Srpt., 1963
FOBMULATION OF SOLUTE EQVILIBRIUM IS B I S M ~ TTRICHLORIDE H
1849
SPECTRA OF DILUTE SOLUTIONS OF BISMUTH METAL I N MOLTES BISMUTH TRIHALIDES. 1I.l FORMULATIOK OF SOLUTE EQUILIBRIUM I N BISMUTH TRICHLORIDE BY CHARLE~S R. BOSTON,G. PEDRO SMITH, Metals and Ceramics Davisaon, Oak Radge Xataonal Laboratory,z Oak Radge, Tennessee AND
LESTERc. H o \ ~ I C K 3
Department of Chenzzstrq, Cnzverszty of Arkansas, Fayettevills, Arkansas Receiued March 23, 1963
A procedure was devised for extracting from spectrophotometric data the concentration of the two solute species formed when metallic Ri is dissolvled in molten BiC1,. The functional relation between these concentrations was iound to be in accord with a family of solute equilibria of which the simplest was 4Bi+ = Bid4+. The equilibrium constant K A was computed to have a value of 3.8 X lo6 a t 264”. This is within experimental error of the value, 2.7 X 106, obtained by a previous e.rn.f. study.
Introduction During the past two years the large uncertainty in the identification of the solute species formed when bismuth metal dissolves in molten bismuth trichloride4 has been reduced substantially a1though not obliterated. Topol and Osteryoung5 obtained polarographic evidence that Bi+ may be the dominant solute species a t solute-bismuth concentrations below about 0.2 mole % (about 0.018 AI). Then Topol, Yosim, and Osteryoung6 in a careful study of the e.m.f. of concentration cells observed strong deviations from Henry’s law which they attributed to the presence of a second solute species. Their results mere consistent with the polymerization equilibrium 4Bi+ = Bid4+ (1) in which the species Bi+ predominates a t low concentrations of total solute. Later, Boston aiid Smith7 made a spectrophotometric study of Bi-BiC1, in which it was found that deviatioiis from Beer’s law qualitatively paralleled deviations from Henry’s law. At very low concentrations of bismuth Eeer’s law was obeyed, while at higher concentraticns de1 iations froin Beer’s law became very large. The el-anges in spectral profile which accompanied breakdown in Beler’s law were found to follow the pattern required by two solute species. Although the spectrophotometric measurements provide strong, nontherniodynaniic reinforcement for the e.m.f. work, it is clearly desirable to have a more quantitative comparison between these two studies. This comparison is made in the present paper. Nomenclature and Previoiis Results In this section the nomenclature is introduced and some results from part I7 are summarized. The formal concentration of solute bismuth metal added to molten BiC13 to make a given solution is denoted Mf in units of ~noles/Iiter. The formal extinction coefficient (1) P a r t I is ref 7. (2) Opetated b y Union Carbide Corporation for the United States Atomic Energy Commission (3) Research paiticipant a t the Oak Ridge National Laboratory in the summer of 1961 (4) See review in ref 5 . (5) L E Topol a n d R. 4. Osteryoung, J Clectiochem Soc , 108, 573 (1961). (6) L E Topol, S. J. Yosiin, a n d R. A . Osteryoung, J P h y s C h e m , 66, 1511 (1961) (7) C R. Boston a n d C . P Smith, zhzd , 66, 1178 (1962).
(formal molar absorptivity) of solute bismuth is defined by the relation
A/bMf (2) where A is the absorbance and b the path length in centimeters. Additional subscripts will be added when needed to designa1,e quantities pertaining to particular solutions. The spectra obtained a t a given temperature for Bi-BiC13 solutions have been shomn7 to obey the following relation over the wave length range of 450 to 750 mp, the coiiceiitration range of 0.002 to 0.7 mole/l. of solute bismuth, and a t temperatures of 264 and 350 O cf =
+
-
(3) where the subscript 0 denotes any solution, the subscripts h and 1 denote reference sohtions of high and low concentrationir, respectively, and R is an empirical function of coiicentration but not wave length. The experimental relation between A / b and illf a t 264’ and 560 mp is showii on a log-log plot in Fig. 1. Measured values are represented by circles. On such a plot Beer’s law behavior is represented by a straight line with unit slope. The A/b intercept of this straight line a t unit M fgives the molar extinction coefficient. For small Mf the data obey Beer’s law with Ef equal to 5.8 X loal./mole-cm. At higher Mf the data show large negative deviations from Beer’s law. The significance of other lines 011 this graph is discussed later. It was sh0w17~that eq. 3 may be interpreted to represent the behavior of two solute species which obey the law of additive absorbances. Henceforth in this paper we assume that this is the correct interpretation and we develop some of the mathematical consequences of this two-species model. Quantities pertaining to these species will be distinguished by the subscripts m and n. Conservatioii of mass requires that Ef3
= Efh
R(ari
Efh)
+
Mf = DmMm D,Jd, (4) where Dm arid D, are the numbers of moles of bismuth metal required to form one mole of the mth aiid nth species, respectively. The law of additive absorbances stipulates that d/b
=
Mfer = Mmam (BmLqlrn)
+ Mnen =
(eni/Dm)
+
(DnJJn) ( ~ n / D n )
By combining eq. 3’4, and 5 it niay be shown7that
(5)
C. R. BOSTOS,G. P. SMITH,ASD L.C. Hox71cic
1850
Vol. 67
tion of one species is negligibly small compared with the concentration of the other species. We choose X m j to be negligibly small. Hence, from eq. 4 and 5 il/lfl
N
Efl Y
DnMni
(7)
EnlDn
(8)
Thus en/Dnis given directly by the data in part I' and eq. 3 may be written EfO
I
I
I
I
1
E = 5 8 x 103
1.0 -3.0
/'
= 5.6 x 10'
/
