95
International Journal of Mass Spectrometty and Ion Processes, 64 (1985) 95-113 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
HETEROLYTIC DISSOCIATION OF POTASSIUM THE GAS PHASE AND THE ELECTRON AFFIiVITY OXIDES
E.B. RUDNY,
CHROMATE IN OF CHROMIUM
L.N. SIDOROV
Department of Chemistry,
L.A. KULIGINA
Moscow
State
University,
Moscow
117234
(U.S.S.R.)
and G.A. SEMENOV
Scientific-Research (U.S.S.R)
Institute
of Chemistry,
Leningrad
State
University,
Leningrad
199004
(First recieved 10 April 1984; in final form 17 September 1984)
ABSTRACT The Knudsen effusion method has been used together with mass spectral analysis to study the evaporation process of potassium chromate and ion/molecule equilibria in its saturated vapour. From the calculated equilibrium constants the enthalpies of the following reactions have been established. (The square brackets in the equations indicate a substance in the condensed state.) [K,CrO,]
= K,CrO,
[K,CrO,]+BO;
= [KBO,]+KCrOi
[K,CrO,]+KSO; 00; KCrO;
AH,0 = 329.5 f 15.1 kJ mol-l
= [K,SO,]+KCrO;
+ SO< = CrO; +SO;
A@
=KSO;
+ SO, +CrO;
=125_3+15.4
A@=
kJ mol-’
-32.9f16.9kJmolw’
A@’ = 90.9 + 10.8 kJ mol-* A@‘=
-65.6f17.0kJmol-1
Based on these values of enthalpy, the following thermodynamic values (in kJ mol-i) been estimated: ArH$(K,CrO,,) = - 1067.1 + 15.2, A&‘(KCrO~) = - 1000.0 f ArH,O(CrO; ) = -674.4 f 26.8, Ar@‘(CrO; ) = - 784.5 + 30.0, D(K+-KCrO; ) = D(K+-CrOi-)= 809, EA(Cr0,) = 357 and EA(Ci-0;) = -85. The abnormal behaviour observed during the evaporation of potassium chromate has studied by the method of ion/molecule equilibria.
have 16.0, 576, been
INTRODUCTION
The energy of heterolytic dissociation is an important characteristic of alkali metal salts because these compounds are considered to be highly ionic. The expression “the energy of heterolytic dissociation” is taken to mean the 0168-1176/85,‘$03.30
0 1985 Elsevier Science Publishers B.V.
96
enthalpy of the reaction AB=A++B-
0)
at 0 K. This value has already been determined for a series of monobasic salts, such as KBO,, KPO,, KReO, [l] and the dibasic salt, K,SO, [2]. The gaseous K ,CrO, molecule is investigated in the present work. For calculation of AH: of reaction (l), it is necessary to know both the enthalpies of formation of the KCrO; ion and the neutral molecule K,CrO, (A f @‘(K’) is well known [3]). Therefore, the evaporation process of potassium chromate was studied initially before investigating the ion/molecule and ion/ion equilibria in its saturated vapour. Molecule/molecule, ion/ molecule and ion/ion equilibria were first investigated by this procedure by Nikitin et al. [4]. The literature values for the enthalpy of formation for K,CrO, are inconsistent. In ref. 5, the saturated vapour pressure of potassium chromate [at 1113 K P(K,CrO,) = 6.58 X 10m6 atm] is estimated. From this can be calculated the value of A,@‘(K,CrO+& = - 1101.7 kJ mol-‘. In ref. 6, the energies of atomization of the sulphates, chromates, molybdates and tungstates of alkali metals were compared and the estimate Af@‘(KZCrO,,) = - 1010 f 50 kJ mol-’ was obtained. In ref. 7, the equilibrium constant for the reaction 2 K + H,CrO,
= K,CrO,
+ 2 H
(2)
in flames at 2250 + 100 K was measured and the value A&t(K&rO& = - 1030.6 + 21 kJ mol-’ was determined. In addition, studies of ion/molecule equilibria in the saturated vapour of K,CrO, are of interest due to the presence of CrO; and CrO; ions in the vapour. The CrO; ion has been shown [8] to be present in the plasma of magneto hydrodynamic (MHD) power generators and the determination of its thermodynamic properties should be carried out to choose the most efficient operational mode of the MHD-power generators. The literature contains only one investigation [9] wherein the equilibrium constant of the reaction HCrO, + e -=CrO,+H
(3)
was measured and the electron-affinity value EA(Cr0,) = 390 kJ mol-’ was -318.0 kJ mol-’ [3] one obtains determined. Then, using A&‘(CrO,) = A$,O(CrO;) = -708 lcJ mol-i. The experimental data given in ref. 9 were recalculated in ref. 3 by using new thermodynamic data and the values A&‘(CrO;) = -623 f 34 kJ mol - l, and EA(Cr0,) = 305 f 30 kJ mol+’ were obtained.
