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Chemical reaction rates of quasi-free electrons in non-polar liquids. The equilibrium CO2 + e− CO2−
:. Volume 31, number 3
:
..
15 March 1975
: -.
C~~EMICA~.PHYSICS LEFERS
.
.. . -,
WPiIICAL PPCTION ILJTES OF QUASI-FREE ELECTRONS IN NON-PO&AR LIQUIDS. THE EQUILIBRIUM CO, + e- * COY’
.
R.A. HOLROYD, T.5. CAkGWER and A.O. ALLEN ., _. Chemistry Dep&dnt;
Brookhaven National Laboratory,
Upton, Nh
York 11973, USA
Received 12 November 1914 -.’
‘.
; ee f?rward and rcvetx rates of the reaction CO2 ‘+ e- --’ COT were determined in tetramethylsilane, neopentane and ?,2,4-trimethylpente as a function of tempcntue. The forward reaction is exothermic in solution but the equilibrium constant skf?s over four &hers of magnitude with changes in solvent. ‘Ihe change in entropy for the fotiard reaction is ‘, approximately the Same (-44 d/m01 degrce).In the three solvents. -.
1 Our measure?entS [ 121’ of the electron mobilities and reaction rates of electrons with added substances, in.solutIons
of non-pbhr
liquids,
dependup
CO2 in 2,2.4-TMP
corn-.
parison of ihe electron current (which’develops cornplete!y, within a few microseconds after X-rays are turned on) with the’steady-state current measured at 1, long times. With a pure solvent the electron current during the pulse is just ha&fof the total steady-state current; h&ever if electron-attaching sblutes are present the electron current is less as a consequence of-the attachment reaction. Curve A in fig. I shows a typical trace of current versus time in a sdution contairiig an electron-attacl-Sng solute. The e!:ctron current is estiblishcd
2 short
time after
X-rays
are turned
.. on at a fraction of the steady-state current:..the cur.
I
rent then increases slowly due to the buildup ofrelatively slow-moving molecular ions in the soliltion. In .. the particuIar case of C,Cl, as solute, as the temperal.. tire is raised a different phenokenon appears, aS shown in curves B and C of fig. 1. After the expected sharp increase, the current continues to Gcrease.more .;apidly ‘Lhan&I be explained by the growth of mole&r ions, and at sufficiently high temperatures ,.(c&ve C) the current incietises and levels off at about on!-half of the steady-state current; but the time required to &t,.+n this level is much longer than re-
under.conti;rct
witi
the
U.S.
Atomic
En%
I
I
I
I
I
I
Fig. 1. Electror..cuPrent versus time for a solution of CO2 in 2,2,4-trimethyl,?entane. &TC A is at 22”, [COz] = 0.9 PM; Curve
B is at 4;“; [CO,] i 0.9 J&; and curve C is at 67’; [CO;] = ?.6 fiBi_500 V applied, d = 0.0966 cm, transit time
of elect’ons in pure liquid is 3.7 bs at.22O.
quired for the growth of current in the pure solvent. Thes’e effects are explained by a spontaneous decom-position of the CO, ion (formed in reaction 1) which yields, the electron back (reaction.2). .; .,
:
k,
i ,‘Research c&&d ugt at Brookha&n National Laboiaioj .. .
I
car_+
Commission.
.’
:
c-
gco,:: ~.
:
-.
_.,
. .
,’
_.
.:
: :
~.’
