NOTES
1672
off at the other. Two side arms with joints and breakseals were attached to the main tube. Into the center tube was placed 0.2929 g. of the AgzS04-Ca0 mixture. After attaching the tube to a vacuum line and evacuating it, the tube was sealed off. The reaction tube was then heated at 500’ for 45 minutes. Previous rate studies indicated that the reaction was 25% complete at this time. The reaction tube was then removed from the furnace and chilled quickly. It was attached to the vacuum system by means of one of the side arms and the system was evacuated. The break-seal was broken and the oxygen which had been liberated by the reaction was collected in a sample bulb by means of a Toepler pump. The reaction tube was again evacuated, sealed off and placed in the furnace. After eight hours, at which time 40% of the material had reacted, the bulb was again chilled and evacuated. The oxygen sample was collected as before. The 34 to 32 m/e ratios for the two oxygen samples were determined with a Consolidated-Nier ratio-type mass spectrometer. Values of the 34/32 ratio obtained were 0.004589 and 0.004574 for the first and second samples of oxygen, respectively. These values are the same within the accuracy of the instrument. If the diffusion of oxygen were the rate-determining step in the reaction, the 0 1 6 would have diffused fafiter than the 0‘8,equivalent to the square root of 16/18,* and it should have reacted faster than the 0 1 8 . The second sample of oxygen coming from a later part of the reaction should have been depleted in Ole and enriched in 0 ’ 8 .
Vol. 61
A COMPLEX ION FORMED FROM BISMUTH AND IODIDE IONS’ BY LoIs J. FROLEN, WILLIAMS. HARRIS AND D. F. SWINEHART Department of Chemistry, University of Oregon, Eugene, Oreoon Receiued August 8 , 1967
I n solutions strongly acidic with sulfuric acid and relatively concentrated in iodide ion, a small amount of bismuth produces a yellow-colored COGplex ion with an absorption maximum a t 4600 A. This complex ion has a Jarge molar extinction coefficient (9200 a t 4600 A.) and has been used for many years t o estimate small amounts of bismuth colorimetrically.2 The characteristic absorption band a t 4600 A. is shown in Fig. 1. 0.5
where IC = ?r2D/a2. D is the diffusivity and a is the particle size. Meson’s graph may be approximated up to X = 0.25 by X
=
Alkt
(2)
and it may be approximated from X = 0.25 to X = 0.40 by X = A& + B (3) Assuming D16 = (18/16)1/2D18, then kid
=t
(16/18)’/Zk16t
(4)
The value of k 1 ~ tis found from Mason’s curve using the total fraction of material reacted (X0.25 and Xo.40) and h a t is calculated using equation 4. Equations 2 and 3 then give the value of X18 at 1 1 6 7 0.25 and 0.40. Using these relationships, it is found that if the ratio O18/Ola were 0.004589 for the first sample, it should be 0.004920 for the second. This difference could have been determined easily with the mass spectrometer used. Since no such enrichment wa8 obtained, it is concluded that the diffusion of oxygen in the solids is not the ratedetermining process, and the hypothesis that the rate-determining step is the diffusion of the silver ion2is thus strengthened. This method of determining whether or not the diffusion of oxygen is rate determining may find applications in the study of the kinetics of other reactions. The author is pleased to acknowledge the advice of Professor Farrington Daniels and the cooperation of Dr. William P. Riemen. He is grateful to the National Science Foundation for a fellowship. (3) This is only approximately correct and ignores several vibrational frequencies of the reacting atom and the activated complex which tend to cancel. See J. Bigeleisen, ibid.,56, 823 (1952). (4) H. F. Mason, ibid., 61, 796 (1967).