97 EXPERIMENTAL
In the present work the pressures and equilibrium constants of the reactions are dimensionless values referred to the standard state: 1 atm = 1.013 x lo5 Pa. Tables l-11 give the values of R In K, (R = 8.3144 J mol-l K- 1 [ 31) in order to demonstrate more explicitly the effect of the equilibrium constant value on the final result, i.e. the enthalpy of the reaction. AHt=T(-RlnK,+,&-) In the present case, T = 1100-1200 K and the value R In K = 1 J mol-l K-l will approximate to 1 kJ mol-r in AH:. In cases where the mass spectrum of the negative ions at a single temperature was recorded several times, the values ‘Iii = R In K were averaged and the standard deviation was calculated.
ZjTij Ti = Pi
vi=pi-1 where j - 1, . . . , pi is the number of measurements at the same temperature; the index i corresponds to the temperature; uj is the number of degrees of freedom referred to the standard deviation si. The brackets used in the equation for the reaction indicate that the substance is in the condensed state.
Determination
of the enthalpy of sublimation of K,CrO,
The composition of the vapour over potassium chromate was studied by means of mass-spectral analysis using an MS-1301 mass spectrometer. Potassium chromate was evaporated from platinum Knudsen effusion cells in the range 1200-1300 K. The temperature was measured with a Pt/Pt-Rh thermocouple (10% Rh). The mass spectrum thus recorded is K+(3.6), KO+(O.OlS), Kl(0.013), K20+(0.035), K,CrO,+(0.012), K,CrO~(0.024), K,CrO,+(l.O) at T= 1215 K and U,,, = 70 V. Relative intensities are given in brackets. The K,CrO, moIecule is the main component of the vapour. The K+ ion has two values for its AE: the first is close to the ionization energy of the neutral potassium atom (4.5 ev), the second one markedly exceeds this value (8.5 ev). This fact in itself indicates that the K+ ion can originate from two sources, namely, from atomic K and from K,CrO,.
99
+ 14.4O). The accuracy of the temperature measurement is estimated as 5 3”. Stability of the crucible temperature was obtained by means of a VRT-3 automatic control device; stability of temperature was + lo. In most experiments, the ion currents were measured on a VEU-6 electron multiplier. To calculate the ratio of ion currents, a correction factor for the ratio of the multiplier gain was introduced, viz. ^ Z&4-) Z,,W)
= Z&A-)
Y@-)
Zin”,W)
Y (A-)
where Z,, is the current measured on the electrometer and ZmUlis the current measured on the multiplier. The assumption that y(B-),+(A-) = [M(A)/ M(B)]*‘2 was used. This hypothesis was further verified by measuring a number of experimental ratios of the multiplier gain, the results being given in Table 2. The results clearly show that the hypothesis works with good accuracy. The ratio of the ion pressures was calculated according to the formula [15]
P@-) = L(A-) M(A) “* i(B-) Ia-) t?,@-) [ WB) 1 -= 60
LdA-) M(A) ZIn”,W) MB) x
x
i(B-) i(A-)
where i is the percentage of the isotope being measured. The numerical coefficients derived from this equation will be used in formulae (5)-(19). The ions CrO;, CrO;, KCrO;, Cr,O; , KCr,O; and K,Cr,O; were recorded over pure potassium chromate. For determination of their enthalpies of formation, a substance must be introduced into the cell so as to TABLE 2 Experimental ratio of multiplier gains
X-
I*
7(x-)
Pi a
si b
-$ln
7(333X)
wx> M(KCrO< )
(exptl.) K,Cr,O; K,CrSO, K3S20,
KCt,O, Cr,O; KSO,CrO; CrO, so,so,
api b
sz
- 0.83 - 0.41 - 0.97 - 0.49 -0.18 0.01 0.06 0.51 0.08 0.41
is the number of dots. is the standard deviation.
1 2 1 1 1 2 1 1 2 1
0.16
0.05
0.17
-
0.41 0.38 0.34 0.25 0.13 0.07 0.14 0.22 0.33 0.44
100
produce in the vapour some ions with known enthalpies of formation. The BO; ions [1,16] and the ions SO;, SO,, KSO; [2 J were used as reference ions. To produce such ions, ion/molecule equilibria in the K,CrOi -KBO, ions appeared in the mass system were studied (the BO; and KB20; spectrum) as well as in the K,CrO,-K,SO, system (the ions of SO,, SO<, KS07 , K&O; and K,CrSO; appeared in the mass spectrum). The data on the substances used and the parameters of the crucible and the ion source are given in Table 3. The studies of the ion/molecule equilibria over pure potassium chromate allowed calculation of the equilibrium constants of reactions (5)-(7) (experiments I-IV). [K&rO,]
+ KCrOi
= K,Cr,O;
[K,CrO,]
+ 2 CrOg + CrO;
Z(3gK352Cr,0<) lnZ&,> = In Z(39K52C o_j r 4
= 2 KCrOT
= ln Z( 3gK52CrOq)2Z(52Cr20c) Z( 52CrO;)2Z(
TABLE
Substance
I
K*CrO,
VII VIII IX X a D,, b D2, ’ E,, ’ E2,
(6)
52CrO;)
3
Exp. no.
