 10 7 8 2 5
Concentrat/on sum limoles/l.) (rail-
c¢
29.8
c~
O, 173
cc cc
c~
cc
gc
,5.3.0 75.1
O. 230 O. 274
1.50 1.44 1.84 b 1.80 1.70 1.57 1.79 1.93
80
J. A. E R I K S O N
AND E. C. L I N G A F E L T E R
TABLE I--Continued Paraffin-chain Thiosulfate Br~°tm°al(~" Concentra- Squareroot [ExDerimental salt co~emn~atS~n salt c~n- c~nce [~" [ tion sum i of the Irate constant Run number concentration [ /t~ / centratlon o tin ra(railconcentrationl (l./mole (mm./l.) ,mm./,q I (ram./1.) (n~.~l.) limoles/L) sum minute) .
.
.
.
.
.
.
E x p e r i m e n t 12. 250C. N a 4 5 7 9' 6 10' 2' 4 3' 7' 9 4 2 6' 1 8 1' 4' 7' 8' 10 9 3
0.0 9.18 18.37 18.37 22.04 36.74 55.12 0.0
0.0
0.92
C,0H2,SO,, Fig. 3 0.92
3.68 12.9 22.1 22.1 25.7 40.4 58.8 3.68 3.68 6.66 7.34 3.68 10.7 10.7 17.7 23.4 6.53 6.66 6.66 6.66 7.35 7.34 7.34
~c ~c
~c ~c
c~ ~c
c~
7.02 7.02 14.05 19.67 0.0
cg c$ {c
cg lc
cg
c¢
1.66 1.84 0.92 ~c
1.07 1.39 1.66 1.94 0.92 1.84 2.14
1.67 1.83 0.92 ~c
3.33 2.50 1.67 0.83 4.58 1.83 0.92
E x p e r i m e n t 13.25°C. (CH3)4N 4'
I
0.0
i
0.0
4
I
"
[
"
0.62 1.28
0.61 1.22
E x p e r i m e n t 14.40°C. N a 3
0.0
0.0
8
"
8" 2
" 11.65
" " "
0.33 1.63 3.27 0.33
0.33 1.64 3.28 0.33
0.060 0.113 0.149 0.149 0.160 0.201 0.243 0.060 0.060 0.082 0.086 0.080 0.104 0.104 0.133 0.153 0.081 0.082 0.082 0.082 0.086 0.086 0.086
0.325 a 0.408 0.462 0.459 '0.481 0.531 0.562 0.325" 0.325 ~ O. 352~ O. 351~ O. 325~ 0.388 ~ 0.385" 0.429" 0.459 a 0.356 ~ 0.352 ~ 0.352 ~ O. 338~ 0.357 • 0.351 ~ 0.356 ~
0.050 0.071
0.318 ~ 0.342 ~
0.036 0.081 0.114 0.114
1.11 b 1.25 b 1.44 b 1.50
C14H29SOa 2.46 5.05
C,~H2~SO3 1.31 6.53 13.07 13.0
t h e f i g u r e s , is d e f i n e d t o b e e q u a l t o t h e s u m of t h e c o n c e n t r a t i o n s of paraffin-chain salt, nitrate salt, and bromoacetate salt plus three times the c o n c e n t r a t i o n of t h e t h i o s u l f a t e s a l t . I n t h e a b s e n c e of m i c e l l e s t h e c o n c e n t r a t i o n s u m is e q u i v a l e n t t o t h e i o n i c s t r e n g t h .
PRIMARY
SALT
EFFECTS
WITH
PARAFFIN-CHAIN
0.540"$E:~OATA OF A.KISS AND P.VASS i(~ EXPERIMENTAL DATA WITHOUT NITRATE ION
~
O~O0"'EX"RI""TAL OATAWTH HITN.T, ON o...
SALTS
J
81
j
~
•~
O.46
o,2 0.44
•
o~s
0.40
0
O,:N~
~
031 O.32 03C O.Zl 02E 0240
0.02
0.04 GOS O.OS 0.10 GIE SQUARE ROOT GONGENTRATIONSUM
0.14 OJ6 O.IS (moles/ llfle) I/2
O.ZO
0.24 (~26
O.Z2
FzG. 1. Rate constants for reactants w i t h and without nitrate ion at 25°C.
J J
/
'8[,~0ATA0 ..... .AND .... . ....
° .......
o....
T.T,o.
"
16 I
~"15f
~ 1.4
=
I.I
1.0~"
0
.
.
.
0.02
.
.
.
.
I
;
T
I
'
I
t
I
I
'
[
0.04 0.06 0.08 0.10 O,t2 0.14 0.16 O.IS ~ 2 0 SQUARE ROOT GONGENTRATtONSUM (moles/ liter)'"
I
~
0.22
I
I
I
I
I
0 2 4 026
FIG. 2. Rate constants for reactants with and without nitrate ion at 40°C.
Reactants and Simple Ions One or more runs of each experiment contained no paraffin-chain salt. When the results from these runs were compared with each other on a single rate constant versus ionic strength graph, the average spread of the results was a b o u t 3 To (Figs. 1 and 2). The lower solid curve represents the results of Kiss and Vass (10) using solutions which contained only reactants. T h e upper solid curve represents their results where increasingly larger amounts of nitrate salt were added to a constant (0.00125 M) concentration of reactants. T h e reactant concentrations employed here for all the runs indicated by black dots were not the same, although most of the reactant concentrations were nearly the same (0.001 M).
82
J, A, ERIKSON AND E, C, LINGAFELTER
e
0.56 NUMBERS REFER TO RUN NUMBERS 054 ] ~ IRGREASlI'+¢ F~IUaLRI~I~'IIJ,IT ¢¢RGE.TRA.,.IORE 052 o . . + . . ' T O=O,:.TR.'.OR +.R..+,+," +,+ ,. RU. + QSC ARONOClol-lttS03CO.CENTRE'ION mCnmAS~O 0 RE.°-,.+,,,.,.~,.=','R.,O, 0=,=~T+'+,.RU.+
"| 0 4 £
ANDNONO3.GO~
~ o~
®
/ ~+
/
J
®/
/
/
~ O4~
~- Q42 04C
Q3fi ~o~ 034 Q32
~ o~ o2a Q2e
, , / . ,.. • . . . . . . . . . . . . . . . , • Q02 Q04 0.06 O.OS O.IO 0.12 0.14 0.16 0.18 0.20 0.22 O.24 SQUARE ROOTGONGENTRATt© SUM (~I (nlOhll/ liter]I/z
024 o
Fro. 3. Comparison of the rate constants from solutions containing decanesulfonate ion and similar solutions containing nitrate ion.
+-
Reactants with Para~n-Chain Ions
In solutions of paraffin-chain salts which did not contain micelles, especially with sodium decanesulfonate (Fig. 3), no change in the rate constant was observed if paraffin-chain ion were substituted for nitrate ion. This indicated that in spite of the very different nature of the paraffin-chain ion compared with the nitrate ion, these singly charged ions influence the thiosulfate-bromoacetate reaction in the same manner.
