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Enthalpy of solvation, ΔHsolv0(CrO42−) (g), of gaseous chromate ion as estimated from lattice energy calculations
Volume 35, number
CHEXICAL
3
ENTHALPY
OF SOLVATION,
AS ESTIMATED HDB.
FHY SICS
&Y$JCrO;-)
FROM LATTlCE
(g), OF GASEOUS
ENERGY
15 Sqtember
J_ETTERS
CHROBIATE
1975
ION
CAECULATIONS
JENKWS
Department
of ,!fo-lolecufarSciences,
Cfniwersiry of Warwick,
Gxrelrtry CV4 YAL, Warks. UK Received 14 April 1975 Revised manuscript received 9 hiay 19?5
of sohtion of the gaseous chromate ion, bHOWlv(CrO~-) (g) is estimated on the basis of recent lattice studies made in this laboratory, and P charge distribution assigned to the ion. On the basis of the xsignrd charge of -057 Protoll Units t0 the oxygen atoms of the GO:-unit, the told lattice potential ener$es xe fguad to be: ~~ot(N;sC1041 = 1836 kT mol-’ ; Upot(KzCr04) = 1717 kJ molmL; U,,ot(RbzCrOG) = 1645 kJ mol-’ and (IP~~(cs~C~O~) 598 W mol-' . The corresponding value for LY$‘~~,(CIO$-) &) = -1077 kJ mol-’ . The enth3b:f
energy
~~lv(CrO~7(g) = ~~InW2Cr04) Cc>
1. Zntrcduction
The Born,-Habe:r-Fajans
(3)
- ZA@mb(Mi) (g) - Upot(M2Cr04) - 3RT.
“cycle”
and, following the work of HaUiweU and Nyberg &mly(hl+)
(9) = 4bs.
[i3! (4
i-,y&(M+) 6).
We have: A&@+)
k) = @WnV.r,y,(M+)
(8) (5)
•t 4bs_,rydjH+)(6),
can be written for the alkali-metal chromates, which the folIowinE: equations derive: fE(MzCr04)
from
= Upt(M2CrOS),
where aE(M2Cr04:)
where AI8 &s. hyd.(“+) (&) 2nd A@&,v. h d (Mf) (id are the absolute and conventional enth aVpies ofhy-
(1)
is the total internal energy change
in producing gaseous ions from the crystalhne lattice and U,,(M2Cr04) is the total lattice potentia! energy. M is an alkali metal.
@&(CrO:-) - U&,(M+)
(g) =: MW,,(M&rOc) (g) - ti(M2Cr04)
hydration
.@~r”(Cr@-)
(g)
(2)
- 2dmnv_ -
where &E$,Ln(M2C~04) (c) is the standard enthalpy of solution of the crystalline chromate and .U&,(M’) (g) and AI&(CrO~-) the entha!pies of salvation of the ions to unit activity. Ccmbining
eqs.(l)and(2):
of Mf gaseous ion and L?&,
the absolute ton, thus:
= @(M,CrO,)
(c) - 3RT,
dration
hyd_(Hf) (6) is
of the gaseous pro-
(c) - 4(M,CrO,) h,&(M+) &!) -
Cr&M,CrO,)
A!$,v(CrCI~-.)
enthalpy
(as)
'eb,hyd_@-+)
k)
- 3RT.
(6)
(6) can be c&&ted
the total lattice potential energy of
zs a fucction
of
2
given chromate salt (i.e., M = Na, K, Rb, Cs) which, itself is 2 function of the distributed charge: qo, placed on each of 417
Volume -
:
35, numbe;
3
CHEMICAL
PHYSICS
oxygen.atoms
the of the CrOz- ion. Af~&~(Crf$-) (g) is plotted as a function of qn and the intersection(s) of the family of curves for M2CrUq allows an assignment of A&,(CrO~-) &) for the gaseous chromate
ion,
and aIso an assessment
of the charge,
to be made. Sodium cbxomate having orthorhombit symmetry and spxe group, VA’(Cmcm) [3) and differing from that of potassium, rubidium and caesiurn chromates which I%ve the K2S04 arrangement [&6] offers a discriminant in order that the thermodynamic parameter, &WIv(CrO~-) (g) can be assigned a value. qo,
LIXTERS
forms:
Ur,,-,&Na2Cr04j
= 1793.9
- 76.2~
- 3.S&,
(9)
U&K2
C&J
= 1771.6
f 90.14,
- 7.5q&
(10)
UP,(RblCrO,)=
1699.2
+71_5~+,
- 5.9420,
(11)
+ 74.2qo
- 7.Qq;,
(12)
UP,(Cs,CrOs)
= 1643.0
so that combination of standard thermochemical data [S--10] with the above lattice energy functions enables us to formulate equations of the general form: 2
and re:nrl:s
@
= ,g
The thermodynamic table 1, the specific
The parametiic dependence of UP,,(M2Cr04) on the distributed charge which is placed on the cluomate ion such that:
Ai$~l,(CrO$-)(g)
I;a+*0=-2
AE&,(CrO~-)(g)
from the sodium
(7)
has been established the general form:
u-r previous
work
[7] and takes
using the NBS.