VI
(5)
In KpcBj
+ In 5.649
Substances and systems under investigation:
II III IV V
+ Cr,O;
+ ln 3.04
K2Cr04 K2-34
K,CrO, K,CrO, r 95 mol% KBO, x 5 mol% K,SO, z=-97 mol% K,C!rO, < 3 molW K,Cr04 -z 3 mol% K,SO,, 76 moI% K,CrO,, 24 mol% K,CrO,, 24 mol% K,SO,, 47 mol% K,CrO~, 53 mol%
parameters of the ion source
El d
Recording
86 57 57 53 57
0 157 10 0 157
Multiplier Multiplier Electrometer Electrometer Multiplier
2.2
11
100
Multiplier
0.8 0.8
2.2 1.2
57 66
119 0
Multiplier Multiplier
0.8 0.1
1.2 2.0
17 ?
10 ?
Multiplier Multiplier
Crucible size
D, a (mm)
D2 b (mm)
E, =
+4x 14 +4x 14 +10x12 +10x12 +4x 14
0.7 0.7 1.7 1.0 $7
2.2 2.2 2.2 1.5 2.2
94x
0.8
94x 14 +10x 12 +10x 12 +10x 12
14
vmm-’
Vmrll--’
diameter of the crucible orifice. diameter of the orifice in the draw-out electrode. field intensity between the crucible and the draw out electrode. field intensity behind the draw-out ektrode.
101 [K2Cro4]
CrO;
+
In Kp(,, = In
= KCrOL + KCr,O;
+ CrO;
)1(‘9K52Cr20;)
1(3gK52CrO; 1(%rO;)
+ In 4 629
1(52CrO;)
(7)
*
For experiments III and IV (the measurements were taken on the electrometer), the numerical constants in equations (5)-(7) are equal to 2.023, 2.775 and 2.508, respectively, The experimental data are given in Table 4. In the K,CrO,-KBO, system (experiment V) the equilibrium constant of the reaction [K2Cr04]
+ BO;
= [ KB02]
+ KCrO;
(8)
was measured. In &a)
= In
1(3gK52CrO;) I(llBO_)
+ In a(KB0,)
+ In 3.73
2
The potassium chromate activity [a(K,CrO,)] was assumed to be equal to one since the system contained more than 95 mol% of K,CrO,. Thus, In a(K,CrO,) = 0. The potassium metaborate activity was calculated according to the formula In a (KBO, ) = In
TABLE
I( 3gK’1B20i)
- In 0.26 - In KpllOj
I(,‘lBO;)
(9)
4
Equilibrium constants of reactions (5)-(7) Exp.
T
No.
(K)
- Rln&, (J mol-’ K-‘)
I
1191.4 1200.6
14.53 13.72
si
pi
- R In Kpf6) (J mol-’ K-‘)
si 1.83 2.73
1.66
4
71.92
0.61
2
73.38
pi 4 2
pi
- R In K,(,, (J mol-’ K-l)
si
29.02 30.03
1.18 1.21
2 2
1209.7
13.76
1.07
4
70.41
1.08
4
27.46
1.38
4
1218.8 1227.9
13.21 14.29
0.75 0.72
2 3
73.17 68.26
3.74 0.89
2 3
28.41 26.56
0.94 1.06
2 3
1.03
2 1
1126.8
14.41
0.61
3
71.97
1
30.07
1145.4 1163.9
15.57 15.06
73.40 72.42 69.41 69.21
2 1
32.82 28.77
14.29 14.20
6 3 2 2
1.04
1182.3 1209.7
0.65 0.46 0.02 0.27
0.49 0.16
2 2
27.63 27.09
0.65
1 2
III
1209.7
13.63
0.93
16
70.66
2.72
15
28.21
1.41
15
IV
1218.8 1227.9 1236.9
12.75 15.17 15.62
1.87 0.53 1.21
3 3 4
75.29 74.73 73.64
3.19 1.05
3 3
30.76 30.06
0.85
4
30.20
2.54 0.88 1.13
3 3 4
II
1
102
whereJ&(10)is [KBO,]
+ BO,
the equilibrium
constant of the reaction
= KB,O,
(10) The numerical values of KtilO) were obtained from measurements taken over pure potassium metaborate. They can be approximated by means of the equation T (10) =
115 700
R In Kp(lO) = -
T
The standard deviation
s[.r(,,)]
+ 100 Jmol-’
can be calculated
T-l - 997-l 0.616 x 1()-3
1 K Pt8j was determined In Kti8) = In
K-i
according
to
)I
according
to the formula