Reactants with Micelles Three experiments, 3, 5, and 14, demonstrated that the rate constant at 40°C. was slightly increased as reactants of equal concentrations were reI ~ I E ~ R $ REFER TO RUNS OF (XPF.RIMF.I/T 5
1.80 1.70 1.60
t.40 0
,~ ' ~+' + ' ~ , ' , ~ ' ,~' ~' ,~ ' + ' mo GOlIGIENTRATIOOF N SODIUI4000~ANI[$ULFONATI[ (miNilM4u/litlrl|
FIG. 4. Variation of the rate constant when reactants are replaced b y sodium dodecanesulfonate at 40°C.
PRIMARY SALT EFFECTS WITH PARAFFIN-CHAIN SALTS
83
placed by an ionic strength equivalent amount of sodium dodecanesulfonate. The results from the more elaborate experiment are shown on Fig. 4. An earlier experiment (1) likewise indicated this increase, but the results are in error and the increase should not be as much as is recorded. The corrected results and the old results are shown together on Fig. 5. The primary error was caused by calculating the rate constants with the method for equal reactant concentrations, even though the reactant concentrations were slightly different. This method has been recommended for this situation by Daniels, Mathews, and Williams (11). The corrected rate ORIGINAL VALUES CORRECTED VALUES
2.10
200
| e
| Lgo
O
=-" 1.8o ~
1.70
. . . . . . .
I
,,,
4 6 B I0 12 I 16 ¢0NCENTRATIONOF THE SODIUMDODECJlNESUt.FONATE ( m ~ t l h e r )
0
18
20
FIG. 5. Variation of the rate constant when reactants are replaced by sodium dodecanesulfonate at 40°C. 056 0.54 0.52
N~RIBERS RIrFER TO RUN NUMBERS (~ FXPERIMIrNTALVALUES ~
o
~ ~o ~o.,~ s
0.44 0"42 0.40 038
;
~) .
036
034 o 0.32
)
J
~
=: 0.30 O28 0.26 024
./
. . . . . .
0,02
i
i
i
i
i
i
.
.
.
.
.
.
.
.
.
0.04 0.06 0.08 0.10 0.12 QI4 0.16 0 . 1 8 0.20 SQUARE ROOT OONGI[NTRATIONSUM ( molls / lltlr) I/;[
.
.
0.22
0.24
FIG. 6. Rate constants at 25°C. for various solutions of (CH3)4NC.H~S03 containing a constant amount of reactants.
84:
J. A. ERIKSON AND E. C. LINGAFELTER
constants have been recalculated taking into account this slight difference in reactant concentrations b y the method already described. The addition of tetramethylammonium tetradecanesulfonate to a constant amount of reactants resulted in an increase in the rate constant which, from a comparison with the results of Kiss and Vass, appeared to be nearly the same as if an ionic strength equivalent amount of equal concentration reactants had been added instead. This was demonstrated b y experiment 8 (Fig. 6) and also b y runs 3, 10, 9, and 4 of experiment 11. Within experimental error, these data are in agreement with the above-mentioned slight increase in the rate constant produced b y replacing reactants with paraffinchain salt. NUIMIERSR~FER TO RUNS OF EXPERIMENT 4
i
0.47
t
®
E a4~
®
0.~
O
~o.,~ O.43 0
. .~. . ., . .
~
COf~PJ~TN/mONOF ~
~,'
~
'o',
,2'
'
,:,'
~' , , ~ '
[nNIIIIl~es/ I l i a )
Fzo. 7. Variation of the rate constant when nitrate ion is replaced by dodecanesulfonate ion at 25°C.
@~
o.39c
0.3 e(
,
0
,
i
I
,
2 4 GORGENTRATIO~I OF |GH3)4NCt4R2~O~
i
,
6 (mliRmotes/ l i t e r )
,
8
=
i..
I0
FzG. 8. The rate constant when NO3- is replaced by C14H29SO3-at 25°C. in experiment 2.
PRIMARY SALT EFFECTS WITH PARAFFIN-CHAIN SALTS
85
Nitrate Ion with M icelles If nitrate salt were replaced by the equivalent amount of paraffin-chain salt, the rate constant decreased; the decrease was somewhat more than the increase noted above. This was observed with tetramethylammonium dodecanesulfonate at 25°C. (Fig. 7) and with tetramethylammonium tetradecanesulfonate at both 25°C. (Figs. 8 and 9) and 40°C. (Fig. 10). These data are not in disagreement with the data in which an increase was observed, since the primary salt effect produced by nitrate salt is greater than the effect produced by an ionic strength equivalent amount of reactants. The difference of 0.0075 min. -1 between the two groupings of the results in e x ()
NUMO~R$REFERTO RUNSOF EXPERIMENT7' THE FOLLOWINGGONGENTRATIOSU~ fl WERE S .41E.0 0.139 O AND 0.145. :
0,47 ~ - ~ - -
0.46
~
U
0.45
~s.~s
0,44 0.43 ~ 0.4 _
.
.
0
.
.
.
.
l
2 4 6 8 I0 CONCENTRATIONOF TETRADEGANESULFONATE
I
~ I (miII~oI~s / liter}
I
FIG. 9. Variation of the rate constant when nitrate ion is replaced by tetradecanesulfonate ion at 25°C. 1.9
NUMBERSREFERTO RUNSOF EXPERIMENI I I CONGENTRATIONSUMSOF OA35ANDO.173WI[REU~EO
I.S s
1.6
!
,
0
.
.
.
.
.
.
,
.
.
.
.
.
.
.
.
.
2 4 6 8 I0 12 14 CCNGENTRATIOHOF TETRAO4EGANESULFONATIE
.
.
,
~, 18 20 ( millimcles/lilf|
,
,
,
22
FzG. 10. Variation of the rate constant when nitrate ion is replaced by tetradecanesulfonate ion at 40°12.
86
J. A. ERIKSON AND E. C. L I N G A F E L T E R
periment 2 (Fig. 8) is believed due to a systematic error, since the lower group of runs was performed two days after the higher group. DISCUSSION
The indifference of the rate constant to the presence of micelles, in solutions containing micelles, can be crudely predicted from the theoretical behavior of the rate constant in solutions containing simpler complexes. Since theoretically the rate constant is a function of the ionic strength, it will be sufficient to calculate only the ionic strength of solutions containing singly, doubly, triply, etc., charged ions in various degrees of association. In order to keep the calculations simple, only two ionic species will be considered to be present in each solution; the singly charged positive ions, and the complex anions containing singly charged positive and negative ions. In the case of a solution containing a neutral aggregate, only the neutral aggregate will be present. A solution will, therefore, contain either the ions M + and M ~ .... , or the neutral molecules M~km; where m is 1, 2, 3 , . . . , n is 0, 1, 2 , . . . , and for each solution n is equal to, or less than, m. It will be assumed that all the solutions can be constructed from a single solution, 0.02 M in MA. The concentration of the M ~ "-~ complex is (0.02) (I/m), and the concentration of the M + ion is 0.02(1 -- n/m). The ionic strength for a given solution is u
(0.01) (l/m) (m -- n) (1 + m -- n).