Volume 31, number 3
CHEMICAL
PHYSICS
Such dec,omposition of the biphenylide ion has re-
Table 1
c&tly been detected by different methods tetkmethykilane [3] and liquid ammonia
Rate
in both. [4] _
IS hlvch
LETTERS
constants for CO2 f e-e
kl
i975
CO,
Toanalyzeour resultsquantitativelyin termsof therate constantsof the forward and backward reactions kl and k2, we note that the observed electron &-rent per unit area depends upon the integral across the measuring cell of the concentration of the electrons: -1
33 40
6.94 X 10" 6.97 x 1012
1.12 XL@ 6.3 x LOS 2.05 x 104 3.4 x LO8
47 60 67 75
7.07 4.9 7.0 6.8
x 10’2 x10’2 x 1oL* x 1012
6.1 1.82 7.0’ 1.2
x LOS 1.0 x 10’ x L36 5.5 x106
neouentane
4 10 24 28
6.7 7.4 5.5 5.4
x 10L’, x 10” x lOL’ xlolL
25 4.6 3.2 4.0
X104 2.8 X10’ x104 1.5 x 10’ x LO5 1.7 xL06 x105 1.4x106
TMS
0 9 20 2.5
1.54 X 10” 1.09 x10” 1.30 x 10”
1.89 x 1a4, 7.8 x LO6 9.0 x 104 L-2 X LO6 3.13 x 10s 4.2 x 105
1.16 x 10” 1.27 x 10”
4.6 1.5
k0actnne
(1) .
”
where d is the’electrode gap, u, = pV/d is the drift velocity and ne ‘is the concentration of electrons. If the motion of the product ion COT in the field is neglected compared to the much more rapid motion of the electron, the concentrations of ion and electron are given by the continuity equatior,s -a
[CO21 /at = k, [CO21 n, - k2 [CO%] ,
an,/at
= u - v,
+k&013
an,/ax
- kg4
- kin,
34
2.5 x 10”
x LO” 2.5 xLOs x LO6 8.5 x104
(2)
[CO21
I
X104 1.2x108 XIOS
I
I
I
I
I
I
I
e-t CO?& CO,
(3)
where a is the rate of gene&ion of electrons per cm3 and k3 is the rate of disappearance of electrons by reactions with adventitious impurities. We have not found 2 useful analytical solution of eqs. (2) and (3)
I
9 -
b
:
B-
and instead have obtained numerical solutions, using the finite difference approximation to compute n,(x, t) from which the electron current, ie(t), is derived by eq. (1). For any given set of conditions, values of i,(lj were.cornputed for different values of kl , k2 and “3 u@l g match to an obs:rved curve was obobt&ed for CO, in the solvents 2,2,4-trimethylpentane(iso-octane), neopentane and ‘tetramethylsilane (This) are shown in table 1. The
6-
rate constant k for the forward reaction increases from 1.8 X 10 14 .m normal hexane [S] to about 7 X 1012 in iso-octane, then drops sharply in neopentane and Th!S, very similarly to our previous
5-
tained. The AsuIts
ftidings
[2] for the all three solvents kl ‘ture while k2.shows equilibrium constant pekature, indicating ye&is exotherrrk.
isoelectronic molecule N20. In changes very little wkh tempraa large activation energy. The K = kl/k2 decreases with tern-’ that electron capture in the solIn fig. 2 we give a graph of IogK
againstl/T. Frondthe least-squares bnesshownin the .
I
I
eo
60 I
i:g
I 3.0
I
I ‘?O -r(‘C) z-0 I
I
3.2
1
3.4
I 0 I
I 3.6
I /TX IO3 Fig. 2. iogk (k: = kl/k&as a function Gf l/Tfor the reaction e- + CO2 d. CO; in three !iqui&: q‘2,2.4-tiimethylpentanc.
d nwpentane, 0 tetramethyklane. .’
Volume’31.Fnumber
3
:
iable 2 ‘, ._ Free energy, enthalpy and‘entropy .idn ‘CO, + e- = co, in solvents jOlVCIIt +tane
;eopentane
[us 0 At stab&d
’
a)in
0 AC&?)
A@(Q)
2SgAS,O(Q)
-12.72 -8.53 -7.33’.
-24.9 -22.3 -21.1
-12.2
The valueqof .laboratoh-and
we take Aw,(e-)
about 0.05 eV. The entropy,for gaseous CO2 is well know?, arid for the ion CO, the bond length of 1.25 A and the bond angle’ of 134” are reported in the literaiure [9], from -a+ich the entropy may be calculated b,y weil kno.wn fortiulas. The entropy of the electron gas under standard conditions is governed by Fermi-Dtiac statis tics and is negligibly small [lo]. We fmc! that 298 &S,(G) = +q.O5 eV. The heat and en-tropy of solution of COZ in heptane and iso-octane has been carefully determined [I I] and as the values
‘.
state of i mol/liter.