2 r/2 J mol_* K-1
I( 39K52CrOq) 1(39K’1BZOc)
_ ln K
I(11B0;)2
Pooj + In 14.346
(11)
which was obtained by substituting into Eq. (9) for reaction (8). The experimental data are given in Table 5. The values of the KBO, activity are given in the same table as an example. In the K,CrO,-K,SO, system (experiment VI-X), we calculated the equilibrium constant of the similar exchange reaction [K,CrO,]
+ KSO;
= [K2SOd] + KCrO;
I( 39K52 CrO;
>
02) -In
a(K,CrO,)
The potassium sulphate activity was determined
according
In Kti12) = In
In a(K,SO,)
I( 39K52SOl)
= In
+ In u(K,SO,)
~(3gG2S2w
_
In
K pc14j
I(39K32SO;)
-
+ In 1.3 to
In 0.36
03)
TABLE 5 Equilibrium constants of reaction (8) Exp. no. V
(‘(, 1108.1 li26.8 1145.4 1145.4 1126.8
- RIrlK~,) (J mol-’ K-l)
‘i
Pi
A#(*, (kJ mol-‘)
-In
116.59 113.89 108.58 108.89 112.13
1.66 0.83 1.74 1.72 0.91
3 3 3 3 3
128.6 127.1 122.4 122.8 125.1
6.98 7.08 6.79 7.45 7.83
a(KB0,)
103
where Kfi14) is the equilibrium constant of the reaction
[K2S04] + KSO,
= K,S,O,
04
Its numerical values are taken from ref. 2. R hl Z&4) = -
21600 T
- 4.1 J mol-’ K-l
The potassium chromate activity can be determined by three different procedures using the constant of reactions (5)-(7) obtained in experiments I-IV. For example In a (K ,CrO, ) = In
z(3gG2cr20s) _ ln
p(5j+ In 3.04
K
I( 3gK52CrOc)
(15)
For reactions (6) and (7), similar expressions are obtained_ However, for calculation of Kp(12j we used expression (15) alone, for in this case it is necessary to measure only two ion currents, while for calculating the activity by means of Kti6) and Kp(,) we have to use four ion currents. Substituting for Eqs. (15) and (13) in Eq. (12), we obtain Z(39K52CrO~)2Z(3gK~2S20~) In
Kp(12)
=
ln
_ ln K
Z(39K32SO;)2Z(39KyCrzO;)
P(14j+ In KpcSj+ In 1.19
The experimental data are given- in Table 6. For ease of comparison, Table 6 also contains the values of the K,SO, and K,CrO, activities calculated according to Eqs. (13) and (15), as well as the K,CrO, activities calculated according to KPc6) and Kti7). The activities calculated for K,CrO, by means of three different procedures are seen to be in good agreement. The equilibrium constants of ion/ion reactions were calculated for estimating the enthalpies of CrO; and CrO; in the K ,CrO,-K *SO4 system KCrO;
+ SO;
In Kfi17) = In CrO;
+ SO,
In Kdlsj = In
= KSO,
+ CrO,
Z(39K32SO;) Z( 52Cr0;) Z( 39K52 CrO; = CrO;
) Z( 32S0,
)
+ In 1.093
+ SO;
I( 52cro~) z(32so,_) + ln o Z( 52Cr0;)
07)
Z(32SO;)
928 s
The presence of the mixed ion K,CrSO;
, made it possible to calculate the
1209.7 1245.9 1272.8
1209.7 1272.8
1254.9
VIII
IX
X
2 1 2
2 2 2 2
2 3
Pi
2
3.35 2 1.80’ 4
0.79
1.17
0.37 0.77 0.47 1.40
1.79 0.64
si
Kti5), Eq. (15). KN6). Kti7). Q,,,, Eq. (13).
18.82
14.72 17.92
16.02 16.08 16.66
21.69 18.65 19.22 18.69
18.27 18.82
R In ql(lZ) (J mol-’ K-‘)
using using using using
1254.9 1272.8 1290.7 1308.4
VII
a Calculated b Calculated ’ Calculated d Calculated
1281.8 1299.6
(K)
T
VI
Exp. no.