7
0.4
Mason4 has published a graph of the fraction, X , of material reacted in a solid-solid reaction vs. lct obtained from the equation
I
I
I
I
I
9
0.3
3 -E: 8
4
0.2
0.1
t 3000
Fig. 1.-Each
5000
4000
6000
(A).
solution was 1.0 nz in HZS04, 0.050
IC1 and 0.001 m in NazSOa: o, 0.0 m bismuth; A, 5 X m bismuth; 0,20 x 10-6 m bismuth.
rtl
in
The present investigation had its inception in an attempt t o establish the formula and instability constant of this complex ion using the method of continuous variations.as4 It immediately developed, however, that such a study could not be made because, when solutions approximately 0.1 m in Bi+++ and I- were mixed in 1.0 m HzS04, a black precipitate was formed which presumably was Bi13. On using more dilute solutions it was found that (1) Taken in part from research performed by L.J. F. and W. S. H. while they were undergraduates at the University of Oregon. (2) E. E. Sandell, “Colorimetric Determination of Traces of Metals,’’ Interscience Publishers, lnc., New York, N. Y.. 1944, P. 161. (3) Job, Ann. Chim., [lo] 9, 113 (1928). (4) W. C. Vosburgh and G. R. Cooper, J . A m . Chem. Soc., 63, 437 (1941)
1673
NOTES
Dee., 1957 with concentrations equal to 1 X 10+ m or less, equimolar solutions of Bi+++ and I- (in strongly acidic solutions) could be mixed without formation of a precipitate, but no visible yellow color was formed. Absorption spectra for such mixtures are shown in Fig. 2. These curves are similar in form to those in Fig. 1 except th$ the absorption maximum now appears at 2800 A. Since HzS04, "01 and NazSOa absorb in this region, these solutions were made 0.5 m in HClOd and 0.025 m in HsP02, the latter to prevent the appearance of free iodine by atomospheric oxidation of iodide ion. It was evident that a new complex ion was formed under these conditions and its formula and instability constant have been established by spectrophotometric methods. Experimental Solutions were prepared from reagent grade materials and distilled water with a conductivity of 1 X mho. Solutions of bismuth perchlorate were prepared by weighing Biz03and dissolving in HC1O4. Solutions of KI were prepared by weighing KI directly. For the application of the method of continuous variations, stock solutions of bismuth perchlorate were prepared, 2 X 10-8 m in Bi+++,0.5 m in HClO4 and 0.05 m in HsPOa. The iodide solution was 2 X m in I-, 0.5 m in HClO4 and 0.05 va in HsPOe. These solutions were mixed, x ml. of the bismuth solution and (50 - x) ml. of the iodide solution and diluted to 100 ml., yielding the sum of the bismuth and iodide concentrations constant at 1 X 10-8 m and the HC104 and H3P02concentrations at 0.25 and 0.025 m, respectively. For the measurement of the instability cdnstant, the final stoichiometric concentrations of iodide ion, HClO4 and HaPO2were 3.9 X 1.0 and 0.01 m, respectively. T h e bismuth ion concentrations were varied between 1 X 10-4 and 0.1 rn. Absorbance was measured at 2800 A. Measurements were made on a model DU Beckman spectrophotometer using 1.00 cm. quartz cells. No attempt was made to thermostat the solutions. Runs were made at room temperature (25 i 3").
Results Figure 3 shows the results of the application of the method of continuous variations at three wave lengths. Clearly the bismuth and iodide ions react in a stoichiometric ratio of 1:1. Assuming one bismuth ion per complex, the formula must be BiI f f . No state of hydration can be inferred either from these data or those taken to estimate the instability constant and the formula is written in the anhydrous form. The instability constant was estimated by holding the total iodide ion concentration constant at 3.9 X 10-4 m and varying the bismuth ion concentration. The data are shown in Table I.
7
0.4
0.3 ai 0
8
e53 0.2 2 0.1
2500
3700
3300
2900
x (A).
Fig. 2.-Each solution was 0.50 m in HC104 and 0.025 m in HaPOs: 0,1 x 10-3 m bismuth, 0.0 m iodide; A,0.0 m bismuth, 1 x 10-3 m iodide; 0 , 2 x m bismuth, 8X m iodide; 0,5 X m bismuth, 5 X m iodide.