‘me ve+ similar we asSume these our other solvents: AIf~(CO~>
AG,O;CD,-) = (-e2,12r)(l
.
AS: = -a@laT=
e may write&the equatim: !$(Q)-U~(~)=dx~(CO~)-AX.f(e-)-AX~(C02)
,
(4) lere X may be H, G, or S. AU thermodynamic quanigs refer tq a standard state of 298 K and one mole
r liter in both gas and liquid phases. The subscript efers to the free energy, enthalpy.and entropy of .ution of the reagents. eF
for
- 11~) ,
where E is the dielectric constant of the liquid. For this process we then find
Ai”@
is the stsbiiization
values aIso hold eY and
= LO.1
298 ASf(CO,) 7 -0.08 eV, for our standard conditions. The free energy of solution of an ion can be estimated by the Born equation [ 121:
+ CG2 -CO,-
quantity
.for
fol nlopentane, -0-40: Parisoactane, 4.22 -‘0.05 = 4.27 eV*; these dues are good td
‘,
An important
= VO : Eaa&):
TMS, -0.55;
-13.8 -13.7
_, .-.
*he electronfrom ;i trapped state to a-conducting state. V,J iave b&en’d&tem&ed [6-31 in this
kcal/moi cf the r&c-
igure we derive the thermodynamic quantities shown n ,tabie 2. Thd free enerG of reaction A G,“(Q)char?ges by5.4 k&/mole in going from iso-bctane to TMS due 3 changes in AiYf(2); however, the entropy term is !ea& very important in estabIish&g the equilibrium. ‘alues of A e(Q) are reliable to about +0.06 kcal/mol, ut’@(Q) and 298 ASf(Q),are subject to errors of kht 2 1;l kcallmol or t0.-35 eV. The characteristics of >hc equilibrium can be exlained in terms of the properties of the thermoynamic cycle: ISphase: e-
15 March 1975
CHEMICAL PHYSICS LETTERS
‘,
‘.
energy
the quasi-freeelectron in the liquid phak. V,,
:he energy of the electron in the conduction band the solvent and has a characteristic value for each. ve;:. Since the electron in most hydrocarbons rees in shall&traps most of the time, the thermoltamic energy of the electrons is samewhat lower Lny,-,; an appr&im$e correction tan be made by )+cting from V,, the observed actiMtior1 energy the mobility, which is the energy reqtiJed to raise
(e2j2re2)aE/aT,
and A@ = A Gf + 298 AS:. The effective radius’ of the ion COT is of amrse not exactly known; it is estimated by Henglein [13]’ to be about 2.3 8, based on the vohme occupied by a CO2 molecule in liquid C02. From the above values of the heat and entropy terms together with the observed thermodynamic quantities for the equilibrium In the three solvents and for an assumed value of r(CO,), we calculate values for the AI@(g), which is the negative of the electron affiiity of CO2 in the gas pLase, and for the quantity 298 A.!?f(e-). Since the electrons in the solvents are at least partially 1ocpJized we believe that the latter quantity
must
be a’pasitive
number.
given in table 3 we sic +Lhatthe
From
the values
values of Ati(g)
for
the
three solvents arc the &me within the combined experimental error of the V,-,values and the present thermodynamic data. This agreement holds indcpendently of the assumed effective radius. Cooper and Compton [9] find A@(g) to lie betwedn 0.0 and td.5 eV: From the eLfect of the assumed value of the ;
* Chaqes
in V. with tr:mqeraturc! [8] have been tieglected~~
._
,, .:
‘.