Equilibrium constants of reaction (12)
TABLE 6
-
w&J
2.36 2.06 2.19 2.17 1.06 1.04 1.09 1.29 1.35 1.26
37.1 34.0 35.5 35.6 28.2 29.7 31.5 26.6 33.1 33.5
-1n a(K&rO,) 2.29 2.40
)
33.9 35.4
(Wmol-
a
0.42
1.70
0.87 0.53 1.28
1.13
0.96
0.70
1.59
0.88 0.75 0.73
0.74
0.66
1.40 2.04 1.71 1.43
0.04 0.02 0.04 0.05
-1n a&SO,J
1.80 2.17 2.02 1.90
-In a(KzCr04> ’
0.27 0.33
b 2.48 2.34
2.38 1.99
-In a(K&rO,)
d
X
IX
45.18
1272.8
46.45
48.61 49.29
1163.9 1209.7
1254.9
48.25 48.04 47.22
1209.7 1245.9 1272.8
42.54 41.81
1290.7 1308.4
VII
49.08 49.84
43.77 44.41
‘1254.9 1272.8
VI
1136.1 1163.9
42.72 40.05
1281.8 1299.6
tion
VIII
RlnK ly7) (J mol- 9-l)
T
(IQ
Reac-
0.37 0.76 1.52 1
2 2 4
2
0.60
0.51
2 1 2 1
2 2 2
0.07 0.51 0.35 0.21
2
3
0.70 1.16
2
Pi
0.67
si
Equilibrium constants of reactions (17)-(19)
TABLE 7
67.4
71.04
82.29 78.18 70.89
65.0
68.34
81.25 78.28 76.44 70.27
71.00 70.59 67.90 66.15
70.66 67.18
- R In Kti181 (J mol-’ K- )
68.4 66.8
69.4
63.9 66.4 67.2 68.9
64.1 65.8 64.4 64.3
61.6
64.1
- AH&, 1 (W mol- )
2
2 2 4
0.60 0.26 1.50 6.60
1 2
2 1 1
2 2 2 2
2 3
Pi
0.27
1.31
2.46 0.05 0.82 0.91
2.35 0.47
si
89.9
95.4 91.1
96.5
93.3 88.4 87.8
93.1 91.9
90.0 90.7 88.5 87.4
88.1
91.4
AH&) (kJ mol-‘)
10.95
11.18
10.53
12.86
13.20 12.64 12.16
12.87 12.42
R In &I,, (J mol-’ K-l)
2 2 2 2
0.02 1.11 0.52 1.41
0.62
2
2
3
2.45
2 1.21
Pi 0.81
si
c
106
equilibrium K,S,O;
constant
+ K,Cr,O;
In KP(i9) = In
of the reaction -+ 2 K,CrSO;
Z(39K:2Cr32SO;)2 Z( 39K:2S20;)
The experimental
Z(39Ki2CrZO;)
data on Eqs. (17)-(19)
+ In ’ ”
09)
are given in Table 7.
DISCUSSION
En thalpies of reactions The enthalpies for reactions (4), (8), (12), (17) and (18) were estimated by treating the equilibrium constants according to the Third Law Tlrl=R
ln
K=
-
AH,o(III) T
(20)
+ *“T (III)
In Eq. (20), the parameter &‘$ is given a priori and is calculated by using statistical thermodynamics for gases and the calorimeteric measurements for solids (see Table 9). To determine AH~(III), the residual sum of squares &( r;r* - Q2pj [17] is minimized resulting in
AH,O(III) was calculated temperature A H$ m.=
0
‘iA H,OPi ‘iPi
as the arithmetic
mean of the enthalpies
for each
(22)
In this case, approximately the same values of enthalpies were obtained as for Eq. (21). However, there is a difference between formulae (21) and (22) in principle. Calculation according to formula (22) results in a situation where the equilibrium constants measured at the higher temperature give a greater contribution to AH:, while formula (21) suggests equivalence of the constants. This is due to the fact that formula (22) is obtained by minimization of the expression Ci( ?I?‘I1 - Ti)2piq giving the equilibrium constants different weights (temperatures). To determine the total error of AH:, we took into account statistical and systematic errors resulting from inaccuracy of the thermodynamic functions. Thus, the values obtained were: AH&) = 329.5 k 15.1, AH,&, = 125.3 f 15.4, AH&) = - 32.9 f 16.9, AH&) = - 65.6 + 17.0, AH&,) = 90.9 + 10.8 kJ
107
mol-‘. When estimating the molecular constants, the thermodynamic functions for Cr,O;, KCr,O;, K,CrSO, and K,Cr,O, were not calculated since these ions have not been so completely studied. Thus, even the choice of an appropriate structure for these ions appears to be a complicated matter. We treated the equilibrium constants of reactions (5)~(7) and (19) according to the Second Law ~11 = R In K=
- AH$11)
+ AS;(H)
(23)
All the parameters given in Table 8 were determined in the usual way by the least squares method. The standard deviation of the equations of regression can be calculated according to the formula @?l_
s(‘I’“)=s(Rln
F-1)'
BZ
K)=si
1 l/2
All the necessary coefficients are given in Table 8. Enthalpies
uf formation,
electron affinity and dissociation
energies
Additional thermodynamic information used in the present work as well as the final enthalpies of formation of K,CrO,,, CrO;, CrO; and KCrO; are given in Table 9. The enthalpy of formation AtHz(K,CrO+j) = - 1396.6 kJ .mol-’ is taken from ref. 18. The value obtained in ref. 19 is ArHl(K2CrOqsJ)= - 1397.3 kJ mol-‘. The enthalpies of gas-phase reactions of anion exchange with the participation of BO;, viz MBO, + AlF,-
TABLE
+ MAlF, + BO,
8
Enthalpies of reactions (5)-(7) Reaction no.
and (19)
AH;”
T
(kJ mol-‘)
A
B
si
X1O-3
K--l)
5 6
14.2 f 20.4 5.1+ 69.0
- 2.4 - 75.9
1197 1206
57 48
0.164 0.112
1.68 3.86
7 19
28.7 f48.8 28.8 f 25.6
-5.0 34.7
1208 1275
45 18
0.110 0.075
2.68 1.16
a Double
standard deviation is given.
