NOTES
1754
KBr in 2800 nitrate molecules (paragraph 3, above), was also covered by the hypothesis and by the model of Figure 5, ref. 1. It is not clear why the bromide case was not used for illustration instead of the chloride system. Could it be that the authors themselves did not quite understand how a single Br- ion would immobilize a t least as many as 40% or slow down all of the 2800 Li+ and K + ions? The model, obviously, is not able or meant to explain the enormous alleged mobility of the fluoride ion (paragraphs11 and 2, above). ( 5 ) Very large conductance changes were also described in the second paper which is said to support the existence of transition metal halide complexes, partly of extreme stability (e.g., ref. 1, Figure 6, cobalt fluoride), in astoundingly dilute solution and in absence of halide ion excess. In summary, instead of accepting what would indeed be an unexpected development in the field of fused salt chemistry, it seems preferable to assume that these effects are not real but are artifacts. Some may have been produced by gas bubbles from catalytic decomposition of nitrate, especially LiN03. Others, such as the large increases in conductivity, all of which occurred in melts containing LiN03, probably had their origin in partial short-circuiting through the wall of the capillary cell (glass? quartz?) as a result of penetration by the decomposition product, lithium oxide, with its highly mobile Lif ions.
An Examination of the Johnston-Ogston Equation and the Moving Boundary Equation
by L. W. Nichol and A. G. Ogston Department of Physical Biochemistry, John Curtin School of Medical Research, Australian National University, Canberra, A.C.T., Australia (Received October 23,1964)
When a mixture of two components is subjected to mass transport, the resulting experimental pattern is markedly dependent on the operation of either chemical or physical interactions or both.'-* With interactions of either kind, it is advantageous to consider the constituent concentrations and v e l o c i t i e ~ ,as ~ ~ this ~ results in the same fundamental relation expressing conservation of matter. 3v6 The constituent concentration of a component at any point in the cell is merely the total concentration of that component regardless of the form in which it exists. In a rapidly reacting The Journal of Physical Chemistry
+
system, A €3 e C, there are two Gibbs components and their constituent concentrations in the undisturbed equilibrium mixture (termed the a-phase) may be chosen as EA" and EBa; in the transport of two components which interact only physically, the same terminology may be employed to define their concentrations in the mixture (a-phase). The corresponding constituent velocities, SA" and sB", are defined by the mass action law in the case of chemical interaction, but they may be explicitly described when physical interactions operate, only if the precise nature of the hydrodynamic forces involved is known. Nevertheless, in both cases the modified or constituent velocities must vary monotonically with concentration and it is this correlation which permits the behavior of interacting systems of both kinds to be viewed in conjunction.8 If the A constituent moves faster than the B constituent in a transport experiment, leaving pure B behind in the Pphase, a relation expressing the conservation of B across the a@boundary may be written as
Equation 1 is the Johnston-Ogston expression' describing the effect of physical interaction where VB@ and SB" are numerically different. Moreover, with the terminology adopted it is also the moving boundary equation frequently applied to the study of chemically interacting systems.a~6It might be noted that in the ,&phase, where B exists alone, EBB = CB' and SB' = OB'. Equation 1 is generally visualized as applying to sedimentation velocity,' to the descending side in electroph~resis,~~~ and to the trailing edge of a zone moving down a column while preserving a plateau r e g i ~ n . ~An analogous expression may be written for the corresponding ascending side in terms of the A constituent which does not disappear across the boundary separating the mixture and pure A (termed the ab boundary3), with the caution that in chemically reacting systems the model selected involving the separation of B alone on the descending side and A alone on the ascending need not necessarily apply in all (1) J. P. Johnston and A. G. Ogston, Trans. Faraduy SOC.,42, 789 (1946). (2) G. A. Gilbert and R. C. L. Jenkins, Proc. Roy. SOC.(London), A253,420 (1959). (3) L.W.Nichol and D. J. Winzor, J. Phys. Chem., 68,2455 (1964). (4) A. Tiselius, Nova A& Regrim? SOC. Sci., Upsdiemis, [4] 7 , 1 (1930). (5) L. G. Longsworth' in "Electrophoresis, Theory, Methods and Applications," M. Bier, Ed., Academic Press, New York, N. Y., 1959,p. 91. (6) M. Davies, L. W. Nichol, and A. G. Ogston, Bwchim. Bwphys. Acta, 75,436 (1963).