.=
[12]
The degree of neutralization of the charge of the complex ions is given by n/m. Figure 11 is a graph of the square root of the ionic strength for various degrees of association of the "monomer," dimer, trimer, etc. The lines r
G2
~%
9
i 0
II
I
I
I
OEWI[E OF AG$iOCUI,TIC$i
I him
FIG. 11. T h e o r e t i c a l i o n i c s t r e n g t h s for s o l u t i o n s 0.02 M of MA, w h e r e t h e r e a c t i o n A~ "--'~ -t- m M ÷ --~ M.A,~ '~-'~ -'I- (m -- n ) M + h a s g o n e t o c o m p l e t i o n .
PRIMARY SALT EFFECTS WITH PARAFFIN-CHAIN SALTS
87
result from considering n as a continuous variable, but only the points represent physically possible solutions. An empirical line correlating an "ionic strength" for a micelle containing approximately 50 or 60 paraffinchain units is assumed to be in the location labeled "micelle?". This particular location is assumed in order to correlate the effective ionic strength of a micelle having a degree of association of approximately 0.8 to 0.9 with the results of this research: that the rate constant of the reaction in a solution containing micelles, is comparable to the rate constant of the reaction in a hypothetical solution containing the same amount of completely dissociated paraffin-chain salt. This line does not appear out of position when compared with the lines for the simple ions, even though the ionic strength principle is not valid in this region. McBain (12, 13) regarded the charges on the exterior of the micelle to be too widely spaced to exert a mutual and therefore large effect, and concluded that ionic effects of solutions of micelles would not be much different from those of uni-univalent electrolytes. The conclusion drawn from the experiments of this research regarding the ionic effects of paraffin-chain salt solutions is that the ionic effects of the charged micelles are quite large, at least large enough to compensate for the decrease in ionic effect due to the simple ions that have associated to form micelles. The net effect of this compensation is that the influence of these paraffin-chain salt solutions containing micelles on the ionic reaction is approximately the same as if the paraffin-chain salt were behaving as a uni-univalent electrolyte. It appears, therefore, that the activity coefficients of simple ions of charge of the same sign as the micelle charge, in solutions of paraffin-chain salts which contain micelles, have a value which is not much different from the value that they would have in a hypothetical solution containing a completely dissociated paraffin-chain salt of the same stoichiometric concentration. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
ERIKSON, J. A., AND LINGAFELTER,E. C., jr. Colloid Sci. 4, 591 (1949). HARTLEY, G. S., Trans. Faraday Soc. 31, 31 (1935). LA MER, V. K., jr. Am. Chem. Soc. 51, 3341, 3678 (1929). WYATT,P. A. H., AND DAVIES, C. W., Trans. Faraday Soc. 45,774 (1949). LAMER, V. K., J. Am. Chem. Soc. 63, 2832 (1931). LAMER, V. K., AND FESSENDEN, R. W., jr. Am. Chem. Soc. 54, 2351 (1932). RAY, S. K., AND BHATTACHARYA,R. 1~., J. Indian Chem. Soc. 13, 456-463 (1936). BRADBURY,J. H., Trans. Faraday Soc. 49, 304 (1953). HAHN, F. L., Anal. Chim. Acta 4, 573 (1950). KIss, A., AND VASS, P., Z. anorg, u. allgem. Chem. 217,305 (1934). DANIELS, F., MATHEWS, J. H., AND WILLIAMS, J. W., "Experimental Physical Chemistry," 3rd ed., p. 169. McGraw-Hill Book Co., New York and London, 1941. 12. McBAIN, J. W., J. Am. Chem. Soc. 50, 1639 (1928). 13. McBAIN, J. W., AND BETZ, M. D., jr. Am. Chem. Soc. 57, 191 (1935).
The Department of Chemistry, University of Washington, Seattle, Washington Received August 24, 1954 ABSTRACT The primary salt effect of tetramethylammonium dodecanesulfonate, tetramethylammonium tetradecanesulfonate, and sodium decanesulfonate all at 25°C. and sodium dodecanesulfonate and tetramethylammonium tetradecanesulfonate at 40°C. on the displacement reaction between thiosulfate and bromoacetate ions has been studied. It was found that the measured rate constant from a paraffin-chain salt solution containing micelles had nearly the same value that it had in a solution containing an equivalent amount of simple, completely dissociated electrolyte. Since it is well established that a considerable number of gegenions are attached to the micelle, the above result indicates that the micelle has a rather large ionic effect. This effect compensates for the decrease in ionic effect brought about by the decrease in simple ion concentration due to the aggregation of the simple ions to form micelles. INTRODUCTION
This paper is concerned with the ionic catalysis of an ionic reaction, the thiosulfate-bromoacetate displacement reaction, by some paraffin-chain salts, the sodium and tetramethylammonium salts of decane-, dodecane-, and tetradecanesulfonates. A previous experiment (1) indicated that the rate constant at 40°C. was increased as reactants were replaced by sodium dodecanesulfonate. This was found to be true here, but to a much smaller magnitude. The previous results are in error mainly owing to the use of an inadequate calculation method. This will be discussed later. Paraffin-chain salts are ionic compounds which have paraffin chains incorporated in one or both ions. Because of the hydrophobic nature of the paraffin-chain part there exists a threshold concentration of paraffin-chain 1 Taken from a thesis submitted by J. A. Erikson to the University of Washington in partial fulfillment of the requirements for the Ph.D. degree, June, 1954. Presented before the Division of Physical and Inorganic Chemistry at the Northwest Regional American Chemical Society Meeting, Riehland, Washington, June, 1954. a A part of this work was carried out under United States Army Ordnance Corps Basic Research Contract No. DA-04-200-ORD-236. 4 Procter and Gamble research fellow 1950-1951. Present address: Department of Petroleum Refining, Colorado School of Mines, Golden, Colorado. 71
72
J.A.
ERIKSON AND E. C. LINGAFELTER
ions in aqueous solution, called the critical micelle concentration, above which the excess paraffin-chain ions associate to form aggregates of colloidal dimensions. The electrical charge of this aggregate is partially neutralized by an "atmosphere" of simple ions whose charge is of the opposite sign to the charge of the micelle. These simple ions are called gegenions and the resulting aggregate of paraffin-chain ions and gegenions is called a micelle. One of the many questions concerning micelles is the question concerning the effect of the micelle charge on the activity coefficients of simple ions. An analysis of the values of the activity coefficients of gegenion and micelle has been given by Hartley (2). Activity coefficients which may behave more rationally and therefore may be simpler to discuss are those of simple ions whose charges are of the same sign as the micelle charge. No method exists to determine such activity coefficients individually, but a value for a group of some of these coefficients may be determined by studying the primary salt effect. The rate constant of the thiosulfate-bromoacetate reaction, $203- + B r C H 2 C O O - --~ ( A c t i v a t e d C o m p l e x ) ~ --* B r - + S~O~CH2COO-
[1]
is related to the activity coefficients vr, vB and v* of the thiosulfate, bromoacetate, and activated complex ions, respectively, by 7rTB
koxp = k0 ~,.