108
(where M = K, Na) have been determined [l, 161. We used the value A,@(AlF;) = - 1945.4 + 10 kJ mol-’ [20]. It resulted in the difference between the value of A,&‘(BO,) given in Table 9 and that given in refs. 1 and 16. Estimation of the enthalpy of KCrO; formation according to reactions (8) and (12) give the values - 1005.5 f 20.2 and - 994.6 + 20.8 kJ mol-‘, respectively. We recommend the mean value A,H,O(KCrO;) = - 1000.0 + 16.0 kJ mol-‘. The enthalpies of formation of K,CrO,, and CrO; differ from those estimated in refs. 5 and 7 according to reactions (2) and (3). Flames were used as a medium in refs. 5 and 7: these procedures for estimating the equilibrium constants are substantially different from those used in the present work. It should be noted that the inaccuracy in ref. [5] concerning the estimated constants may be due to disregard of the dissociative ionization. Besides, inadequate investigation of the compounds HCrO, and H,CrO, could also account for the inaccuracy’in the final results given in refs. 5 and 7. For calculation of the dissociation energy and the electron affinity, the enthalpies of formation of 0, O-, Cr, CrO, CrO,, CrO, and K+ at 0 K were taken from ref. 3: the values are 246.8, 105.6, 395.0, 184.8, -106.0, - 318.0 and 508.7 kJ mol-‘, respectively. The crystalline lattice energies of alkali metal chromates have been calculated [21] and the value A,W,“(CrO,‘-) = -700 kJ mol-r is obtained. We estimate the accuracy of this value as f 100 kJ mol-‘.
TABLE
9
Thermodynamic
values and enthalpies of formation
Substance
A f III: (kJ mol-‘)
A(A,,Hz) (kJ mol-‘)
Ref.
&oo (J mol-’ K-‘)
P&o0 (J mol-’ K-‘)
Ref.
K2SQiW
- 1427.183 - 978.122 - 1396.6 - 712.3 - 992.3 -400.064 -601.1 - 1067.1 - 674.4 - 784.5 - 1000.0
0.5 5.0 1.9 12.0 11.0 3.5 7.4 15.2 24.8 30.0 16.0
3 3 18,19 a 1,16 ’ 2 3 2 This work This work This work This work
260.8 124.0 287.3 237.6 378.1 277.9 299.4 449.8 311.5 333.6 397.4
1.6 5.0 4.0 1.5 7.8 2.0 3.7 9.4 4.0 5.8 9.7
3 3 19,22 a 3 2 3 2 This work 3 This work This work
KBO, (cr)
K ZCrQ (cr) BO; KSO,so, so; K GQ (g) 00, CrO; KCrO;
a See text.
109
The enthalpy of the reaction CrO;
+ H -+ CrO,
+ OH
(24)
= 152 f 40 kJ mol - ’ [93. This value was mean of the enthalpies of reaction (24) calculated in ref. 9 according to the Second and Third Laws. Hence, using our data for CrO; and the data taken from ref. 3 for H and OH, A&~(CrO;) = - 345.5 kJ mol- ’ is obtained. Based on this, we calculated the following dissociation .energies and electron affinities (in kJ mol- ‘): D(Cr-0) = 457; D(CrO-0) = 538, D(CrO-O-) = 636, EA(Cr0,) = 240; D(CrO,-0) = 459, D(CrO,-O-) = 674, D(CrO,-0) = 576, EA(Cr0,) = 357; D(CrO,-O-) = 572, D(CrO,-0) = 357; D(K+-KCrO,) = 576, D(K’-CrOi-) = 809, EA(Cr0;) = - 85.