NOTES
1755
sharp boundary of B is present a t the meniscus (z = cases.2 The additional assumptions are implicit in eq. 1 that the cell is of uniform cross section and the 0) and is shown by the line AB. The total amount of B in whatever form is given by the area of the rectangle applied field is homogeneous. A more detailed exABJM, where J M represents the bottom of the recpression for the ewe of sedimentation velocity involving only frictional interactions has been formulated to tangular cell. A potential gradient is applied in the direction indicated, and the distribution of B a t account for the sector shape of the cell and the inhomogeneous field.’ time t is shown by the solid line DEFIJ. Within this time t , a quantity of B will have piled up on the A fundamental difliculty arises in applying eq. 1 cell bottom, and this amount is represented by the to characterize a physically or chemically interacting area of the rectangle MJKL, extending hypothetically system in that the parameter v has not been explicitly defined. Originally, Johnston and Ogstonl interpreted below the base of the cell. As matter must be conserved, it follows that v as the velocity of a sharp boundary of A, which is necessarily the velocity of A in the plateau region 8 ~ ~ ; area of ABJM = area of DEFIKL (2) they gave a differential equation applying to any The concentration gradient of B in the ,$-region lamina in a diffuse boundary of A, but did not integrate after time t has elapsed is now spread and has been this expression. Essentially the same interpretation arbitrarily drawn as a negative gradient to correspond has been give to v in the detailed expression for sedito the situation normally encountered in the frictional mentation velocity’ and in the moving boundary equat i ~ n . The ~ intuitive approach that v is the mean vecase where vg8 > BB= and from eq. 1, CB@ > A vertical line GHON is constructed perpendicular to locity of the A boundary was reasonable in that the the distance or x coordinate, bisecting the curve FI derivation of eq. 1 requires v to be the velocity of some point in the &-region and it is within this region that at the median position H. It follows that the areas FGH and OH1 are identical and that the A constituent disappears. However, the following argument shows that the reasoning is not rigorously area of DEFIKL = area of CEGO correct and moreover provides a definite interpretaarea of DCJM area of MJKL (3) tion of the parameter v. The model selected is presented diagramatically in We may note that the line ECD may be regarded as the Figure 1, which shows the distribution of the constituent median of a curve describing a diffuse boundary of pure concentration of B a t two times, t = 0 and t = t. B, which in practice might be observed. It is evident (The gradient in the constituent concentration of A that which primarily separates the a- and p-phases has area of ABJM = area of ABCD area of DCJM been omitted for simplicity.) Initially, a t t = 0 a
+
+
+
(4) Combining eq. 2,3, and 4 gives area of ABCD = area of CEGO
L-I I
1 1
I 1 I
c--/3
PHASE
-!!
, I
I PHASE
I 1 I I
Figure 1. Diagram of a rep-entative distribution of the constituent concentration of slow moving constituent (B) in a descending limb at two different times.
I I I I
I I
+ area of MJKL
(5) It is also clear that the lengths of the following lines are given by
AB =
=
-
CE =
(CB’
AD =
VBBt
ML =
SBat
co
=
JM
(v’ - v B @ ) t
(6) where v’ is the velocity of the median GHON. Combining eq. 5 and 6 gives (7) R. Trautman, V.,N. Schumaker, W. F. Harrington, and H. K. Schachman, J . Chem. Phys., 22, 555 (1954).