[2]
Equation [2] has been tested many times (3) and shown to be correct. Where anomalies were found, these anomalies were shown to be due to side reactions between associated ions (4), orientation effects (5), or anomalies in the activity coefficients (6). If the activity coefficients in Eq. [2] depend upon the charge of the corresponding ions and on the common environment in a manner no more complicated than the Debye-Hfickel dependence, then a study of the variation of the experimental rate constant may yield an effective ionic strength for this environment. EXPERIMENTAL
Materials
Sodium dodecanesulfonate was prepared by refluxing a Halogen Chemical Co. dodecyl bromide, an analytical-grade sodium sulfite, and water for several days until the bromide layer disappeared. A weighed amount of the recrystallized material was diluted to the mark of a liter volumetric flask and the concentration computed, taking into account the water content of the material, which was determined by drying a sample in a vacuum oven. The tetramethylammonium alkanesulfonates were made from the corresponding sodium alkanesulfonates by first converting them to the silver alkanesulfonates and then reacting these with tetramethylammonium chloride. Solutions were made in the same manner as the sodium dodecane-
PRIMARY SALT EFFECTS W I T H PARAF F IN -C H A IN SALTS
73
sulfonate solutions and also by preparing a solution of the approximate concentration and then drying a sample of this solution to constant weight in a vacuum oven. Sodium decanesulfonate was already in stock and was recrystallized before being used. A reagent-grade potassium hydrogen phthalate was dried at 100°C. in a vacuum oven, without any previous purification. A weighed amount was diluted to volume in a volumetric flask. Carbonate free sodium hydroxide was prepared by filtering a 50 % solution into a liter of cooled, boiled, distilled water. The solution was protected as completely as possible from the air by two drying tubes filled with Ascarite, one on a piece of tubing through a rubber stopper on the bottle, and the other on the end of the pipet, which also went through the stopper of the bottle. The pipet was used to transfer the solution. An Eastman 10% solution of tetramethylammonium hydroxide was diluted to an approximate concentration with cooled, boiled, distilled water. The hydroxide solutions were standardized against the standard acid phthalate solutions, with a Beckman pH meter used to detect the end point. A reagent-grade bromoacetic acid was recrystallized three times from benzene, and then once from acetone. It was stored in a desiccator over phosphorus pentoxide. An approximate amount was quickly transferred to a weighed weighing bottle, and weighed. The bromoacetic acid was rinsed into a beaker and transferred to a liter volumetric flask. The solution was standardized against the hydroxide with the pH meter to detect the end point. The normality obtained from the initial weight of the bromoacetic acid was used as a check on the experimental technique and on the purity of the compound. The bromoacetic acid solution and the appropriate hydroxide solution were mixed to form the corresponding bromoacetate solution by adjusting the pH of the mixture to the standardization end point pH. A reagent-grade potassium iodate was dried at 150°C., weighed, and diluted to volume in a 2-liter volumetric flask. The solutions were approximately 0.005 N. An approximate amount of reagent-grade sodium thiosulfate was placed in a liter pyrex bottle, which had just been rinsed with boiling, distilled water. A liter of boiling, distilled water was added, and the bottle was stored to permit the solution to cool. The solution was standardized by the potassium iodate solution; the dead-stop technique was used to detect the end point. Tetramethylammonium thiosulfate was prepared from tetramethylammonium sulfate and barium thiosulfate. The tetramethylammonium sulfate was prepared from silver sulfate and tetramethylammonium chloride, and the barium thiosulfate was prepared from sodium thiosulfate and barium
74
J. A. ERIKSON AND E. C. L I N G A F E L T E R
chloride. Solutions were prepared and standardized in the manner described above for solutions of sodium thiosulfate. A reagent-grade sodium nitrate was dried at 110°C., and a weighed amount was diluted to volume in a liter volumetric flask. Sometimes, as a check, the solution was standardized by evaporating a known volume to constant weight. Tetramethylammonium nitrate was prepared from tetramethylammonium chloride and silver nitrate. Iodine solutions containing 4 % potassium iodide were prepared in the usual manner. They were filtered through a sintered glass filter to remove any small crystals of iodine. Concentrations varied, but most solutions were approximately 0.005 N. Iodine solutions containing 5 % tetramethylammonium iodide were prepared by dissolving the iodine in a hot solution of the required amount of the iodide and then allowing the solution to cool. Any tetramethylammonium iodide or tetramethylammonium tri-iodide was removed by filtration. The concentration of iodine was limited to less than 0.002 N because of the insolubility of the tetramethylammonium tri-iodide (7). Iodine would not dissolve in the cold solution of tetramethylammonium iodide because the crystals of iodine became coated with the insoluble tri-iodide. Both iodine solutions were standardized against the calculated initial concentrations of thiosulfate salt present in the kinetic solutions. Sometimes the iodine solutions were checked against the potassium iodate solution by employing a thiosulfate solution of a comparable concentration as an intermediate standard.
The Dead-S~p Titration The end point of the iodine-thiosulfate reaction was determined by a dead-stop technique (8). A potential difference of about 10 my. was used. A 10-cm. deflection of the galvanometer indicated an iodine concentration 3 X 10-~ N. The end point was almost always noted before the deflection attained 1 cm., but in a number of titrations the variation of the galvanometer deflection was measured and graphed versus the volume of iodine solution so that all the readings could be extrapolated back to zero deflection.
Apparatus The 500-ml. Erlenmeyers in which the runs were performed were thermostated in a 20-liter water bath, regulated by a Sargent zero current relay. The temperature was regulated to -+-0.1°C. All the temperatures were adjusted with the same 0 ° to 50°C. thermometer. The sampling pipets were left in the Erlenmeyers according to an arrangement described by Hahn (9). Volumetric glassware was calibrated at 25°C. and computed correc-
PRIMARY SALT EFFECTS WITH PARAFFIN-CHAIN SALTS
75
tions were applied when the glassware was used at 40°C. Time was measured with a stop watch.
Experimental Procedure The solutions used in the kinetic experiments were assembled by various methods by adding stock solutions to volumetric flasks by means of burets and pipets. Usually solutions of thiosulfate salt and other electrolytes were made and thermostated. To these were added aliquots of the stock solution of the bromoacetate salt. The time at the addition was observed, Samples of 50 ml. each were titrated with standard iodine. The reaction was stopped by adding the sample to an amount of iodine solution, delivered from a buret, which was insufficient to react with all of the thiosulfate in the sample. The titration was completed using the dead-stop technique to detect the end point. The time was recorded when the 50-ml. sample was released from the pipet. Two drops of 0.1 N acetic acid were added initially to the iodine solution to suppress the formation of hypoiodite.