Bj
sb.
(13)
parameters used are given in forms of eq. (13) take the form: = -1034.4+76.2~~~+3.5q;
(14)
salt data = -1149.1 data
-90.1q0+7.5q$r
[9] for the potassium
(15) salt and
~~,,(CrO~-)(g)=-1143.2-90.1~~t7.5q:, Up,,($CrO,) Table
=i
-+I&
parameters
for chromates
Puame ter ~~(M2CrO4~
$
(cl
(M5Cro4j (3q)
q&x.!zCW
%,v_
(c)
hyd.@*+) d”)
qbs. $t
t+d.(H’
[lo]
data for the potassium
(MzCr04)
arenga
viducs
NazCr04
KzCr04
-1328.8
-1382.8
-1373.6
-1396.7
-1389.5
- 1396.7
-1387.2
-1389.7
8.0
6.5
0.2
768.8
789.9
814.2
-1090.7
- 1090.7
-1090.7
-1090.7
1771.6
1771.6
1699.2
1643.0
-76.2
90.1
90.1
71.5
74.2
-3.5
-7.5
-7.5
-5.9
-7.0
-1149.1
B2
3.5
= -0.57
-1380.?
13.9
76.2
40
-1388.7
768.8
Bl
qo@O;-)
cs2cro4
44.8
-1034.1
Bo
Rbz no.+
685.8
1793.9
Ao
.42
@wlv(CrO~_)e,
(kJ mol-‘)
-1090.7
@
Al
.-al8
using the more recent
(8)
(16)
1
Thermodynamic
-90.1 7.5
Cp) = - 1077 kJ ml-’ FrOtOr,
Units
1975
and the specific
A~$&+)
2. Calculation
!S September
-1143.2 -90.1 7.5
-1111.5 -71.5 5.9
-!097.6 -74.2 7.0
Volume
sit
3.5, number
CHEMICAL PHYSICS LITTERS
3
15 September
1975
and
~~,,(cro~-)~)=-1111.5-71.5~~~5.9q~,(17) ~&~(Cr+)(g)
= -1097.5
-74.2q0+7.0q;
(18)
for the rubidium and caesium salts respectively. The five curves (14) through (18) are plotted
in fig. 1 and the results are summariszd in the following statements: (i) no unique intersection point is found; (ii) the two curves for the potassium salt give very similar intersection points (A and B) on the expanded scale of fig. 1;
(iii) the values for rubidium
(C) and caesium (D) are reasonably close to (A) and (B ; 1 (iv) the best value for A@Wlv(CrOq-) (g) that can be assigned corresponds to
A&,(CrO~-)($) (v) the corresponding
qcl = -0.57
= -1077 kJ mol-’ ;
1 a-o
- a:4
-1-2
-03
I
0-e
(19)
Fig. 1.
value for q. is
proton units
(20) References
111D.F.C. hforris and EA. Short, Nature 224 (1969) 950.
3. Discussion
[2i H.F. HaliiweU 2nd S.C. Nyberg, Trans. Farnday Sac. 59 (i963) 1126. 131 X. Nigli, Acta tiyst. 7 (1954) 775.