Volume 80, Number 6 May 1066
NOTES
1756
cBavB’t
= (cB’
- E B ~ ) ( v ’ - v B @ ) t + cBauBat
(7)
Rearranging eq. 7 results in the relation
which is identical with eq. 1 provided v = v’. The identical conclusion is reached if the B gradient in the ®ion is taken as positive, the situation frequently encountered in the transport of chemically reacting systems where cB’ < It may therefore be concluded that the value of v appropriate to eq. 1 is the velocity of the median bisector of the concentration gradient in the a@-regionof the B constituent which does not disappear across it. For the ascending side, the comparable value to v refers to the rate of movement of the median bisector of the gradient of the faster moving constituent, A, in the region of the ab boundary.* It should be emphasized that the value of v is found from the median in the gradient of the constituent concentration of B (for the descending side), and this implies for the case of chemical interaction that the gradients in the ®ion due to uncombined and combined B must be summed. If v could be found rigorously by the independent analysis of each constituent, it is clear that the system could be characterized without the assistance of eq. 1. However, in most practical cases, the experimental record does not differentiate between the constituents present, frequently recording a plot of the total concentration of‘ all constituents vs. distance or a curve of the total refractive index gradient us. distance as in a schlieren pattern. The problem is then to locate a position in the observed cup-region which will give an exact or reasonably approximate measure of v. The ap-boundary is the algebraic sum of the contributions of A and B components, whether it is represented by a plot of concentration or of gradient of concentration. The range of x within which the contribution of B varies is necessarily coextensive with that in which A varies. However, the forms of the two gradients need not be, in general are not, the same and the resulting form of the cup-boundary may deviate in any way from gaussian, even to the extent of being (8) I n discussing the electrophoresis of a mixed electrolyte system, V. P. Dole, J . Am. Chem. SOC.,67, 1119 (1945), has already shown that the velocity parameter v,aS for the ion species, j , may be calculated from the position corresponding to the first moment of the boundary due to the gradient in the jth species. He then assumed that the function, 8&, had the same value, vu@, for all species and accordingly the moving boundary equation was written in terms of the single generalized parameter, 04. The above discussion emphasizes the necessity of reconsidering particular values of v,a@ when these are different and uniquely defines the value pertinent to the moving boundaiy equation for a two-component system.
The Journal of Physical Chemistry
bimodal, according to the type and degree of interaction between A and B. The contribution of B to the combined ap-boundary and the proper value of v‘ could be calculated only if exact analytical expressions were available to describe them in terms of their interactions and including the effect of diffusion. There is likely, therefore, to be some error in identifying v’ with any parameter of the combined boundary.
Validity and Limitations of the Gas Titration of Atomic Nitrogen with Nitric Oxide
by Hanns Von Weyssenhoffl and Norris Patapoff Jet Propulsion Laboratory, California Institute of Technology. Pasadena, Cdifornia 91 103 (Received November 10, 196.4)
One of the standard methods for measuring the concentration of nitrogen atoms in active nitrogen is the gas titration with nitric o ~ i d e . ~Two , ~ other techniques in which the atomic nitrogen was titrated with ethylene or molecular oxygen4 were found to yield consistent results which were, however, considerably lower than the values given by the nitric oxide titration. It was suggested4 that this discrepancy might be due to the intervention of excited species in the reaction with nitric oxide. In the reaction of N150 with active nitrogen (isotope 14), Back and Muij observed quantitative conversion of consumed N’j0 into N14N15. This result appeared to preclude the decomposition of nitric oxide in collisions with excited species as a possible source of additional nitrogen atoms; yet it presented no direct proof for the stoichiometry of the nitric oxide titration with respect to nitrogen atoms. Data obtained by the nitric oxide titration method have been compared with absolute nitrogen atom concentrations measured by quantitative e.s.r. spectrometry.“* Good agreement between the two has recently (1) Department of Chemistry, Northwestern University, Evanston, Ill. 60201. (2) M. L. Spealman and W. H. Rodebush, J . Am. Chem. Soc., 57, 1417 (1935). (3) (a) G.B.Kistiakowsky and G. G. Volpi, J. Chem. Phys., 27, 1141 (1957);(b) F. Kaufmam, ibid., 28, 992 (1958); (0) P. Harteck, R. R. Reeves, and G. Mannella, ibid., 29, 608 (1958). (4) For a comprehensive review see A. N. Wright, R. A. Nelson, and C. A. Winkler, Can. J . Chem., 40, 1082 (1962). (5) R. A. Back and J. Y. P. Mui, J. Phys. C h m . , 66, 1362 (1963). (6) S. Krongelb and M. W. Strandberg, J . Chem. Phys., 31, 1196 (1959).