CALCULATIONS Three methods were used in the calculations of the rate constants. The magnitude of the difference between the reactant concentrations in a run determined which method was to be employed for that run. If the reactant concentrations were equal, the equation kt -
1 a -- x
1 a
[3]
was used with the following modification. Since
[41
[I~lU = (a - x) V ,
where M is the volume of iodine required for a sample of volume V, Eq. [3] became 1
M-
[I~]k
1
V t -F M-~o
[5]
so that the rate constant, k, could be obtained from the slope, [I,] k/V, of the graph of 1/M versus t. The intercept 1/Mo was used together with the initial concentration of the thiosulfate to calculate the normality of the iodine. A normality of the iodine solution was calculated from each intercept and an average value was found from all the runs using the same iodine solution, and this average was used to calculate the rate constants. The equation for the unequal reactant concentration case
( a - b)kt_ l o g a - - x 2.303
b -- x
loga b
[6]
76
J. A. ERIKSON AND E. C. LINGAFI~LTER
was modified using Eq. [4] and V (a - b)
[7]
to give M log M - D -
[I~]Dk °-~ 2.303~ t + log M
D"
[8]
I t was thought t h a t D could be chosen to give the straightest line for a M graph of log M - - - ~ versus t. Roughly this was true, but usually there was a range of D where the curvature was obscured by the experimental deviations. D was calculated from the initial concentrations of the reactants and the normality of the iodine solution; the latter value was obtained from runs having equal reactant concentrations. When D was small, but not zero, it was found that Eq. [5] was not accurate, and Eq. [8] was too cumbersome. Equation [8] was therefore rearM ranged by expanding log M - D' that is,
-
-
D - 2,303M
and simplified to
2
+ ~
+ ~
+ .--
1 (o)
F
--- - i f - t + Mo
= 1 +-~
+3\M]
Moo
[9]
[10]
where
F
+4
+ ...
[11]
To facilitate the computations, a large graph of F(D/M) versus DIM was drawn. D was computed from Eq. [7] as before, and the rate constant was computed from the slope of a graph of (1/M)F(D/M) versus t. For all runs, the method of averages was used to calculate all slopes and intercepts directly from the co-ordinates of the points. Deviations of the points from this average straight line were calculated and compared. Points with too large a deviation were investigated for mistakes, and if an error could not be found, the point was discarded from the data. ACCURACY A N n P R E C I S I O N OF THE R E S U L T S
If the required volumes of iodine solutions were calculated for a hypothetical run using reactant concentrations which differed slightly, and a
PRIMARY SALT EFFECTS W I T H PARAFFIN-CHAIN SALTS
77
rate constant were calculated from these data on the assumption that the reactants had equal concentrations, two results were apparent. First, the usual reciprocal volume of iodine solution versus time graph was a slightly curved line, and, therefore, the average deviation from the best average line was no longer zero and, second, the calculated rate constant from the slope of this best average line no longer agreed with the assumed rate constant. The curvature of the data or the average deviation of the data from a straight line, the difference in the reactant concentrations, and the change in the rate constant were all related. Thus it was found b y calculation that a 2.8, 5.5, and 11% decrease in the bromoacetate concentration gave curves concave downwards, whose average deviations were 0.052, 0.11, and 0.30 %, respectively, and whose "slopes" yielded rate constants which were too small by 4.5, 10, and 20 %, respectively. I t should be emphasized that these curves all appeared approximately straight. The actual magnitude of the per cent average deviation in an actual run does not mean too much, since any curvature probably would be obscured by the random scatter of the titration values. Thus a small average deviation, although desirable, did not necessarily mean that the rate constant was accurate. T h e errors in the rate constants are primarily due to the errors in the concentrations of the solutions employed, and secondarily due to the error in setting the temperature of the water bath. The change in the rate constant with temperature, dk/dt, at 25°C. and an ionic strength of 0.014 M is 0.034 min. -1 degree -1. A tenth of a degree temperature change corresponds to a 1% error in the rate constant. However, the effect on the rate constant due to the variation in temperature during a 3000-minute run will be averaged to a smaller value than this, and the relative error of the rate constants from runs produced at the same time will likewise be smaller than this, but rate constants compared from runs produced at different times or compared to literature values will be influenced proportionally b y any error in the temperature. I t is reasonable to assume that the thiosulfate concentration is known to 0.5 %, while the bromoacetate is known to 1%, twice as much because two standard solutions had to be made to make the one bromoacetate solution. The error in the rate constants is accordingly about 3 %. The precision of the rate constant values in an experiment where the same stock solutions were used and the same temperature setting of the bath was used for all the runs, is much better, and the agreement and reproducibility are about 1%. Errors due to other causes are negligible. RESULTS
The results are tabulated in Table I. The concentrations are expressed in millimoles per liter. The concentration sum, used here and on some of
78
J. A. ERIKSON AND E. C. LINGAFELTER TABLE I
Experimental R~sults
I
Paraffm-ehain salt Run number [ concentration I (mm./l.)
Nitrate salt Thiomlfate Bromoace- l Concentra- Square root I Experimental concentration salt con- concentsaof the [rate constant tate salt [ tion sum [ Centration (roll° concentration[ (L/mole (ram./1.) (mm./l.) tion limoles/l.) I sum minute) (nun./1.)
Experiment 2. 25°C. (CHs)~N CI~-I~SO~, Fig. 8 1 2 3 8 5 6 4 U 9 10 7 13
0.0 0.20 0.41 0.61 0.81 1.02 2.03 4.05 5.06 6.07 8.09 10.12
10.12 9.92 9.72 9.51 9.31 9.11 8.10 6.07 5.06 4.04 2.03 0.0
0.854
1:19
too 20.3
c¢ C~ C~
o 0.0 o 21.61 17.86 II.07 II.06 8.94 6.81 4.65 2.16 0.0
o o l o o0.428 oo 22.2
0.92 0.!9 i
Experiment 5.40°C. Na 0.0 0.0 6.25 i i .92 17.90 19.59
0.0 C~ cc
cc ~C
olo
0.149
5.38 5.38 3.84 2.44 0.98 0.46
• These data are illustrated on Fig. 1. b These data are illustrated on Fig. 2.