Using the assigned value for 40, the total lattice potential energies of the alts in question are: Clr,,,(Na,
CrO,)
= 1836.2 kJ mol-’
U
,
(21)
mol -1 ,
(22)
,
(23)
(K2Cr04) = 1717.4kJ Pot Upot(R’02Cr04)= 1645.4 kJ mol-’ LTpot(Cs2Cr04)
= 1598.4
kT mol-‘_
(24)
The vaule for AI$,,,(CrO~-) (8) cbtained in this study and corresponding to -1C77 kJ mol-l can be compared to the va!ue AI$,y(SO~-) (g) obtained in a recent study [ I1 ] of -1036 16 mol-1 and seems satisfactory. The value of q. = -0.57 proton units agrees well with the value q0 = -0.6 1 pro ton units obtained in our earlier study [7] and with values for q0 elsewhere in the literature and corresponding to q. = -0.66 [12], -0.69 [13,14] and -0.67 (15,16! proton units.
141 K. Ileimann, 11. Hosenfeld and N. Schonfeld, Mss. VerGffenti. Siemsnskonz. 5 (1S26) 119. 151 W.H. Zachariven and G.E. Zeigler, Z. ‘Gist. 101 (1940) 90.
Colby, Z. Krist. 75 (1931) 168. H.D.B. Jenk-As, A. Winsor and T.C. Waddingon, SLY.
I. Phys. Chem. 79 (1975)578. 181V.B. Parker, D.D. Wqrun and W.H. Evans, N.B.S. Tech. Note 270 (US Dept. of Commerce, Washington, 1971). PI F.D. Rossini et al., Nntl. BUI. Stds. Circular 500 (US Cwt. P&&-IS Office, \V&ington, 1952). [lOI C.N. hfuldiow md L.C. He!per, J. Am. (hem. Sot. 79 (1957)
404s.
H.D.B. Jenkins, hfol. Phys., to be published. S.S. Bstsznou, 2. Neorg. Khim. 9 (1964) 1322. L. C)lea.ri, G. Dehlichelis and L. DiSipio, Mol. Bhys. 10 (1966) 111. C. DeMichelis, L. Olezri and L. DiSipio, Coord. Chem.
Rev. L (i966) 18. 1.H. Hillier and V.R.
Saunders,
J.
Chem. Sot. D (1969)
1275.
I.H. Hillier and V.R. Saunders, (1970) 161.
P;oc. Roy. Sot. A320
419
CHEXICAL
3
ENTHALPY
OF SOLVATION,
AS ESTIMATED HDB.
FHY SICS
&Y$JCrO;-)
FROM LATTlCE
(g), OF GASEOUS
ENERGY
15 Sqtember
J_ETTERS
CHROBIATE
1975
ION
CAECULATIONS
JENKWS
Department
of ,!fo-lolecufarSciences,
Cfniwersiry of Warwick,
Gxrelrtry CV4 YAL, Warks. UK Received 14 April 1975 Revised manuscript received 9 hiay 19?5
of sohtion of the gaseous chromate ion, bHOWlv(CrO~-) (g) is estimated on the basis of recent lattice studies made in this laboratory, and P charge distribution assigned to the ion. On the basis of the xsignrd charge of -057 Protoll Units t0 the oxygen atoms of the GO:-unit, the told lattice potential ener$es xe fguad to be: ~~ot(N;sC1041 = 1836 kT mol-’ ; Upot(KzCr04) = 1717 kJ molmL; U,,ot(RbzCrOG) = 1645 kJ mol-’ and (IP~~(cs~C~O~) 598 W mol-' . The corresponding value for LY$‘~~,(CIO$-) &) = -1077 kJ mol-’ . The enth3b:f
energy
~~lv(CrO~7(g) = ~~InW2Cr04) Cc>
1. Zntrcduction
The Born,-Habe:r-Fajans
(3)
- ZA@mb(Mi) (g) - Upot(M2Cr04) - 3RT.
“cycle”
and, following the work of HaUiweU and Nyberg &mly(hl+)
(9) = 4bs.
[i3! (4
i-,y&(M+) 6).
We have: A&@+)
k) = @WnV.r,y,(M+)
(8) (5)
•t 4bs_,rydjH+)(6),
can be written for the alkali-metal chromates, which the folIowinE: equations derive: fE(MzCr04)
from
= Upt(M2CrOS),
where aE(M2Cr04:)
where AI8 &s. hyd.(“+) (&) 2nd A@&,v. h d (Mf) (id are the absolute and conventional enth aVpies ofhy-
(1)
is the total internal energy change
in producing gaseous ions from the crystalhne lattice and U,,(M2Cr04) is the total lattice potentia! energy. M is an alkali metal.