:: .::
Volume 31, number 3 Table 3 Calculated values of AH;(g) and 298ASF(e_), Solvent
&-octane
E29.3
neopentane
1.934 1.774
l?ils
1.837
15 hlaxch 1975
CHEMICAL FHYSICS LETTERS
-ae/aT
\
assuming effective radius of CO; is 2.3 A
AHI%
298A$s”(e3
(rV/nlolc)
(cvtmolc)
298 aS;(COj) (eV/moIe)
0.0014
+0.41
to.31
-0.95
0.0019 0.0017
to.46 to.33
+0.17 +0.26
-0.56
CO, radius on the value of AH,(g), we find that for the electron affinity to lie within this range the assumed r should be taken between about 2.0 and 2.8 A, while for the entropy of solution of the electron to be positive r should be greater than 2.0 A. The value 2.3 a thus seems to be quite reasonable. The decrease irJ entropy of the reaction in soluticn is seen to arise from both positive entropy of solution of the electron and the negative entropy of solution of the CO, ion. The study of electron-ion equilibria provides a useful tool for obtaining an understanding of the properties of the elctron in various media. It would be particttlarly interesting if such an equilibrium could be found involving a molecule having an exactly known affinity in the gas phase. The authors wish to express their appreciation to Dr. H.A. Schwan for his assistance in programming the solution of eqs. (2) and (3).
:
-0.47
References [ 1J A.O. AUen and R.A. Hohoyd, I. Phys. Chem. 78 (L974) 796. [2] A-0. Allen, T.E. Gangwer and R.A. Kolrayd. 1. Phys. Chem., to be published. [3] J. Warman, private communication. [41 FulutazizandR.R.Wenti. nrivzte cammunicltion. [5]
J.H. Baxendaleand E.J. Rasburn, I. Chem. Sac.
Farachty Trims, I 70 (1974) 705. ]6] R.A. Holroyd and hi. AUen, J. Chem. Phys. 54 (197 1) 5014. [7] R.A. Holroyd and W. Tauchert, J. Chem. Phys. 60 (1974) 3715. [S] R.A. Holloyd and R.L. Russell, J. Phys. Chem. 78 ii974) 2128,
[9]
C.D. Cooper and R,N. Compton, Chem. Fiys. Letters
ii (1972) 29. G. Frappe and G. Lepoutre, J. Chim. Phys. 54 (19.57) 242. [ 11 J E. Wilhelm and R. Battino, Chem. Rev. 73 (1973) I. [12] M. Born, 2. Physik l(1920) 45. [ 131 A. Henglein, private communication.
(lo]
i
:
..
15 March 1975
: -.
C~~EMICA~.PHYSICS LEFERS
.
.. . -,
WPiIICAL PPCTION ILJTES OF QUASI-FREE ELECTRONS IN NON-PO&AR LIQUIDS. THE EQUILIBRIUM CO, + e- * COY’
.
R.A. HOLROYD, T.5. CAkGWER and A.O. ALLEN ., _. Chemistry Dep&dnt;
Brookhaven National Laboratory,
Upton, Nh
York 11973, USA
Received 12 November 1914 -.’
‘.
; ee f?rward and rcvetx rates of the reaction CO2 ‘+ e- --’ COT were determined in tetramethylsilane, neopentane and ?,2,4-trimethylpente as a function of tempcntue. The forward reaction is exothermic in solution but the equilibrium constant skf?s over four &hers of magnitude with changes in solvent. ‘Ihe change in entropy for the fotiard reaction is ‘, approximately the Same (-44 d/m01 degrce).In the three solvents. -.
1 Our measure?entS [ 121’ of the electron mobilities and reaction rates of electrons with added substances, in.solutIons
of non-pbhr
liquids,
dependup
CO2 in 2,2.4-TMP
corn-.
parison of ihe electron current (which’develops cornplete!y, within a few microseconds after X-rays are turned on) with the’steady-state current measured at 1, long times. With a pure solvent the electron current during the pulse is just ha&fof the total steady-state current; h&ever if electron-attaching sblutes are present the electron current is less as a consequence of-the attachment reaction. Curve A in fig. I shows a typical trace of current versus time in a sdution contairiig an electron-attacl-Sng solute. The e!:ctron current is estiblishcd
2 short
time after
X-rays
are turned
.. on at a fraction of the steady-state current:..the cur.