1.60
C12H~6S0~,Fig. 7
0.91 0.88,,
25.3 21.4 ~c ~C
0.159 0.146 l~
"Cc ~
0.408° 0.410 0.408 0.411 0.411 0.410 0.408 0.397 0.394 0.394 0.397 0.385
C1~H25SO~
0.488
Experiment 4.25°C. (CH,)~N 0.0 0.0 6.77 6.77 8.91 II.07 13.21 15.71 17.83
0.118 4¢
Experiment 3, 40°C. Na
1
13,.,9
cc
c¢
0.480~ 0.458" 0.462 0.451 0.449 0.454 0.445 0.442 0.433
C,2Hs5SO3, Fig. 4 5.37 5.37 3.84 2.44 0.98 0.46
21.5 21.5 21.6 21.7 21.8 21.4
0.147 CC
O. 146
1.53 b 1.52b 1.54 1.55 1.57 1.58
TABLE number Run
I--Continu¢d
l f a t e ] B rr oa tme o "a -cIetN i t r a t e s a l t I T shai•l°ts uconconcentration c e n t r a t i.o n c o n ct ie n t r a (mm./L) (mm./L) (n~.~L)
Paraffin-chain salt c o n(cmem n t.r/ al .t)i o n
Experiment 6.25°C. (CH,)~N 7
0.0
{
11.73
I 0.99
0.99
Experiment 7.25°C. (CH~)~N 7 5 8 10 4 4' 2 3 8' 5'
0.0 0.81 4.05 6.08 8.11 0.0 0.81 4.05 16.21 11.05
8.13 7.32 4.05 2.02 0.0 16.22 15.38 12.17 0.0 36.78
6 4 3
2 6 8 4 10
0.0 0.85 1.70 2.54 4.24 7.04 25.44 50.88
0.0
0.0
1.23
o.o 2.33 5.80 11.61 0.0 2.32 11.61 23.22 46.43 68.49
13.0
0.114
21.1
0.145
c¢ " c~ "
gc
¢¢ " "
c~
~c "
1.11
I.II
1.08
1.'
c~
19.2
4.35 5.19 • 6.04 6.89 8.59 11.38 29.79 55.2
Experiment 9.25°C. (CH,)~N
None
0.0
1.21
1.21
cc
2.22 2.22 2.66 3.80
2.21 2.21 2.65 3.80
4.83 8.87 8.86 10.62 15.~
1.65
O. 139
c~
0.066 0.072 0.078 0.083 0.093 0.107 0.173 0.235
0.361" O. 373 O. 379 0.382 O. 396 0.404 0.471 0.548
0.0695 0.0942 0.0941 0.1031 0.1233
0.378 ~ O. 378" O. 389~ 0.415 ~
18.2
O. 135
~c
cc cc
4c
¢c ¢c
cc ~c
c¢
79
0.346"
1.59 a
1.56
cc ¢c
0.418 • 0.422 0.410 0.404 0.398 0.476 ~ 0.472 0.464 0.434 0.433
C u H 2 ~ O , , Fig. 10
1.65
~c
0.434"
C,~H~,S08, Fig. 6
~c
11.59 9.26 5.79 0.0 23.17 20.94 11.59 0.0 0.0 0.0
0.125
"
¢c
~c
I
c¢
"
Experiment 11.40°C. (CH3)~N 5 1 6 3 7 8 2 10 9 4
15.7
~c
c~
~c ~c
None
"
~c
cc
Square root Experimental of t h e rate constant c o n c esum ntration[ m ( Li n/ m u toel)e
C~H2~SO~, Fig. 9
Experiment 8.25°C. (CHs)~N 10 7 8 2 5
Concentrat/on sum limoles/l.) (rail-
c¢
29.8
c~
O, 173
cc cc
c~
cc
gc
,5.3.0 75.1
O. 230 O. 274
1.50 1.44 1.84 b 1.80 1.70 1.57 1.79 1.93
80
J. A. E R I K S O N
AND E. C. L I N G A F E L T E R
TABLE I--Continued Paraffin-chain Thiosulfate Br~°tm°al(~" Concentra- Squareroot [ExDerimental salt co~emn~atS~n salt c~n- c~nce [~" [ tion sum i of the Irate constant Run number concentration [ /t~ / centratlon o tin ra(railconcentrationl (l./mole (mm./l.) ,mm./,q I (ram./1.) (n~.~l.) limoles/L) sum minute) .
.
.
.
.
.
.
E x p e r i m e n t 12. 250C. N a 4 5 7 9' 6 10' 2' 4 3' 7' 9 4 2 6' 1 8 1' 4' 7' 8' 10 9 3
0.0 9.18 18.37 18.37 22.04 36.74 55.12 0.0
0.0
0.92
C,0H2,SO,, Fig. 3 0.92
3.68 12.9 22.1 22.1 25.7 40.4 58.8 3.68 3.68 6.66 7.34 3.68 10.7 10.7 17.7 23.4 6.53 6.66 6.66 6.66 7.35 7.34 7.34
~c ~c
~c ~c
c~ ~c
c~
7.02 7.02 14.05 19.67 0.0
cg c$ {c
cg lc
cg
c¢
1.66 1.84 0.92 ~c
1.07 1.39 1.66 1.94 0.92 1.84 2.14
1.67 1.83 0.92 ~c
3.33 2.50 1.67 0.83 4.58 1.83 0.92
E x p e r i m e n t 13.25°C. (CH3)4N 4'
I
0.0
i
0.0
4
I
"
[
"
0.62 1.28
0.61 1.22
E x p e r i m e n t 14.40°C. N a 3
0.0
0.0
8
"
8" 2
" 11.65
" " "
0.33 1.63 3.27 0.33
0.33 1.64 3.28 0.33
0.060 0.113 0.149 0.149 0.160 0.201 0.243 0.060 0.060 0.082 0.086 0.080 0.104 0.104 0.133 0.153 0.081 0.082 0.082 0.082 0.086 0.086 0.086
0.325 a 0.408 0.462 0.459 '0.481 0.531 0.562 0.325" 0.325 ~ O. 352~ O. 351~ O. 325~ 0.388 ~ 0.385" 0.429" 0.459 a 0.356 ~ 0.352 ~ 0.352 ~ O. 338~ 0.357 • 0.351 ~ 0.356 ~
0.050 0.071
0.318 ~ 0.342 ~
0.036 0.081 0.114 0.114
1.11 b 1.25 b 1.44 b 1.50
C14H29SOa 2.46 5.05
C,~H2~SO3 1.31 6.53 13.07 13.0
t h e f i g u r e s , is d e f i n e d t o b e e q u a l t o t h e s u m of t h e c o n c e n t r a t i o n s of paraffin-chain salt, nitrate salt, and bromoacetate salt plus three times the c o n c e n t r a t i o n of t h e t h i o s u l f a t e s a l t . I n t h e a b s e n c e of m i c e l l e s t h e c o n c e n t r a t i o n s u m is e q u i v a l e n t t o t h e i o n i c s t r e n g t h .
PRIMARY
SALT
EFFECTS
WITH
PARAFFIN-CHAIN
0.540"$E:~OATA OF A.KISS AND P.VASS i(~ EXPERIMENTAL DATA WITHOUT NITRATE ION
~
O~O0"'EX"RI""TAL OATAWTH HITN.T, ON o...
SALTS
J
81
j
~
•~
O.46
o,2 0.44
•
o~s
0.40
0
O,:N~
~
031 O.32 03C O.Zl 02E 0240
0.02
0.04 GOS O.OS 0.10 GIE SQUARE ROOT GONGENTRATIONSUM
0.14 OJ6 O.IS (moles/ llfle) I/2
O.ZO
0.24 (~26
O.Z2
FzG. 1. Rate constants for reactants w i t h and without nitrate ion at 25°C.
