Sept., 19621
TEMPERATURE DEPENDENCE OF KSIGHT SHIFTOF SODIUM-XMMOSIA SYSTEM
aldehyde,ltk and also that the structures of the activated complexes from 2-hydroxypteridine are analogous to those postulated16 for the acid-base catalyzed hydrolysis of esters and amides. Thus, the reactions for the neutral molecule with hydronium and hydroxyl ions would be as set out below. The steps (iij and (ivj involve simple proton trans(15) R. P. Eiell and W. C. E. Higginson, Proe. Roy. SOC.(London), 8197,141 (1949). (16) K. J. Laidler and P. A. Landskroener, Trans. Faraday Soc., 62, 200 (1956).
1693
fers to and from oxygen atoms and would be very fast, so that the steps (i) and (iii), which require more extensive structural rearrangements, would become rate-determining. The reversible acidbase catalyzed hydration of pteridine2t1l and 2hydroxypteridine across their 3 :4 double bonds would be expected to involve similar mechanisms and analogous activated complexes. This accords with the view that the oxygen atom of 2-hydroxypteridine is not directly involved in the formation of the activated complex.
TEJIPERATURE DEPENDENCE OF THE KNIGHT SHIFT OF THE SODIUilrC-A;?~MONI~4SYSTEM BY J. V. ACRIVOS Laurence Radiation Laboratory, Berkeley 4, California AND
K. S . PITZER
Department of Chemistry, Rice University, Houston 1, Texas Received March $9,1962
The Knight shift of NaZ3and "4 in sodium-ammonia solution was measured over the temperature interval -33 to +22" and in the concentration range corresponding to mole ratio 5.7 to 700 (NH,/Na). The results in the dilute region,
R 2 300, were interpreted in terms of the equilibrium constants K1 and K z for the reactions Na(am) = Na+(am) 4. e-(am) and Na(am) = '/ZNa?(am). The effective Knight shifts, k~ for Na23 in Na(am) andkl' for W4in e-(am) were found to be ko = (0.034 f 0.005)T+ and kl' = (13.5 f 1)T-I. The measured standard enthalpy and entropy of reaction for the dissociation and the dimerization equilibria are, respectively, AHlo (298') G -6.6 and AH20 = -7.3 f 1 lwal./mole and Aslo (298") E -34 and ASZO = -24.1 f 3 cal./deg. mole. The change in enthalpy for the dissociation equilibrium was temperature dependent and indicated that a large negative change in heat capacity accompanied the reaction. The electron densities a t the Na23 nucleus were pl(NaZ3)= 0,071 a ~ and - ~ 0.00098 ao-a for the concentrated ( R % 5.7) and dilute solutions ( R 5 300), respectively.
The study of the electromagnetic properties of the alkali snd alkaline earth me-tals in liquid ammonia has supplied a great deal of information about the chemical nature of these solutions. As a result of conductivity measurerrrents, Krausl ha.s proposed that there exist, present in solution, solvated atoms, positive ions, and electrons. The presence of paramagnetic species was indeed verified by Huster2and Freed and Sugarman3from the static magnetic susceptibility, x, and by Hutchison and Pastor" from the paramagnetic absorption by means of e.s.r. The main conclusions to be drawn from these measurements are: (a) the magnetic susceptibility of the metal in ammonia solution always lies below the expected Curie d u e , which is approached asymptotically only as the dilution increases to infinity, and (b) tlhe l / T t'emperature dependence of x is not obeyed. Elecker, Lindquist, a,nd Alder5 oxplained these result's by assuming the existmeliceof four differen.t species, solvat'ed metal dimers, atoms, and positive ions and electrons in the dilute solutions, and t,hen proceeded to evaluate the chemical equilibrium coiista,nts for the dissociation and dimerization of the solvated m e h l (1) C. A. Kraus, J. Am. Chsm. Soc.. 43, 749 (1921); for review work also see J . Chem. Educ., 30, 83 (1953). (2) E. Huster, Ann. P h w i k , 33, 477 (1938). (3) S. Freed a,nd N. Sugarman, J . Chem. Phys., 11, 351 (1943). (4) C. A. Hutohison, Jr., and R. C. Pastor, ibid., 21, 1959 (1953). ( 5 ) E. Becker, R. H. Lindquist, and E. J. Alder, ebid., 26, 971
(1956).