I
rent then increases slowly due to the buildup ofrelatively slow-moving molecular ions in the soliltion. In .. the particuIar case of C,Cl, as solute, as the temperal.. tire is raised a different phenokenon appears, aS shown in curves B and C of fig. 1. After the expected sharp increase, the current continues to Gcrease.more .;apidly ‘Lhan&I be explained by the growth of mole&r ions, and at sufficiently high temperatures ,.(c&ve C) the current incietises and levels off at about on!-half of the steady-state current; but the time required to &t,.+n this level is much longer than re-
under.conti;rct
witi
the
U.S.
Atomic
En%
I
I
I
I
I
I
Fig. 1. Electror..cuPrent versus time for a solution of CO2 in 2,2,4-trimethyl,?entane. &TC A is at 22”, [COz] = 0.9 PM; Curve
B is at 4;“; [CO,] i 0.9 J&; and curve C is at 67’; [CO;] = ?.6 fiBi_500 V applied, d = 0.0966 cm, transit time
of elect’ons in pure liquid is 3.7 bs at.22O.
quired for the growth of current in the pure solvent. Thes’e effects are explained by a spontaneous decom-position of the CO, ion (formed in reaction 1) which yields, the electron back (reaction.2). .; .,
:
k,
i ,‘Research c&&d ugt at Brookha&n National Laboiaioj .. .
I
car_+
Commission.
.’
:
c-
gco,:: ~.
:
-.
_.,
. .
,’
_.
.:
: :
~.’
Volume 31, number 3
CHEMICAL
PHYSICS
Such dec,omposition of the biphenylide ion has re-
Table 1
c&tly been detected by different methods tetkmethykilane [3] and liquid ammonia
Rate
in both. [4] _
IS hlvch
LETTERS
constants for CO2 f e-e
kl
i975
CO,
Toanalyzeour resultsquantitativelyin termsof therate constantsof the forward and backward reactions kl and k2, we note that the observed electron &-rent per unit area depends upon the integral across the measuring cell of the concentration of the electrons: -1
33 40
6.94 X 10" 6.97 x 1012
1.12 XL@ 6.3 x LOS 2.05 x 104 3.4 x LO8
47 60 67 75
7.07 4.9 7.0 6.8
x 10’2 x10’2 x 1oL* x 1012
6.1 1.82 7.0’ 1.2
x LOS 1.0 x 10’ x L36 5.5 x106
neouentane
4 10 24 28
6.7 7.4 5.5 5.4
x 10L’, x 10” x lOL’ xlolL
25 4.6 3.2 4.0
X104 2.8 X10’ x104 1.5 x 10’ x LO5 1.7 xL06 x105 1.4x106
TMS
0 9 20 2.5
1.54 X 10” 1.09 x10” 1.30 x 10”
1.89 x 1a4, 7.8 x LO6 9.0 x 104 L-2 X LO6 3.13 x 10s 4.2 x 105
1.16 x 10” 1.27 x 10”
4.6 1.5
k0actnne
(1) .
”
where d is the’electrode gap, u, = pV/d is the drift velocity and ne ‘is the concentration of electrons. If the motion of the product ion COT in the field is neglected compared to the much more rapid motion of the electron, the concentrations of ion and electron are given by the continuity equatior,s -a
[CO21 /at = k, [CO21 n, - k2 [CO%] ,
an,/at
= u - v,
+k&013
an,/ax
- kg4
- kin,
34
2.5 x 10”
x LO” 2.5 xLOs x LO6 8.5 x104
(2)
[CO21
I
X104 1.2x108 XIOS
I
I
I
I
I
I
I
e-t CO?& CO,
(3)
where a is the rate of gene&ion of electrons per cm3 and k3 is the rate of disappearance of electrons by reactions with adventitious impurities. We have not found 2 useful analytical solution of eqs. (2) and (3)
I
9 -
b
:
B-
and instead have obtained numerical solutions, using the finite difference approximation to compute n,(x, t) from which the electron current, ie(t), is derived by eq. (1). For any given set of conditions, values of i,(lj were.cornputed for different values of kl , k2 and “3 u@l g match to an obs:rved curve was obobt&ed for CO, in the solvents 2,2,4-trimethylpentane(iso-octane), neopentane and ‘tetramethylsilane (This) are shown in table 1. The
6-
rate constant k for the forward reaction increases from 1.8 X 10 14 .m normal hexane [S] to about 7 X 1012 in iso-octane, then drops sharply in neopentane and Th!S, very similarly to our previous
5-
tained. The AsuIts
ftidings
[2] for the all three solvents kl ‘ture while k2.shows equilibrium constant pekature, indicating ye&is exotherrrk.
isoelectronic molecule N20. In changes very little wkh tempraa large activation energy. The K = kl/k2 decreases with tern-’ that electron capture in the solIn fig. 2 we give a graph of IogK
againstl/T. Frondthe least-squares bnesshownin the .