@&(CrO:-) - U&,(M+)
(g) =: MW,,(M&rOc) (g) - ti(M2Cr04)
hydration
.@~r”(Cr@-)
(g)
(2)
- 2dmnv_ -
where &E$,Ln(M2C~04) (c) is the standard enthalpy of solution of the crystalline chromate and .U&,(M’) (g) and AI&(CrO~-) the entha!pies of salvation of the ions to unit activity. Ccmbining
eqs.(l)and(2):
of Mf gaseous ion and L?&,
the absolute ton, thus:
= @(M,CrO,)
(c) - 3RT,
dration
hyd_(Hf) (6) is
of the gaseous pro-
(c) - 4(M,CrO,) h,&(M+) &!) -
Cr&M,CrO,)
A!$,v(CrCI~-.)
enthalpy
(as)
'eb,hyd_@-+)
k)
- 3RT.
(6)
(6) can be c&&ted
the total lattice potential energy of
zs a fucction
of
2
given chromate salt (i.e., M = Na, K, Rb, Cs) which, itself is 2 function of the distributed charge: qo, placed on each of 417
Volume -
:
35, numbe;
3
CHEMICAL
PHYSICS
oxygen.atoms
the of the CrOz- ion. Af~&~(Crf$-) (g) is plotted as a function of qn and the intersection(s) of the family of curves for M2CrUq allows an assignment of A&,(CrO~-) &) for the gaseous chromate
ion,
and aIso an assessment
of the charge,
to be made. Sodium cbxomate having orthorhombit symmetry and spxe group, VA’(Cmcm) [3) and differing from that of potassium, rubidium and caesiurn chromates which I%ve the K2S04 arrangement [&6] offers a discriminant in order that the thermodynamic parameter, &WIv(CrO~-) (g) can be assigned a value. qo,
LIXTERS
forms:
Ur,,-,&Na2Cr04j
= 1793.9
- 76.2~
- 3.S&,
(9)
U&K2
C&J
= 1771.6
f 90.14,
- 7.5q&
(10)
UP,(RblCrO,)=
1699.2
+71_5~+,
- 5.9420,
(11)
+ 74.2qo
- 7.Qq;,
(12)
UP,(Cs,CrOs)
= 1643.0
so that combination of standard thermochemical data [S--10] with the above lattice energy functions enables us to formulate equations of the general form: 2
and re:nrl:s
@
= ,g
The thermodynamic table 1, the specific
The parametiic dependence of UP,,(M2Cr04) on the distributed charge which is placed on the cluomate ion such that:
Ai$~l,(CrO$-)(g)
I;a+*0=-2
AE&,(CrO~-)(g)
from the sodium
(7)
has been established the general form:
u-r previous
work
[7] and takes
using the NBS.
Bj
sb.
(13)
parameters used are given in forms of eq. (13) take the form: = -1034.4+76.2~~~+3.5q;
(14)
salt data = -1149.1 data
-90.1q0+7.5q$r
[9] for the potassium
(15) salt and
~~,,(CrO~-)(g)=-1143.2-90.1~~t7.5q:, Up,,($CrO,) Table
=i
-+I&
parameters
for chromates
Puame ter ~~(M2CrO4~
$
(cl
(M5Cro4j (3q)
q&x.!zCW
%,v_
(c)
hyd.@*+) d”)
qbs. $t
t+d.(H’
[lo]
data for the potassium
(MzCr04)
arenga
viducs
NazCr04
KzCr04
-1328.8
-1382.8
-1373.6
-1396.7
-1389.5
- 1396.7
-1387.2
-1389.7
8.0
6.5
0.2
768.8
789.9
814.2
-1090.7
- 1090.7
-1090.7
-1090.7
1771.6
1771.6
1699.2
1643.0
-76.2
90.1
90.1
71.5
74.2
-3.5
-7.5
-7.5
-5.9
-7.0
-1149.1
B2
3.5
= -0.57
-1380.?
