NOTES
696
Vol: 61
image changed from 0.016 rm. at, 10,000 r.p.m. t,o 0.010 cm. a t 55,000 r.p.rn., while that of the DNA boundary decreased only 0.003 cm. under the same conditions. Part of the dccreawd width of the DNA boundary must he attrihuted to the strong concentration dependence of sedimentation coefficient of DNA. If the crntrifugal forcc a t low spccd werc sufficient to overcome the surface tmsion of the meniscus, the decrease in the width of the meniscus image would have hem somewhat smaller than the decrease in the width of the DNA boundary. That the contrary was found to be the case indicates that at low speed the offect of residual surface tension is manifested a t the meniscus, and that the radius of curvature of the meniscus may be measurably less than the radius of rotation. Thus the effective meniscus position a t which the Archibald mcthod applies may differ, in general, from the center position of the image of the meniscus. As shown by the typical example in Table I, the extrapolated concentration gradient a t the meniscus, hence the molecular weight, is inaccurate by 1%, when an error of 0.001 cm. is allowed in the calculation of the meniscus position. Therefore, because of the surface tension effect alone, the reliability of the molecular weight values obtained by the modified Archibald method is greater for experiments performed at high rotor speeds.
dilute acid is not a partially hydrolyzed one, such as tjhe SnO++ we originally proposed,' but rather is SnS04++. I n addition, our earlier work was based on data on the dissociation of sulfuric acid which appear t o be incorrect in the light of recent studies by Smith.3 Carter4 has suggested that the first spectral change corresponds to the formation of SnSOr++ and has based his argumeats on the sulfate ion concentrations found by Smith.8 However, since our later work showed that, even in very dilute sulfuric acid, SnS04++is the principal species, still another interpretation had to be sought. We now believe that the two spectral changes, which we observe as the sulfuric acid concentration is changed from 1 to 17 M , correspond to the complex formation steps SnSO,++ + sod- = Sn(SO&(aq.) Ki (.I) Sn(SO4)~(aq.) f HsSO, = H2Sn(S04)daq.) K2 (2) Indeed, if we can accept our findings concerning SnS04++ and the evidence6 on the probable existence of the tris-(sulfato) complex in concentrated sulfuric acid, we could scarcely escape such conclusions. Consider, first, reaction 1. We write the equilibrium constant expression
TABLE I REFRACTIVE INDEX-GRADIENT CURVEOF BOVINESERUM ALBUMINSOLUTION'
where y * is the mean activity coefficient for the 2-2 electrolyte (SnSO4++)(SOa). We noted' that the extinction coefficient, €2, of the second species must be much,less than, el, of the initial species. Then in less than 4 M sulfuric acid (Le., when there is negIigible H2Sn(SO&) we see that since
r,
om.
AI,
cm.
Ordinate, cm. adc/dr
A(dc/dr)/ (dc/dr)
5.987 0.126 -0.026 0.6 5.961 0.247 -0.025 0.5 5.936 0.428 -0.025 0.4 5.911 0.648 -0.025 0.3 5.886 0.867 - A 1% protein solution in 0.15 1cf NaCl and 0.05 M sodium acetate buffer, pH 4.4, was centrifu ed at 8,500 r.p.m. for 32 min. " h e curve was obtained by t f e schlieren optical system equipped with a phase plate.'
Acknowledgment.-The author is indebted to Dr. L. G. Longsworth for his critical examination of the manuscript and to Professors G. Munch and J. E. Snoke for making their instruments available.
Dobsd/O.l(Sn'v) Cobid O.lel(SnSOd++)
and (SnrV) % (SnSOd++)
+ (Sn(SO4)d
then, 4. 1 1 1 =; -k ; KdSO4-)1/'r bbsd
(4)
is the observed optical density, 0.1 is the length of cell path and (SnIV) is the total tin(1V) concentration. (6) R. Trautman and V. W. Burns, Biochim. BiOphya. Acto, 11, Following the reasoning we have previously em26 (1954). pIoyed,2 we estimate the empirical correction constants! cyl2, and obtain yl, the corrected activity coefficients for (SnSO4++)(SO4-) from y ~ the , activity coefficients of a typical "pure" 2-2 eleotrol SULFATE COMPLEXES OF TIN(1V) lyte. Then y1 are converted to y*, the activity BY CARLH. BRUBAKER, JR. coefficients on the molar scale (Table I). Rsdris Chemical Laboratory,,Michigan 8 l d s Univsraity. Baed Our values of €.bd a t 240 mp are taken from the Lansrng, Mich. earlier work' and are given in Table I, column 9. t..,4 Rscdued December 4, 19.56 Now according to equation 4, we plot l/eobad I n an earlier paper' we described the changes against (SO4-) yz* (Fig. 1) and find a reasonably which occur in the ultraviolet absorption spectrum good straight line. We obtain €1 = 2.5 X lo8 of tin(1V) solutions as the sulfuric acid concentra- and Rt = 1.9 X lo2. tion is varied and an interpretation of these changes Previously we had estimated e1 = 1.6 X loa was offered. However, l a t c ~work2 indicat,ed that on the basis of spectrophotometric examinations the predominant spocics of tin(1V) present in (3) H. M. Smith, I'h.D. thesis, University of Chicago, 1949. (1) C. H. Brubakor, Jr, J . Am. Cham. SOC., 16, 4269 (1964). (2) C. H.Brubaker, Jr., ibid., 71, 5285 (1055).