0.18
1
1
1
1
1
I
I
1
20 30 40 50 Bismuth soln., ml. Fig. 3.--Method of continuous variations applied to the Bi+++-I- system a t low concentrations. The bismut>h solution was 2 x 10-8 m in Bi+++, 0.5 m in Helo4 and 0.05 m in H8P02. The iodide solution was 2 X loba m in I- and 0.5 m and 0.05 m in HClOd and HJ'Oz, respectively. x ml. of the bismuth solution was mixed with (50 - 2) ml. of the iodide solution and the whole diluted to 100 ml.: 0 , a t 2700 A.; 0,at 2800 A.; A , a t 3000 A. 0
10
bound as complex ions, ie., that the concentration of the complex was 3.9 X 10-4 m. From this asESTIMATION OF THE THE COM- sumption and the measured absorbance, the molar extinction coefficient of the complex ion was calcuConcn. of lated to be 785 a t 2800 8. From this value, the Bit++ Concn. of Concn. of original), Absorb- complex, Concn. of I-, B i t + + , Ki.,t. concentrations of the complex ion were computed 'mile/l. ance mole/l. mole/l. mole/l. X 104 for the other three solutions using the measured 0.10 0.306 3 . 9 X 10-4 .. .. . . . . 0.10 .. absorbances. The equilibrium concentrations of .010 ,299 3 . 8 X 10-4 9 x 10-8 9 . 6 X 10-8 2 . 3 iodide and bismuth ions were then computed by ,0010 ,225 2 . 9 x 10-4 1.0 x 10-4 7.1 x 10-4 2.4 .00010 . O M 5 . 9 x 10-5 3 . 3 x IO-' 4.1 x 10-1 2 . 3 difference. These quantities yield the values of the instability constant, shown in the last column of Since the absorbance changed very little when the table, for the reaction the bismuth ion concentration was changed from BiI++ = Bi+++ + 10.010 to 0.10 m,it was assumed that at the latter It is interesting to note that complex ions of a coiicentration the iodide ions were quantitatively TABLE I INSTABILITY CONSTANT OF PLEX ION BiI++
1674
NOTES
similar type have been observed between bismuth and bromide ion,6 between bismuth and thiocyanate ions,6 and between iron(II1) and thiocyanate ions . 7 3 (5) Babko, Uniu. eta1 Xisv, Bull. Sci. Rec. Chim., 4, 81-100 (Russian), 103-105 (English translation) (1939). (6) W. D. Kingery and D. N. Hume, J . Am. Chem. SOC., 71, 2393 (1949). (7) 8.2. Lewin and R. 5. Wagner, J . Chsm. Ed., SO, 445 (1953). (8) H. 6. Frank and R. L. Oswalt, J . Am. Chem. SOC.,69, 1321 (1947).
