1160
NOTES
0.25-0.35 e v e 6 It is believed that only some 2% or less of the HBr photodissociations in the ultraviolet continuum yield 2Pl,zBr atoms.7 Such transitions will result in a lowering of the H atom recoil energy by about 0.45 eV. The predominant transition to groundstate Br atoms should give the H atom energies indicated in Figure 3 for the various wavelengths used. The three hot atom abstraction yields a t 1.6, 2.0, and 2.9 eV using HBr as the source are consistent and indicate that the present data in this region are best represented as a linear increase of yield with initial energy. The observed HzS-C4Dlo system ordinate of 0.18 then corresponds to an H atom energy of 2.3 f 0.1 eV. The range of reported values of the H-SH bond dissociation energy is 4.1-3.7 eV,8 giving 2.6-3.0 eV as the range of excess energy in the photochemical dissociation a t 1850 hi. Therefore an average of at least 7501, of the excess energy appears as kinetic energy of separation a t 1850 hi. This indicates that the energy partitioning is similar a t 1850 and 2138 hi despite the difference in initial vibrational state indicated spectroscopically, as Gann and Dubrin found that 80% or more of the excess energy goes to the H atom at the latter wavelength. A further conclusion of these results is that even at the high energy end of the 2000-k band the main photodissociation process is H2S + H HS rather than H2S+ H z S. The upper limit on the occurrence of the latter process which is consistent with our results is a quantum yield of about 0.25, corresponding to a quantum yield of 0.75 for hot atom production with all of the excess energy going to kinetic energy of separation. We have determined the quantum yield for Hz from HzS at 1850 as 1.0 4 0.1, but this does not distinguish between hydrogen atom and hydrogen molecule production in the primary process, since the fates of H and HS are expected to be H H2S + H z HS and HS HS +H2S S.8 We have also studied the photolysis of HzS-D~ mixtures a t 1850& and a comparison of the present H2S and HBr data with previous HBr data is presented in Table I. All of the systems in Table I have been found to follow the linear behavior Hz/HD =
+
+
A
+
+
+
+
Table I: H o t Hydrogen Atom Kinetic D a t a for D Abstraction from Deuterated Reactants System4
HBr-D2brc HBr-C4Dlo HBr-C2DGb HBr-CDf H2S-DzC HzS-C~DIO
(I
+ I)-’
0.61 0.23 0.14 0.062 0.43 0.18
w.
A-1
0.49 0.18 0.085 0.012 0.20 0.10
Data for photolysis a t 1850 * Data from ref 4. Intercepts and slopes have been multiplied by 2 to correct for the H D assumed to be produced thermally from reaction with HBr or HzSfollowing the hot atom abstraction producing D. The Journal of Physical Chemistru
A (HX/RD)
+
I, where HX is either HBr or HzS, over a wide range of (HX/RD) . The second column of the table gives the reciprocal of the slope. With the reservations cited previously14JA-l may be taken as an approximate measure of the average relative abstraction cross section ratio ( S R D / S H X ) over the relative energy distribution present in the system, Taking the ratio of the A-I values for the HBr-D2/HBrsystems and the H2S-D2/H2S-C4Dlo systems gives D ~and ~ ) 2.0 where the initial values of ( S D ~ / S Cof~ 2.7 hot atom energies are approximately 2.9 and 2.3 eV, respectively. It is interesting that the complex dynamics of monoenergetic atoms introduced into a thermal gas leads to the linear product dependence on reactant ratio which has now been observed with a variety of systems and initial energies. Further interpretation of such hot atom kinetics and the extraction of more definitive information on reaction cross section behavior above threshold requires more kinetic data than are presently available and the application of nonreactive cross section functions and statistical theory to describe the observed kinetics. (6) B. A. Thrush, Progr. Reaction Kinetics, 3 , 89 (1965). (7) R. 5. Mulliken, J. Chem. Phys., 8 , 382 (1940). (8) T. L. Cottrell, “The Strengths of Chemical Bonds,” Academic Press, London, 1958. (9) D. deB. Darnent. R . L. Wadlinger. and M. J. Allard, J. Phys. Chem., 71, 2346 (1967).