has been determined
as A@&,
obtained by taking the arithmetic
of potassium chromate
Evaporation
In studying the evaporation of potassium chromate we faced the problem of apportionment of the signal of K+, which means that we have to compare the pressures of K,CrO, and K. Firstly, some preliminary thermodynamic calculations were made to show that the basic components of the vapour would be K,CrO,, IS, O,, CrO, and CrO,. We can write three linearly independent equations which correlate the pressures of the compounds listed above with the solid phase as well as with each other. [K2Cr04]
‘= K,CrO,
Q25) = P (K [ K,CrO,]
*CrQl1
(25)
= 2 K + CrO, + 0,
K p(26,=Pw)2
(26)
XP(W
XPWO2)
CrO, + +O, = CrO, K p(27)=P(Crw
XPWW’
xP@,)-1’2
(27)
The thermodynamic parameters required for calculating Kp(25j-Kti27j taken from the present work and ref. 3. The equations of mass conservation in the gas-phase are
were
P‘Et = 2PK,Cr0, + Pg
=
pg; =
PK
2PIc,CrO, + PO, + Pm, PK,CrO,
+
k02
+
h-0,
+ SPcro,
110
where p is the flow of the substance, that is, the number of molecules effusing from the cell through the square unit in unit time. This flow varies with the partial pressure [p =p(2rMRT)]according to the Herts-Knudsen equation. ptot represents the total flow of the substance in all its forms. The ratio between the flows #Et, &i and &i may now be determined. Five equations are obtained with five unknowns which can be solved. First, consider what would happen if evaporation proceeded normally. It means that the composition of the condensed phase must not be changed, that is, OSp’g = &i = 0.5~:. The solution at T = 1209.7 K is given in Table 10. The pressure of the dissociation products would have been three orders of magnitude less than the pressure of potassium chromate. However, in the present case, evaporation proceeds abnormally: 2-3% of the residue remains. This means that $p’;;’ + &‘; + f&:, that is, the composithat without having tion of the condensed phase is changeable. It follo6 additional information it is impossible to calculate the composition of the gas phase. In order to measure the pressure of potassium and oxygen, we made use of the method of ion/molecule equilibria. To this end, the ratio of ion currents of CrO; and CrO;, KCrO; and CrO; in experiments I, III and IV were calculated. Then, using the equations CrO;
+ $0,
1
p(Cr0;)
P(O2)= CrO;
= CrO;
P
tcro;)
*
xKp(28)
+ K = KCrO;
P(K) =
1
p(KCrO;) p(Cro,)
(29)
x %W
one can obtain the pressures of 0,
TABLE
b
I III IV
and K (see Table 10). The pressures of
10
Pressures of dissociation Exp. no.
(28)
1
products over potassium chromate
a
T (K)
P WKfl4) x 1o-6
PW x1o-6
P(W x 1o-6
P wf% x lo+
1209.7 1209.7 1209.7 1218.8
1.7 1.7 1.7 2.1
0.0033 0.42 0.13 0.21
0.0012 0.18 0.18 0.10
0.0015 6.5 x lo- lo 6.8 x 1O-9 1.3x10-*
1
P(CrW x 1o-6 0.0010 4.9 x lo- 9 5.1 x lo- 8 4.3 x 10-s
a Pressures are dimensionless values referred to the standard state: 1 atm = 1.033 X lo5 Pa. b Calculation is given for normal evaporation approximation.
111 TABLE
11
Thermodynamic functions of K,CrO,,,.
K,CrO.,, KCrOr
Temp.
K &rO,
KCrO;
24.4
19.4
13.5
276.1 296.6 329.6 356.1 378.3 397.4 414.2
244.0 258.4 282.3 302.0 318.9 333.6 346.5
K,C~,,*,
a
and CrO; CrO;
W) H,O,,- H,O(kJ mol-‘) 28.5 -(G$ 298.15 400 600 800 1000 1200 1400 a T’ =12&i
- @)/7’
104.8 135.1 183.5 222.6 256.6 287.3 317.5
(J mol-’ K-‘) 300.3 326.0 366.9 399.5 426.6 449.8 470.0
K; +tza = 293.9 J mol-’ K-‘.
chromium oxides are calculated by using equilibrium constants (26) and (27). The pressure of potassium is seen to be one order of magnitude less than that of potassium chromate. Using the pressures of K and 0, thus obtained, one can calculate the percentage of the residue which is expected to remain in experiments I, III and IV. Assuming that the activity of potassium chromate in the course of isothermal evaporation remains constant, the residue should be 8% 3% and 3.5%, respectively. APPENDIX
Calculation
of thermodynamic
functions
K2CrOQ(s). To calculate the potential &.(K 2Cr04(sj), the values S&, = 200.3 J mol-’ K-i and H& - Hi = 28.5 kJ mol-l [18] were used together with data on heat content in the interval of 500-1400 IS [22]. In the interval 298-500 K the heat content of Ci(K,CrO,(, ) was approximated by the d = 146.0 J mol-l K-l [18] equation Cf = 113.2 + O.llT on the basis of Cr,298 and C,O,, = 168.2 [22]. The enthalpies and temperatures of phase transitions are takkn from ref. 18. K,CrO,(g). Structure, D,,; R(K-0) = 2.45 A, R(Cr-0) = 1.675 A; OCrO = 109.47O [23,24]; I,1,1, = 3.72 X 10-lf2 g3 cm6. The frequencies are 850, 443, 183, 364, 895, 412, 245, 875(2), 385(2), 257(2) and 48(2) cm-l [25-273.