SPECTROPHOTOMETRIC DETERMINATION OF 1:l COMPLEXES. INTERFERENCE OF HYDROLYSIS BY MICHAELARDON* Department of Physical Chemiatry, Hebrew University, Jerusalem, Israel Received June 6, 1967
Benesi and Hildebrand' developed a spectrophotometric method for the detection of 1 : 1 complexes and the determination of their equilibrium constants. McConnell and Davidson2 applied this method to aqueous metal-ligand complexes, of the type M 1 A 1 . They used the expression ab a n =1 -s+
1
(El
- E0)Kl
(1)
where a and b are the formal concentrations of the ligand and the metal, respectively, (a >> b). eo and el are the molar extinction coefficients of M and MIAI, respectively. K1 is the equilibrium constant, KI = [ M I A 1 ] / [ M ] [ A ] . D is the optical density of the solution. D' is the optical density of the solution sans ligand. If MIAl is the only complex in the solution one observes a linear dependence of ab(D D'] on a. In this case one can determine the value of el (from the slope) and the value of K1 (from the slope to intercept ratio). It was assumed in the above derivation that hydrolysis of the metal ion M+"is negligible. Lately314 this method was extended to the case where the first hydrolysis product M(OH)+(" - l) cannot be neglected. Burns and Whiteker3 derived an expression which includes the first hydrolysis constant KIH = { [ M ( O H ) + ( " - l)] [H+]]/[M+"] and the molar extinction coefficients EM and EMOH of M+" and M(OH)+(" - '1, respectively. While the hydrolysis constants of many metal ions are available from potentiometric measurements, the values EM and EMOH must be determined spectrophotometrically before the suggested method can be used. It will be shown here that (a) no prior knowledge of EM and EMOH is necessary for the evaluation of K1 and el, (b) the original method (1) can be applied for the general case where the solution contains all the possible monomeric hydrolysis products M+n, M(0H)+(" - l) . . , M(OH),+(" - m) and that only the hydrolysis constants must be known in advance. * Department of Chemistry. Cornell University, Ithaca, N.Y.
-
(1) H. A. Benesi and J. H. Hildebrand, J . A m . Chsm. Soc., 71, 2703 (1949). (2) H. McConnell and N. Davidson, ibid., 73, 3184 (1950). (3) E.A. Burns and R. A. Whiteker, ibid., 79, 866 (1957). (4) M.Ardon, J. Chem. Soe., 1811 (1957).
Vol. 61
Let us define [MT] as the total concentration of all free (uncomplexed) metal species. If no polymers exist in solution we get [MT] = [M+"]
+ + + By use of the hydrolysis constants K I H K ~.H. .
[M(OH) +(n - '1
[M(OH)m+("
m)].
. . . K,H (where K ~ H= [M(OH)i+(" - "1" [H+]/[M(OH)~+I+(~ - + I)]) we get the expression
KiH
It is seen from (2) that [M+n]/[M~]is constant if [H+] and ionic strength are kept constant. By similar reasoning it can be shown that all the fractions [M(OH)(+cn- i)]/[M~]are constant and therefore we can treat MT as one specimen (at constant [H+] and ionic strength). It follows that one can use the original function (1) and get ab -=-
1
a
D - D' e~ - eo -l- ( e l - eO)K where eo is defined at D'/[MT]. From the slope, one can measure el directly and from the ratio of slope to intercept one can measure K. K is the over-all equilibrium constant K = [M~AI]/[MT][A]. I n order to evaluate the true constant K1 = [MIA&' [M+n][A] we express!K in terms of KI and KiH with the aid of (2) and get the general expression ab
-==+
a
KIH l + - -[H+] +-
K~EKOH [Hf]?. + * " Kl(E1 - eo)
+
K I A . .. . K ~ E [H+I" (3)
in the special case* where all but M+n and MOH +(" - are negligible we get
KH
a
ab
-
jaq KI (a - E O ) l+
In order to ascertain that only M + n and none of the hydrolysis products combine with A to give MIAl one has to prove experimentally that K I remains constant at different H+ concentrations (but equal ionic strength). ELECTROMOTIVE FORCE STUDIES I N AQUEOUS SOLUTIONS OF HYDROCHLORIC ACID AND D-FRUCTOSE BY H. D. CROCKFORD, w. F. LITTLE A N D
w. A. W O O D
Contributed from the Venable Chemktrft Laboratory of the Universitu of North Carolzna, Chapel Hill, North Carolina Received October 4, 1966
This paper is a continuation of the studies being carried on in this Laboratory on the effects of mixed solvents on the thermodynamic properties of hydrochloric acid solutions. In this study electromotive force measurements have been made on the cell HP(HCl(m), D-fructose($), H20(y)[AgC1-Ag
a t 25' and in 17 and 25% by weight n-fructose solutions and with acid molalities from 0.01 to 0.20 m. The standard cell potentials, the activity coefficients