J J
/
'8[,~0ATA0 ..... .AND .... . ....
° .......
o....
T.T,o.
"
16 I
~"15f
~ 1.4
=
I.I
1.0~"
0
.
.
.
0.02
.
.
.
.
I
;
T
I
'
I
t
I
I
'
[
0.04 0.06 0.08 0.10 O,t2 0.14 0.16 O.IS ~ 2 0 SQUARE ROOT GONGENTRATtONSUM (moles/ liter)'"
I
~
0.22
I
I
I
I
I
0 2 4 026
FIG. 2. Rate constants for reactants with and without nitrate ion at 40°C.
Reactants and Simple Ions One or more runs of each experiment contained no paraffin-chain salt. When the results from these runs were compared with each other on a single rate constant versus ionic strength graph, the average spread of the results was a b o u t 3 To (Figs. 1 and 2). The lower solid curve represents the results of Kiss and Vass (10) using solutions which contained only reactants. T h e upper solid curve represents their results where increasingly larger amounts of nitrate salt were added to a constant (0.00125 M) concentration of reactants. T h e reactant concentrations employed here for all the runs indicated by black dots were not the same, although most of the reactant concentrations were nearly the same (0.001 M).
82
J, A, ERIKSON AND E, C, LINGAFELTER
e
0.56 NUMBERS REFER TO RUN NUMBERS 054 ] ~ IRGREASlI'+¢ F~IUaLRI~I~'IIJ,IT ¢¢RGE.TRA.,.IORE 052 o . . + . . ' T O=O,:.TR.'.OR +.R..+,+," +,+ ,. RU. + QSC ARONOClol-lttS03CO.CENTRE'ION mCnmAS~O 0 RE.°-,.+,,,.,.~,.=','R.,O, 0=,=~T+'+,.RU.+
"| 0 4 £
ANDNONO3.GO~
~ o~
®
/ ~+
/
J
®/
/
/
~ O4~
~- Q42 04C
Q3fi ~o~ 034 Q32
~ o~ o2a Q2e
, , / . ,.. • . . . . . . . . . . . . . . . , • Q02 Q04 0.06 O.OS O.IO 0.12 0.14 0.16 0.18 0.20 0.22 O.24 SQUARE ROOTGONGENTRATt© SUM (~I (nlOhll/ liter]I/z
024 o
Fro. 3. Comparison of the rate constants from solutions containing decanesulfonate ion and similar solutions containing nitrate ion.
+-
Reactants with Para~n-Chain Ions
In solutions of paraffin-chain salts which did not contain micelles, especially with sodium decanesulfonate (Fig. 3), no change in the rate constant was observed if paraffin-chain ion were substituted for nitrate ion. This indicated that in spite of the very different nature of the paraffin-chain ion compared with the nitrate ion, these singly charged ions influence the thiosulfate-bromoacetate reaction in the same manner.
Reactants with Micelles Three experiments, 3, 5, and 14, demonstrated that the rate constant at 40°C. was slightly increased as reactants of equal concentrations were reI ~ I E ~ R $ REFER TO RUNS OF (XPF.RIMF.I/T 5
1.80 1.70 1.60
t.40 0
,~ ' ~+' + ' ~ , ' , ~ ' ,~' ~' ,~ ' + ' mo GOlIGIENTRATIOOF N SODIUI4000~ANI[$ULFONATI[ (miNilM4u/litlrl|
FIG. 4. Variation of the rate constant when reactants are replaced b y sodium dodecanesulfonate at 40°C.
PRIMARY SALT EFFECTS WITH PARAFFIN-CHAIN SALTS
83
placed by an ionic strength equivalent amount of sodium dodecanesulfonate. The results from the more elaborate experiment are shown on Fig. 4. An earlier experiment (1) likewise indicated this increase, but the results are in error and the increase should not be as much as is recorded. The corrected results and the old results are shown together on Fig. 5. The primary error was caused by calculating the rate constants with the method for equal reactant concentrations, even though the reactant concentrations were slightly different. This method has been recommended for this situation by Daniels, Mathews, and Williams (11). The corrected rate ORIGINAL VALUES CORRECTED VALUES
2.10
200
| e
| Lgo
O
=-" 1.8o ~
1.70
. . . . . . .
I
,,,
4 6 B I0 12 I 16 ¢0NCENTRATIONOF THE SODIUMDODECJlNESUt.FONATE ( m ~ t l h e r )
0
18
20
FIG. 5. Variation of the rate constant when reactants are replaced by sodium dodecanesulfonate at 40°C. 056 0.54 0.52
N~RIBERS RIrFER TO RUN NUMBERS (~ FXPERIMIrNTALVALUES ~
o
~ ~o ~o.,~ s
0.44 0"42 0.40 038
;
~) .
036
034 o 0.32
)
J
~
=: 0.30 O28 0.26 024
./
. . . . . .
0,02
i
i
i
i
i
i
.
.
.
.
.
.
.
.
.
0.04 0.06 0.08 0.10 0.12 QI4 0.16 0 . 1 8 0.20 SQUARE ROOT OONGI[NTRATIONSUM ( molls / lltlr) I/;[
.
.
0.22
0.24
FIG. 6. Rate constants at 25°C. for various solutions of (CH3)4NC.H~S03 containing a constant amount of reactants.
84:
J. A. ERIKSON AND E. C. LINGAFELTER
constants have been recalculated taking into account this slight difference in reactant concentrations b y the method already described. The addition of tetramethylammonium tetradecanesulfonate to a constant amount of reactants resulted in an increase in the rate constant which, from a comparison with the results of Kiss and Vass, appeared to be nearly the same as if an ionic strength equivalent amount of equal concentration reactants had been added instead. This was demonstrated b y experiment 8 (Fig. 6) and also b y runs 3, 10, 9, and 4 of experiment 11. Within experimental error, these data are in agreement with the above-mentioned slight increase in the rate constant produced b y replacing reactants with paraffinchain salt. NUIMIERSR~FER TO RUNS OF EXPERIMENT 4
i
0.47
t
®
E a4~
®
0.~
O
~o.,~ O.43 0
. .~. . ., . .
~
COf~PJ~TN/mONOF ~
~,'
~
'o',
,2'
'
,:,'
~' , , ~ '
[nNIIIIl~es/ I l i a )
Fzo. 7. Variation of the rate constant when nitrate ion is replaced by dodecanesulfonate ion at 25°C.
@~
o.39c
0.3 e(
,
0
,
i
I
,
2 4 GORGENTRATIO~I OF |GH3)4NCt4R2~O~
i
,
6 (mliRmotes/ l i t e r )
,
8
=
i..
I0
FzG. 8. The rate constant when NO3- is replaced by C14H29SO3-at 25°C. in experiment 2.