Activity Coefficients for Ionic Melts by R. Haase Instdtut f a r Physikalische Chemic, Rheinisch- Westfiilische Technische Hochschule, Aaehen, Germany (Received August 26, 1968)
While the definitions of activity coefficients for both nonelectrolyte solutions and electrolyte solutions are straightforward and well known, the situation with ionic melts is less clear and less well understood. It is true that most authors1 proceed in the same way as they do with nonelectrolyte solutions, but it is by no means evident whether this is the adequate scheme of description. As a matter of fact, it will be shown that it is expedient to introduce activity coefficients for ionic melts that are different from those in nonelectrolyte and electrolyte solutions. For simplicity’s sake, we shall restrict the discussion to binary ionic melts such as the systems NaC1 KC1 or PbClz PbBr2. Reciprocal salt pairs of the type NaCl+ KBr may also be treated as binary systems
+
+
(1) See, for example, H.Bloom, “The Chemistry of Molten Salts,” W. A. Benjamin, Inc., New York, N. Y.,1967.
1161
NOTES provided we either exclude heterogeneous equilibria or we consider the melt in equilibrium with a pure (e.g., solid) phase. The macroscopic description of any binary liquid mixture starts from the chemical potentials pl and pz of the two substances (denoted as components 1 and 2) as functions of thermodynamic temperature T , pressure P , and composition. The activity a 1 or az of component 1 or 2 is defined by pLi
In ai
~
- poi RT
and ignore ionic complexes
(i = 1 ) 2 )
where R is the gas constant and poZ the chemical potential of the pure liquid component i a t the same values of T and P. Experimental values of the activities al and az are usually derived from vapor pressure measurements or electromotive force data. The macroscopic composition of the ionic melt is described by the stoichiometric mole fraction X I or xz of component 1 or 2 ( 2 1 xz = 1). We put x x2, 1- x 5 1 , choosing x as the independent composition variable. Thus p 1 and p2 or a 1 and a2 may be considered to be functions of T , P , and x. The microscopic coinposition of the melt is given by the true mole fractions xi of all the species j actually present in the liquid. Let the subscript a refer to ions contained in component 1 only, the subscript b to ions common to both components, and the subscript c to ions occurring in component 2 only. Then the true mole fractions x,, x b , and x,: of the ionic species may, in principle, be expressed in terms of the independent mole fraction x . But these expressions are simple only for complete dissociation and absence of ionic complexes. We denote the number of ions of kind a or b produced by one molecule of component 1 by v, or V b , respectively, and the number of ions of kind b or c produced by one molecule of component 2 by Vb' or vc, respectively. We use the abbreviations
These relations will be used later. We first continue to give some perfectly general formula. The chemical potentials p1 and pz of components 1 and 2 are related to the chemical potentials pa, p b , pc of the ionic species a, b, c by the equations
+
b
Q
=
Vb'Pb b
(5)
+
VcPc C
For the limiting values of the chemical potentials of the ionic species in the pure liquid components we introduce a notation analogous to that in (3) pao
lim pa;
pbo
= lim p b ; 2-90
2-90
pbo'
= lim p b ;
p.00
2-1
2-1
Bearing in mind the definition of from ( l ) ,( 5 ) , and (6)
RT In a1 =
va(pa
(6)
=lim pc
- pao)
a
b
+
pol
and
V b h b
p02
we derive
- Pb0)
(7a)
b
C
In addition to this, there is the general condition
V2
Vb'
-b
b
Vc C
and write for the limiting values of the true mole fractions of the ionic species in the pure liquid components zao
lim zQ; 2-0
$bo'
= lim x b ; 2-1
zbo
lim z b ; 2-0
x$ = lim zo
(3)
z+l
Then there follows, if we assume complete dissociation