atoms or monomers from the e.s.r. data.4 These reactions may be written Sa(am)
=
Na+(amj
+ e-(am)
Na(amj = '/2Naz(am)
(1) (2)
with the combined reaction 1/z;2;a2(am) = Sa+(am) f e-(am) ( 3 ) where the respectiye equilibrium constants are K1, Kz, and Ka. The Knight shift (KS) data of McConnell and Holm6for the YaZ3-W4H8solutions at room temperature in the concentration range R = 5-500 supported these views. Pitzer' and Blumberg and Das8 were able to explain some of the features of the KS data6 by calculating the distribution of electron densities in the solvated paramagnetic species. Moreover, both Dye, Smith, and Sankuerg and Evers and Franklo derivecl sets of rquilibrium constants from conductance measurements of Krausl at t = -33" together with transference number data. Their respective results are in fair agreement. (6) H. M. McConnell and C. H. Holm, zbzd., 26, 1517 (1957). (7) K. S.Pitzer, zbid., 29, 453 (1958). ( 8 ) W. D. Blumberg and T. P. Das, pbzd., 30, 251 (1959) (9) J. L. Dye, R. F. Sankuer, and G. E. Smith, J . A m . Chem. Soc., 82, 4797, 4803 (1960). ( I O ) E. C. Evers and P. W. Frank, J . Chem. Phys., 30, 61 11959).
J. V. ACRIVOS AND K. S.PITZER
1694
tained from e.s.r.6 are larger, by a factor of three, than those computed from the conductance experiments.Q.10 However, K3 has substantially the same value from either source. I n this work, the KS of S a 2 3and W4 in the Na-NH3 solutions has been determined in the temperature interval -40 to 22". In the concentration range where the chemical equilibria given in eq. 1 and 2 are valid, the constants K1 and Kz are evaluated from the KS data together with the activity coefficient of the charged species obtained from the Debye-Huckel theory. Although the relative accuracy of the measurements is very Iow a t -33", fair agreement is obtained with the values obtained from the conductance measurements. lo
Regular silver Dewar surface t
T
- C n thermocouple (wax seal)
190mm Dewar surface
I
I!/ l b
SO m m
1
VJ-----12-12-
?
-15-
-
-17-
Pi surface (Hanovia cut every 2 m m across and lengthwise)
( I
-
sQ,
Experimenta1 Results
glass
---Thin-woled
m m thick)
(Wilmod .N.J.)
3040-
-52mm-
Fig. 1.-Rf. permeable dewar flask.
j *oo" '
rn. I .o
10
4
1 r
-
=re 0
x
0
0.1
z c :
-I
100
10
Vol. 66
The KS's of the Na-lu", solutions with respect to a standard of 0.5 m NaCl in NHI were measured with a Varian V4200 wide line n.m.r. spectrometer operating a t 10.0 and 2.77 Mc./sec. for Na*a and N14 resonance, respectively, in a constant magnetic field of 8881 oersteds. The stabilities of the magnetic field and radiofrequency were the determining facton in the experimental accuracy. The radiofrequency was determined with a Hewlett-Packard counter No. 524B to &2 C.P.S. while the field, stable to k 5 p.p.m., was swept with a linear potentiometer. The spectra were recorded by means of the sideband techniquela with a modulation frequency VM = 412 C.P.S. The separation between the sidebands of 824 C.P.S. was then used to calibrate the potentiometer reading. The temperature of the samples was measured to f0.5", by means of a copper-constantan thermocouple in contact with the sample tube. The sample tubes were immersed in a freezing mixture and contained in a dewar flask which allowed the rf. to penetrate. The constant temperatures were obtained as follows: 0' with an ice-water mixture, -15.3" with a solid-liquid mixture of benzyl alcohol, -30.6" with a solid-liquid mixture of bromobenzene, and below -33" with acetone-Dry Ice mixtures. The samples then were allowed to attain the equilibrium temperature inside the closed dewar. The dewar flask is shown in Fig. 1. The tip which contained the samples was not silvered but was covered with a thin layer of Pt (Hanovia) in which a cross and lengthwise grill was cut a t 2 mm. intervals in such a manner that the inner and outer surfaces would be concentric so as to allow perfect rf. penetration. The Na-NH3 samples were prepared in vucuo by first distilling a known weight of Na into the side arm of a sample tube and then distilling the required volume of NHI from a Na-NHa solution. The sample tubes were first aged in dilute HCI, then passed through hot cleaning solution, and finally steamed and.dried in the absence of dust. No decomposition was noticed when warniing the samples to room tem erature for long periods, as shown by the reproducibility of tEe n.m.r. measurements within the expected accuracy. The samples were stored in liquid nitrogen when not in use. The concentration qf the Na-NHa .solution is reported in terms of the mole ratio, R , or the sodium molality, m.