PRIMARY SALT EFFECTS WITH PARAFFIN-CHAIN SALTS
85
Nitrate Ion with M icelles If nitrate salt were replaced by the equivalent amount of paraffin-chain salt, the rate constant decreased; the decrease was somewhat more than the increase noted above. This was observed with tetramethylammonium dodecanesulfonate at 25°C. (Fig. 7) and with tetramethylammonium tetradecanesulfonate at both 25°C. (Figs. 8 and 9) and 40°C. (Fig. 10). These data are not in disagreement with the data in which an increase was observed, since the primary salt effect produced by nitrate salt is greater than the effect produced by an ionic strength equivalent amount of reactants. The difference of 0.0075 min. -1 between the two groupings of the results in e x ()
NUMO~R$REFERTO RUNSOF EXPERIMENT7' THE FOLLOWINGGONGENTRATIOSU~ fl WERE S .41E.0 0.139 O AND 0.145. :
0,47 ~ - ~ - -
0.46
~
U
0.45
~s.~s
0,44 0.43 ~ 0.4 _
.
.
0
.
.
.
.
l
2 4 6 8 I0 CONCENTRATIONOF TETRADEGANESULFONATE
I
~ I (miII~oI~s / liter}
I
FIG. 9. Variation of the rate constant when nitrate ion is replaced by tetradecanesulfonate ion at 25°C. 1.9
NUMBERSREFERTO RUNSOF EXPERIMENI I I CONGENTRATIONSUMSOF OA35ANDO.173WI[REU~EO
I.S s
1.6
!
,
0
.
.
.
.
.
.
,
.
.
.
.
.
.
.
.
.
2 4 6 8 I0 12 14 CCNGENTRATIOHOF TETRAO4EGANESULFONATIE
.
.
,
~, 18 20 ( millimcles/lilf|
,
,
,
22
FzG. 10. Variation of the rate constant when nitrate ion is replaced by tetradecanesulfonate ion at 40°12.
86
J. A. ERIKSON AND E. C. L I N G A F E L T E R
periment 2 (Fig. 8) is believed due to a systematic error, since the lower group of runs was performed two days after the higher group. DISCUSSION
The indifference of the rate constant to the presence of micelles, in solutions containing micelles, can be crudely predicted from the theoretical behavior of the rate constant in solutions containing simpler complexes. Since theoretically the rate constant is a function of the ionic strength, it will be sufficient to calculate only the ionic strength of solutions containing singly, doubly, triply, etc., charged ions in various degrees of association. In order to keep the calculations simple, only two ionic species will be considered to be present in each solution; the singly charged positive ions, and the complex anions containing singly charged positive and negative ions. In the case of a solution containing a neutral aggregate, only the neutral aggregate will be present. A solution will, therefore, contain either the ions M + and M ~ .... , or the neutral molecules M~km; where m is 1, 2, 3 , . . . , n is 0, 1, 2 , . . . , and for each solution n is equal to, or less than, m. It will be assumed that all the solutions can be constructed from a single solution, 0.02 M in MA. The concentration of the M ~ "-~ complex is (0.02) (I/m), and the concentration of the M + ion is 0.02(1 -- n/m). The ionic strength for a given solution is u
(0.01) (l/m) (m -- n) (1 + m -- n).
.=
[12]
The degree of neutralization of the charge of the complex ions is given by n/m. Figure 11 is a graph of the square root of the ionic strength for various degrees of association of the "monomer," dimer, trimer, etc. The lines r
G2
~%
9
i 0
II
I
I
I
OEWI[E OF AG$iOCUI,TIC$i
I him
FIG. 11. T h e o r e t i c a l i o n i c s t r e n g t h s for s o l u t i o n s 0.02 M of MA, w h e r e t h e r e a c t i o n A~ "--'~ -t- m M ÷ --~ M.A,~ '~-'~ -'I- (m -- n ) M + h a s g o n e t o c o m p l e t i o n .
PRIMARY SALT EFFECTS WITH PARAFFIN-CHAIN SALTS
87
result from considering n as a continuous variable, but only the points represent physically possible solutions. An empirical line correlating an "ionic strength" for a micelle containing approximately 50 or 60 paraffinchain units is assumed to be in the location labeled "micelle?". This particular location is assumed in order to correlate the effective ionic strength of a micelle having a degree of association of approximately 0.8 to 0.9 with the results of this research: that the rate constant of the reaction in a solution containing micelles, is comparable to the rate constant of the reaction in a hypothetical solution containing the same amount of completely dissociated paraffin-chain salt. This line does not appear out of position when compared with the lines for the simple ions, even though the ionic strength principle is not valid in this region. McBain (12, 13) regarded the charges on the exterior of the micelle to be too widely spaced to exert a mutual and therefore large effect, and concluded that ionic effects of solutions of micelles would not be much different from those of uni-univalent electrolytes. The conclusion drawn from the experiments of this research regarding the ionic effects of paraffin-chain salt solutions is that the ionic effects of the charged micelles are quite large, at least large enough to compensate for the decrease in ionic effect due to the simple ions that have associated to form micelles. The net effect of this compensation is that the influence of these paraffin-chain salt solutions containing micelles on the ionic reaction is approximately the same as if the paraffin-chain salt were behaving as a uni-univalent electrolyte. It appears, therefore, that the activity coefficients of simple ions of charge of the same sign as the micelle charge, in solutions of paraffin-chain salts which contain micelles, have a value which is not much different from the value that they would have in a hypothetical solution containing a completely dissociated paraffin-chain salt of the same stoichiometric concentration. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
ERIKSON, J. A., AND LINGAFELTER,E. C., jr. Colloid Sci. 4, 591 (1949). HARTLEY, G. S., Trans. Faraday Soc. 31, 31 (1935). LA MER, V. K., jr. Am. Chem. Soc. 51, 3341, 3678 (1929). WYATT,P. A. H., AND DAVIES, C. W., Trans. Faraday Soc. 45,774 (1949). LAMER, V. K., J. Am. Chem. Soc. 63, 2832 (1931). LAMER, V. K., AND FESSENDEN, R. W., jr. Am. Chem. Soc. 54, 2351 (1932). RAY, S. K., AND BHATTACHARYA,R. 1~., J. Indian Chem. Soc. 13, 456-463 (1936). BRADBURY,J. H., Trans. Faraday Soc. 49, 304 (1953). HAHN, F. L., Anal. Chim. Acta 4, 573 (1950). KIss, A., AND VASS, P., Z. anorg, u. allgem. Chem. 217,305 (1934). DANIELS, F., MATHEWS, J. H., AND WILLIAMS, J. W., "Experimental Physical Chemistry," 3rd ed., p. 169. McGraw-Hill Book Co., New York and London, 1941. 12. McBAIN, J. W., J. Am. Chem. Soc. 50, 1639 (1928). 13. McBAIN, J. W., AND BETZ, M. D., jr. Am. Chem. Soc. 57, 191 (1935).