13.9
76.2
40
-1388.7
768.8
Bl
qo@O;-)
cs2cro4
44.8
-1034.1
Bo
Rbz no.+
685.8
1793.9
Ao
.42
@wlv(CrO~_)e,
(kJ mol-‘)
-1090.7
@
Al
.-al8
using the more recent
(8)
(16)
1
Thermodynamic
-90.1 7.5
Cp) = - 1077 kJ ml-’ FrOtOr,
Units
1975
and the specific
A~$&+)
2. Calculation
!S September
-1143.2 -90.1 7.5
-1111.5 -71.5 5.9
-!097.6 -74.2 7.0
Volume
sit
3.5, number
CHEMICAL PHYSICS LITTERS
3
15 September
1975
and
~~,,(cro~-)~)=-1111.5-71.5~~~5.9q~,(17) ~&~(Cr+)(g)
= -1097.5
-74.2q0+7.0q;
(18)
for the rubidium and caesium salts respectively. The five curves (14) through (18) are plotted
in fig. 1 and the results are summariszd in the following statements: (i) no unique intersection point is found; (ii) the two curves for the potassium salt give very similar intersection points (A and B) on the expanded scale of fig. 1;
(iii) the values for rubidium
(C) and caesium (D) are reasonably close to (A) and (B ; 1 (iv) the best value for A@Wlv(CrOq-) (g) that can be assigned corresponds to
A&,(CrO~-)($) (v) the corresponding
qcl = -0.57
= -1077 kJ mol-’ ;
1 a-o
- a:4
-1-2
-03
I
0-e
(19)
Fig. 1.
value for q. is
proton units
(20) References
111D.F.C. hforris and EA. Short, Nature 224 (1969) 950.
3. Discussion
[2i H.F. HaliiweU 2nd S.C. Nyberg, Trans. Farnday Sac. 59 (i963) 1126. 131 X. Nigli, Acta tiyst. 7 (1954) 775.
Using the assigned value for 40, the total lattice potential energies of the alts in question are: Clr,,,(Na,
CrO,)
= 1836.2 kJ mol-’
U
,
(21)
mol -1 ,
(22)
,
(23)
(K2Cr04) = 1717.4kJ Pot Upot(R’02Cr04)= 1645.4 kJ mol-’ LTpot(Cs2Cr04)
= 1598.4
kT mol-‘_
(24)
The vaule for AI$,,,(CrO~-) (8) cbtained in this study and corresponding to -1C77 kJ mol-l can be compared to the va!ue AI$,y(SO~-) (g) obtained in a recent study [ I1 ] of -1036 16 mol-1 and seems satisfactory. The value of q. = -0.57 proton units agrees well with the value q0 = -0.6 1 pro ton units obtained in our earlier study [7] and with values for q0 elsewhere in the literature and corresponding to q. = -0.66 [12], -0.69 [13,14] and -0.67 (15,16! proton units.
141 K. Ileimann, 11. Hosenfeld and N. Schonfeld, Mss. VerGffenti. Siemsnskonz. 5 (1S26) 119. 151 W.H. Zachariven and G.E. Zeigler, Z. ‘Gist. 101 (1940) 90.
Colby, Z. Krist. 75 (1931) 168. H.D.B. Jenk-As, A. Winsor and T.C. Waddingon, SLY.
I. Phys. Chem. 79 (1975)578. 181V.B. Parker, D.D. Wqrun and W.H. Evans, N.B.S. Tech. Note 270 (US Dept. of Commerce, Washington, 1971). PI F.D. Rossini et al., Nntl. BUI. Stds. Circular 500 (US Cwt. P&&-IS Office, \V&ington, 1952). [lOI C.N. hfuldiow md L.C. He!per, J. Am. (hem. Sot. 79 (1957)
404s.
H.D.B. Jenkins, hfol. Phys., to be published. S.S. Bstsznou, 2. Neorg. Khim. 9 (1964) 1322. L. C)lea.ri, G. Dehlichelis and L. DiSipio, Mol. Bhys. 10 (1966) 111. C. DeMichelis, L. Olezri and L. DiSipio, Coord. Chem.
Rev. L (i966) 18. 1.H. Hillier and V.R.
Saunders,
J.
Chem. Sot. D (1969)
1275.
I.H. Hillier and V.R. Saunders, (1970) 161.
P;oc. Roy. Sot. A320
419