following from the Gibbs-Duhem relation. We now introduce a standard type of ionic melts in a similar way as one usually does in the case of nonelectrolyte solutions, but we take account of the fact that the primary units are the ionic and molecular species actually present in the melt. Writing for the chemical potential pj of any species j in the whole composition range p~j= poi
+ RT l n x j
(9)
we define an ideal ionic melt. This is the natural exVolume 73, Number 4 April 1069
NOTES
1162 tension of the concept of an “ideal mixture” to ionic melts. It should be stressed that PO^ is the chemical potential of the hypothetical pure liquid species j at the given values of T and P . Thus we have in particular Poa
Pa
+ R T In Sa; pC = PO^
where Poa=
lirn Ma;
Pb = poa -k
( 10)
pac=
lim p,
+ R T lnXaO;
@bo
= /.Lob
(11:
-/- RT1nxb0 (12aj
Pb0’
= poa
3- R T In xb“;
p00 = poC -I-
R 1’ In x,O
d In alid d In aZid 4-2=0 dx dx
can be shown to be valid for expressions 16. We accordingly define the activity coeficients f~of components 1 and 2 in any ionic melt by
= ai/aiid
fi
xc-1
zb-1
in contrast to expressions 6. We derive from (3), (6), ( l o ) , and (11) Pao = Poa
(1 -x)-
R T In xb;
+ R T In xc
lim Pa;
POb”
xo-1
and 2 in a completely dissociated ideal melt. They only depend on x and no longer on T and P. The condition following from (8)
(i = 1, 2)
(17)
fi
and (18)
The quantities f1 and f2 are functions of T, P , and x. They measure the deviations from the behavior of a completely dissociated ideal melt. If f c Z 1 the melt is either ideal with incomplete dissociation or nonideal with any degrees of dissociation. From (8) and (17) we find
(12b) Inserting (10) and (12) into (7), we find Furthermore, we have according to (1), (16), and (18) lim fl = 1; -0
all these relations holding for ideal ionic melts. Now a standard type of ionic melt, as a reference system for actual melts, is useful only if the activities al and a2 can be given explicitly in terms of the independent variables T, P, and x. Therefore, we decided to choose the completely dissociated ideal melt as our reference system since here, in view of ( 4 ) , the true mole fractions can be expressed as functions of x. We repeat that, in deriving (4),we assumed both complete dissociation and absence of ionic complexes. Introducing the abbreviations a
0
we obtain from (4)and (13) a1
= a1’d;
(15)
a2 = a2id
the functions slid and azid being defined by In alid= VI In v1
+ uo ln(1 - 2)
- VI In [VI
+
In UP
5 v2
In v2 -
+ (v,
Vbln[l b Vb’
+
(rb
- l)x]
(16a)
In rb
b
+ v In x -
+
vb’
b
v2
ln[vl
+
(u2
-
VI)X]
+ (rb - 1)%] (16b)
Thus slid and aZidare the activities of components 1 The Journal of Phyeical Chemistry
(20)
5-1
The relations (19) and (20) are analogous to those for nonelectrolyte solutions. The usual definition’ of “activity coefficients” yl and YZ y1= a1/l - 2; yz az/x only coincides with our convention (18) for simple cases such as NaCl KC1 or KzC03 KzS04. There are three main reasons for using fl and fi instead of y1 and y2. (1) The procedure of fixing a reference system is analogous to that already known from “associated ideal mixtures” in the case of nonelectrolyte solutions. (2) Complicated ionic melts often can be described to a first approximation by f i = 1 but not by yi = 1 (i = 1, 2). Thus the melting point diagram of AgK03 (1) K2S04(2) seems to indicate2 that this system is nearly a completely dissociated ideal melt since the relations resulting from (15) and ( 16)
+
+
+
ln al = 2 In
- vdx]
limfp = 1
2(1 - 2 ) 2+x
,
3s In a2 = 3 In 2+x
are fulfilled to a good degree of approximation within a considerable range of compositions (pure silver nitrate being the solid phase). (2) Y. Doucet, “Les aspects modernes de la cryom6trie.” Mdm. Sciences Phys., Fascicule LIX,Gauthiar-Villars, Paris, 1964.