112
Kcro,- . Structure, Czo; R(K-0) = 2.45 A, R(Cr-0) = 1.675 A; I,I,,I, = 7.21 X 10-113 g3 cm6. The frequencies are 875, 850, 443, 385, 257, 364, 875, 385,48,895,412 and 245 cm-l. The molecular constants were chosen on the basis of those for K,CrO,. G-0,. Structure, C,,; go = 2, 1,1,,1, = 7.85 X 1O-“4 g3 cm6. The frequencies are 856, 483(2), 876(3) and 508(3). The molecular constants were chosen on the basis of those for CrOz[28], the distorted tetrahedral structure being assumed due to orbital degeneration. Inaccuracy of the calculated functions was estimated by assuming that the inaccuracy in IAIBIc is 10% 30% and 20% for K,CrO,, KCrO; and CrO;, respectively. The errors in the frequencies are: AY = 15 cm- ’ for K,CrO,, AV = 100 cm-’ for KCrO; and CrO; (except for r+ and y12, Av = 50 cm-l, and vg, AV = 20 cm-l, in KCrOJ. To this was added the error of approximation of the rigid rotator harmonic oscillator estimating it as 5% from the vibrational component in &- (as recommended in ref. 3). Thermodynamic functions thus calculated are given in Table 11, their accuracies are given in Table 9. REFERENCES 1 L.N. Sidorov, E.B. Rudny, M.I. Nikitin and I.D. Sorokin, Dokl. Akad. Nauk SSSR, 272 (1983) 1172. 2 E.B. Rudny, L.N. Sidorov and 0.M Vovk, Teplofii. Vys. Temp., 23 (1985) N2. 3 V.P. Glushko (Ed.), Thermodynamic Properties of Individual Substances, Vols. 1-4, Nauka, Moscow, 1978-1983. 4 MI. Nil&in, N.A. Igolkina, A.Ya. Borshchevsky and L.N. Sidorov, Dokl. Akad. Nauk SSSR, 272 (1983) 1165. 5 N.H. Afonsky, Zh. Neorg. Khim., 7 (1962) 2640. 6 U.V. Choudary, K.A. Gingerich and Y.E. Kingcade, J. Less-Common Metals, 42 (1975) 111. 7 M. Farber and R. Srivastava, Combust. Flame, 20 {1973) 33. 8 J.C. Wormhoudt and C.E. Kolb, N.B.S. Spec. Publ. 561, Vol. 1, 1979, p. 457. 9 W.J. Miller, J. Chem. Phys., 57 (1972) 2354. 10 G.A. Semenov, E.N. Nikolaev and K.V. Ovchinnikov, Vestn. Leningr. Univ. Fiz. Khim., 22 (1978) 85. 11 G.A. Semenov, L.A. Kuligina and K.K. Frantseva, Tezisy VI Vsesouznoi Konferenzii po Kalorimetrii i Kbim. Termodinamike, Mezniereba, Tbilisi, 1973, p. 329. 12 N.D. Sokolova, O.G. Volubeev and G.F. Voronin, Izv. Akad. Nauk SSSR, Neorg. Mater., 15 (1979) 1438. 13 M.B. Mann, In K. Ogata and T. Hgyakawa (Eds.), Recent Developments in Mass Spectrometry, University Park Press, Baltimore, 1970. 14 L.N. Sidorov, MI. Nikitin, E.V. Skokan and I.D_ Sorokin, Int. J. Mass Spectrom. Ion Pbys., 35 (1980) 203. 15 L.N. Sidorov, I.D. Sorokin, M.I. Nil&in and E.V. Skokan, Int. J. Mass Spectrom. Ion Phys., 39 (1981) 311.
113 16 V.I. Semenikhin, II. Minaeva, I.D. Sorokin, M.I. Nikitin, E.B. Rudny and L.N. Sidorov, High Temp. Sci., 18 (1985). 17 D.M. Himmelblau, Process Analysis by Statistical Methods, Wiley, New York, 1970. 18 Thermal Constants of Substances, Vol. 10, Akad. Nauk SSSR, Moscow, 1982. 19 P.A.G. O’Hare and J. Boerio, J. Chem. Thermodyn., 7 (1975) 1195. 20 N.A. Igolkina, Dissertation Thesis, Department of Chemistry, Moscow State University, Moscow, 1984. 21 H.D.B. Jenkins, A. Winsor and T.C. Waddington, J. Phys. Chem., 79 (1975) 578. 22 D. Sirousse-Zia, Thermochim. Acta, 19 (1977) 244. 23 V.A. Kulikov, V.V. Ugarov and N.G. Rambidi, J. Strukt. Khim., 23 (1982) 184. 24 G.V. Girichev, N.I. Giricheva, E.A. Kuligin and KS. Krasnov, J. Strukt. Rhim., 24 (1983) 63. 25 MI. Dvorkin, Ph.D. Thesis, Leningrad University, 1977. 26 J.R. Beattie, S.J. Ogden and D.D. Price, J. Chem. Sot. Dalton Trans., (1982) 505. 27 M. Spoliti, in A.Y. Bems (Ed.) Matrix Isolation Spectroscopy, Reidel, Dordrecht, 1981, p_ 473. 28 KS. Krasnov, Molecular Constants of Inorganic Substances, Khimiya, Leningrad, 1979.