I
I
eo
60 I
i:g
I 3.0
I
I ‘?O -r(‘C) z-0 I
I
3.2
1
3.4
I 0 I
I 3.6
I /TX IO3 Fig. 2. iogk (k: = kl/k&as a function Gf l/Tfor the reaction e- + CO2 d. CO; in three !iqui&: q‘2,2.4-tiimethylpentanc.
d nwpentane, 0 tetramethyklane. .’
Volume’31.Fnumber
3
:
iable 2 ‘, ._ Free energy, enthalpy and‘entropy .idn ‘CO, + e- = co, in solvents jOlVCIIt +tane
;eopentane
[us 0 At stab&d
’
a)in
0 AC&?)
A@(Q)
2SgAS,O(Q)
-12.72 -8.53 -7.33’.
-24.9 -22.3 -21.1
-12.2
The valueqof .laboratoh-and
we take Aw,(e-)
about 0.05 eV. The entropy,for gaseous CO2 is well know?, arid for the ion CO, the bond length of 1.25 A and the bond angle’ of 134” are reported in the literaiure [9], from -a+ich the entropy may be calculated b,y weil kno.wn fortiulas. The entropy of the electron gas under standard conditions is governed by Fermi-Dtiac statis tics and is negligibly small [lo]. We fmc! that 298 &S,(G) = +q.O5 eV. The heat and en-tropy of solution of COZ in heptane and iso-octane has been carefully determined [I I] and as the values
‘.
state of i mol/liter.
‘me ve+ similar we asSume these our other solvents: AIf~(CO~>
AG,O;CD,-) = (-e2,12r)(l
.
AS: = -a@laT=
e may write&the equatim: !$(Q)-U~(~)=dx~(CO~)-AX.f(e-)-AX~(C02)
,
(4) lere X may be H, G, or S. AU thermodynamic quanigs refer tq a standard state of 298 K and one mole
r liter in both gas and liquid phases. The subscript efers to the free energy, enthalpy.and entropy of .ution of the reagents. eF
for
- 11~) ,
where E is the dielectric constant of the liquid. For this process we then find
Ai”@
is the stsbiiization
values aIso hold eY and
= LO.1
298 ASf(CO,) 7 -0.08 eV, for our standard conditions. The free energy of solution of an ion can be estimated by the Born equation [ 121:
+ CG2 -CO,-
quantity
.for
fol nlopentane, -0-40: Parisoactane, 4.22 -‘0.05 = 4.27 eV*; these dues are good td
‘,
An important
= VO : Eaa&):
TMS, -0.55;
-13.8 -13.7
_, .-.
*he electronfrom ;i trapped state to a-conducting state. V,J iave b&en’d&tem&ed [6-31 in this
kcal/moi cf the r&c-
igure we derive the thermodynamic quantities shown n ,tabie 2. Thd free enerG of reaction A G,“(Q)char?ges by5.4 k&/mole in going from iso-bctane to TMS due 3 changes in AiYf(2); however, the entropy term is !ea& very important in estabIish&g the equilibrium. ‘alues of A e(Q) are reliable to about +0.06 kcal/mol, ut’@(Q) and 298 ASf(Q),are subject to errors of kht 2 1;l kcallmol or t0.-35 eV. The characteristics of >hc equilibrium can be exlained in terms of the properties of the thermoynamic cycle: ISphase: e-
15 March 1975
CHEMICAL PHYSICS LETTERS
‘,
‘.