1163
NOTES (3) Series expansions of lnfi and lnf2 in powers of the simplest case of which is lnfi
=
Bs2;
lnfi = B(1 - z ) ~
bridge and a null detector. Two branches of the bridge are glass covered thermistors of 100,000 ohms resistance each; a rheostat is connected in series with one of them. The thermistors are located in a glass container containing the solvent. The entire apparatus is enclosed in a thermostat maintained a t 25’. The original instrument was improved in two ways: the thermostat was adjusted to control the temperature to within fO.OOlO, and the original syringes were replaced by micrometer syringes permitting control of the volume of a drop to within ~ 1 % . The procedure is as follows. A drop of water is deposited on one thermistor and a drop of fixed volume of solution is deposited on the other thermistor. Due to the absorption of water vapor by the solution, there is an increase in temperature and decrease in resistance of the solution-bearing thermistor. This decrease in resistance is balanced with the rheostat (range of 01100 ohms and accuracy of kO.1 ohm) ; a measured AR is obtained. The temperature increases with time and after several minutes reaches a plateau. This condition remains constant for a relatively long time (over 10 min) in the range of molalities measured, AR is read a t this stage, and no extrapolation is done to zero time. An equilibrium of heat content of the drop is assumed to be a t the plateau condition at which the heat absorption is assumed to be
2,
(21)
where B depends on T and P , are correct only for fi and f i but not for y1 and yz (unlessfi coincides with yi). This is due to the fact that the proper form of the limiting laws for infinite dilution3J results from an expansion such as (21) and this implies logarithmic terms for the functions In 71and In yzin general. More details have been given elsewhere.6 (3) R. Haase, Compte6 rendus de la 28 Reanion Chimie Physique, Paris, 1952, p 131. (4) R . Haase, “Thermodynamik der Mischphasen,” Springer, Rerlin-G6ttingen-Heidelberg, 1958. ( 5 ) R. Haase, Z . Phys. Chem. (Frankfurt am Main) 63, 95 (1969).
Determination of Water Activities of Dilute Electrolyte Solutions by S. Amdur Israel Atomic Energy Commdsslon, Soreq Nuclear Research Centre, Yanne, Israel (Receiaed October 9 , 1 9 6 8 )
The problem of integrating the McKay-Perring equation for ternary systems using isopiestic mensurements has recently been under consideration.‘ Difficulties arise especially in the range of very dilute solutions, i e . , less than 0.1 m where measurements are not available. Therefore, a method of water activity determination in this range is suggested.
where kl is a constant, S is the surface area of the drop, po is the vapor pressure of the solvent, and p is the vapor pressure of the solution. The rate of heat dissipation
Table I: Water Activities and A E Values for KCl and NaCl Solutions Molality
0.02075 KCI 0 04026 NaCI. 0.06070 KCI 0.07929 NaCl 0.09956 KCI 0.15639 NaCl 0.20402 KCI I
a
Calcd from eq 8.
AR
16.7 29.9 45.7 58.5 70.5 108.4 137.0
a,,
a wa
% Aa
awb
%Ab
0.99935 0.99869 0.99790 0 99726 0.99666 0.99476 0.99333
4-0.007 0.006 -0.005 -0.009 0 -0.008 0.010
0.99926 0.99867 0.99793 0.99732 0.99673 0.99479 0.99325
-0.002 0.003 -0,002 -0.003 $0.007 -0.005 $0 002
standard
0.99928 0.99863 0 I99795 0.99735 0.99666 0 99484 0.99323 I
I
Calcd from eq 9.
The method is an osmometric one; the rate of water vapor adsorption by a drop of solution in a solvent atmosphere is determined potentiornetrically.*J Generally speaking, this procedure may not be considered better than the usual isopiestic method; however, it was found to be relatively fast and to increase the range of measurements down to 0.02 m. Measurements were taken using an isothermal molecular weight apparatus4which contains a dc Wheatstone
is assumed to be
dQd = k,(T - TO) dt
(1) C . Pan, J . Phys. Chem., 7 2 , 2548 (1968). (2) A. P. Rrady, H. Hue, and J. W. McRain, J . Phys. Coiloid Chem.. 55, 304 (1951). (3) E. E Schrier, J . Chem. Educ., 45, 176 (1968). (4) Manufactured by Arthur H . Thomas C o . , Philadelphia, Pa. Volume 75, Number 4 April 1869