8
Dobsd.
(4) P. R. Carter, piivate communication. (6) R. F. Weinland and € Kuhl, I. Z . anoro. Chem., I C , 244 (1907).
c
r
NOTES
May, 1957
OBSERVED
3.48 3.19 2.24 1.80 1.50 1.35 0.910
697
TABLE I MOLAREXTINCTION COEFFICIENTS, SULFURIC ACIDCONCENTRATIONS, ACTIVITYCOEFFICIENTS DERIVED QUANTITIES FOR 1.65 X 10-8 M Sn(1V) I N SULFURIC ACID 1.13 1.03 0.703 .554 .450 .400 ,248
6.70 6.02 3.98 3.12 2.56 2.26 1.45
0.0364 .0368 .0434 .0488 .0543 .0590 .0759
0.174 ,157 .130 .124 .124. .123 $130
0.067 .069 ,078 .085 .091 ,093 .lo5
0.102 .096 .089 .090 .093 .096 .lo7
AND VARIOUS
0.119 .llO .097 .097 ,099 ,101 .llO
0.648 0.743 1.02 1.33 1.41 1.51 1.56
In the course of studies of the mutual solubility of partially miscible solids it became necessary to measure the variation of lattice constant with composition for solid solutions of potassium bromide in potassium iodide. The only previous values of lattice constants in this system are those of Havighurst, Mack and Blake,2 but the range of compositions studied was very limited and the data inconsistent and meager. These two salts form an incomplete series of solid solutions at room temperaturea but their mutual solubility increases to complete miscibility at temperatures well below the melting point.4 By quenching molten mixtures of the two salts it is easy to obtain solid solutions over the entire range of composition at room temperature 0 2 4 6 8 10 12 14 16 even though the solids in the large central portion of (S04-)y,' x 108. this range are then metastable. Fig. 1.-The deDendence of the observed molar extinction Reagent grade otassium bromide and potassium iodide coeifficient on sulfate ion activity.
of tin(1V) in perchloric acid, but in view of our later findings that SnS04++ is the predominant species in dilute sulfuric acid, we can hardly expect the limiting molar extinction coefficient, €1, in sulfuric acid to be the same as is observed in perchloric acid. In view of the values of the activity coefficients for 2-2 electrolytes and the fact that there is necessarily some uncertainty in the correction of them, we should probably accept €1 and Ki as representing orders of magnitude only. However, we have found that the treatment is not particularly sensitive to the magnitude of y+ and thus the scatter (Fig. 1) is probably experimental. Thus it seems safe to conclude that the &st spectral change does correspond to the formation of Sn(SOS2 from SnS04++ and that the equilibrium constant is about lo2. The second spectral change should correspond to equation 2 and the interpretation which was offered in the previous work will still apply. This work was supported by the U. S. Atomic Energy Commission.
LATTICE CONSTANTS O F POTASSIUM BROMIDE-POTASSIUM IODIDE SOLID SOLUTIONS' BYEUQENEI T. TEATUM A N D NORMAN 0. SMITH Deparfmenf 01Chsmisfry, Fordhom University, New York,N. Y. Received December $0, 1866 (1) Presented before the Division of Physical and Inorganic Chemiatry of thc American Chemical Society at Atlantic City, September, 1966.
were recrystallizecPfrom water and dried. Various mixtures, weighing about one gram, were placed in Pyrex tubes (7 mm. 0.d.) sealed at one end, and melted together under vacuum. (This was necessary to revent decom osition and dimcoloration.) They ' were tgen sealed of! while evacuated, and quenched in mercury. Compositions which fell within the miscibility ga maintained their metastability for a period more than Lng enough to permit taking X-ray powder photographs. This was done using a G.E. XRD-3 unit with Cu Ka radiation, the wedge technique being ado ted in all cases. The films were measured wlth a G. E. Auorline Illuminator and the various lattice constants calculated. Simultaneously each sample was analyzed by potentiometric titration with standard silver nitrate, using silver and saturated calomel electrodes with an ammonium nitrate salt bridge. Both the bromine and iodide end-p0int.s were observed. Such analysis was necessary because the composition of the original mixture could not be relied upon after the heating under vacuum.
TABLP~ I LATTICE CONSTANTS OF KBr-KI SOLID SOLUTIONS
--_-
Cnm.
cnm.
position, mole fraction of KI
0.0000 .0707 ,0977 .2128 .2685 ,3352 .448 ,495
Lattice constant,
Dev. from additivity
A. A. x 108 6.599 ... 6.624 -8 6.641 -3 8 6.705 6.734 +ll 7 6.760 6.820 +15 6.848 +21
+ +
pc&on,
mole
fraction
of KI
0.568 .658 .740 .766 .878 .902 .918 1.000
Lattice constant,
A. 6.881 6.925 6.947 6.949 7.001 7.030 7.060 7.059
Dev. from sdditivity
Ax
10'
t2l +23
+- 122 -2
+16
+39
...
(2) R. J. Havighurst. E. Mack, Jr., and F. C . Blake, J . A m . Chsm. SOC.,47, 29 (3925). (3) M. Amadoti and G.Pampanini, Atti. accad. Lineei, 40, [I11 475 (1911). (4) J.
B. Wrcsnewsky, 2.anorg. Chem., 74, 95 (1912).