energy
the quasi-freeelectron in the liquid phak. V,,
:he energy of the electron in the conduction band the solvent and has a characteristic value for each. ve;:. Since the electron in most hydrocarbons rees in shall&traps most of the time, the thermoltamic energy of the electrons is samewhat lower Lny,-,; an appr&im$e correction tan be made by )+cting from V,, the observed actiMtior1 energy the mobility, which is the energy reqtiJed to raise
(e2j2re2)aE/aT,
and A@ = A Gf + 298 AS:. The effective radius’ of the ion COT is of amrse not exactly known; it is estimated by Henglein [13]’ to be about 2.3 8, based on the vohme occupied by a CO2 molecule in liquid C02. From the above values of the heat and entropy terms together with the observed thermodynamic quantities for the equilibrium In the three solvents and for an assumed value of r(CO,), we calculate values for the AI@(g), which is the negative of the electron affiiity of CO2 in the gas pLase, and for the quantity 298 A.!?f(e-). Since the electrons in the solvents are at least partially 1ocpJized we believe that the latter quantity
must
be a’pasitive
number.
given in table 3 we sic +Lhatthe
From
the values
values of Ati(g)
for
the
three solvents arc the &me within the combined experimental error of the V,-,values and the present thermodynamic data. This agreement holds indcpendently of the assumed effective radius. Cooper and Compton [9] find A@(g) to lie betwedn 0.0 and td.5 eV: From the eLfect of the assumed value of the ;
* Chaqes
in V. with tr:mqeraturc! [8] have been tieglected~~
._
,, .:
‘.
:: .::
Volume 31, number 3 Table 3 Calculated values of AH;(g) and 298ASF(e_), Solvent
&-octane
E29.3
neopentane
1.934 1.774
l?ils
1.837
15 hlaxch 1975
CHEMICAL FHYSICS LETTERS
-ae/aT
\
assuming effective radius of CO; is 2.3 A
AHI%
298A$s”(e3
(rV/nlolc)
(cvtmolc)
298 aS;(COj) (eV/moIe)
0.0014
+0.41
to.31
-0.95
0.0019 0.0017
to.46 to.33
+0.17 +0.26
-0.56
CO, radius on the value of AH,(g), we find that for the electron affinity to lie within this range the assumed r should be taken between about 2.0 and 2.8 A, while for the entropy of solution of the electron to be positive r should be greater than 2.0 A. The value 2.3 a thus seems to be quite reasonable. The decrease irJ entropy of the reaction in soluticn is seen to arise from both positive entropy of solution of the electron and the negative entropy of solution of the CO, ion. The study of electron-ion equilibria provides a useful tool for obtaining an understanding of the properties of the elctron in various media. It would be particttlarly interesting if such an equilibrium could be found involving a molecule having an exactly known affinity in the gas phase. The authors wish to express their appreciation to Dr. H.A. Schwan for his assistance in programming the solution of eqs. (2) and (3).
:
-0.47
References [ 1J A.O. AUen and R.A. Hohoyd, I. Phys. Chem. 78 (L974) 796. [2] A-0. Allen, T.E. Gangwer and R.A. Kolrayd. 1. Phys. Chem., to be published. [3] J. Warman, private communication. [41 FulutazizandR.R.Wenti. nrivzte cammunicltion. [5]
J.H. Baxendaleand E.J. Rasburn, I. Chem. Sac.
Farachty Trims, I 70 (1974) 705. ]6] R.A. Holroyd and hi. AUen, J. Chem. Phys. 54 (197 1) 5014. [7] R.A. Holroyd and W. Tauchert, J. Chem. Phys. 60 (1974) 3715. [S] R.A. Holloyd and R.L. Russell, J. Phys. Chem. 78 ii974) 2128,
[9]
C.D. Cooper and R,N. Compton, Chem. Fiys. Letters
ii (1972) 29. G. Frappe and G. Lepoutre, J. Chim. Phys. 54 (19.57) 242. [ 11 J E. Wilhelm and R. Battino, Chem. Rev. 73 (1973) I. [12] M. Born, 2. Physik l(1920) 45. [ 131 A. Henglein, private communication.
(lo]
i