IO00
The vapor pressure studies of Dewaldll and the calorimetric results of Gunn and Greenl2 also support the proposed equilibria of Becker, et aL5 However, the equilibrium constants K 1 and Kz as ob-
where B is the volume of ammonia determined before the solution was made, p its density at that temperature (see, for instance, Yost and R ~ s s e l l ' ~ )and , TU is the weight of sodium. For the more dilute samples, a chemical analysis for total sodium was carried out after the measurements were finished. For R = 730, the nuclear resonance signal to noise ratio at room temperature for Na23 was barely unity hut rose t o 10 at -33". The KS data are given in Table I. Figure 2 shows the isothermal concentration dependence of the KS, according to the data given in Table I. The
(11) J. F. Dew&, Fh.D. Theeis, California Institute of Technology, 1948. (12) R. S. Gunn and L. R. Green, J. Chem. Phyu., 36, 363, 368 (1962).
(13) J. V. Acrivos, ihid., 36, 1097 (1962). (14) D. M. Yost and E€. Russell, Jr., "Systematic Inorganic Chemiatry," Prentioe-I-Iall, New York, N. Y., 1948, p. 138
R. Fig. 2.-Isothermal concentration dependence of the Knight shift in the N a 4 H a solutions.
TEMPERATURE DEPENDENCE OF KNIGHT SHIFTOF SODIUM-AMMONIA SYSTEM
Sept., 1962
TABLE I KNIGHT SHIFT OF Naza AND 4" IN Na-NHS SoLurrIoxsWITH I~ESPECT TO 0.5 MOLALNaCl IN "2" k(N&) Sample no.
1 20
x
R
5.7 12.2
m
10
4.8
t ("C.)
9.5 0 22 0 27 46 22 0 27 30
18
25
2.4
10
46
1.3
15 25
49 52
1.2 1.1
'3
GO
12
78
2ti
'30
0.98
-31 -60 22.5 0 0 26.3 22 14 5 0 - 15 -31.2 - 47 0 -19 5 -24 -G5 0
,75
22 - 7 .(iG 25.1 23 15.5
4 0
12 -22 -- 31) -- 5G .53 22 .53 22 - 7 -19.5 -24 .50 22 10 - s
I1 17
7
t10 111
118
0 -46
13 210 323
31
.28 .I8
-7
22.8 21 13.5 9 4.5 0 - 9 -22
-27.5 -31
104 10.10
1.40 1.25 1.45 1.06 1.oo 0.94 .87 .68 .63
{ .:E .
x
104
*0.10 U
.
x
91 87 70
2.82 0.26d
71 7d
a
a
a
U
..
..
..
2.23 2.05 1.61
116 107 84
.*
..
0.28 1.54 1.40
.27
..
..
.40 11.20" 1.73 a
1
.bo ..
.27
..
..
.. I . 11
.err
0.x2
.47
..
.. ..
.20
1.GG
.. .89 a
.. ..
1.11 1.14
..
.35
0.90 .81
..
-46
.15
..
..
.44 .37
..
168
..
103 $15 74 42
.. 1s
730
184
..
99 a
..
..
358 368
..
291 262 149
..
142 120
.29
.53 .31 .30
.83 .78
94 374 351
.48
216
..
..
.20
..
..
.55
..
..
247
..
.. ..
..
..
..
.07 .07
.. ..
.080
-
.. ..
isotherm a t 243°K. was obtained by interpolating or extrapolating the data in Table I. The values at room temperature are in agreement, within the exporimental accuracy, with the results of McConnell and Holm,$ when a correction is made for the chemical shift of Na+(am) with respect to Na+(aq) of 17 p.p.m.
Knight Shift The valuc of the effective field a t the nucleus under observation, He, is in general diffcrent from that of the extcrnally applied one, Ho,Thus, wtierc H, is the contribution due to the magnctization, M155'16
a
,42
..
n
..
.07 .03 .56 .51 .26 .21 .46 .37 .29 .03 .28 .64
.. 24 72 104
..
. 13
..
..
15 80 84
.. 1.87
I
..
..
.. .10 45 18.5 .62 .53 387 11.5 -53 .60 438 4.2 .49 .57 416 0 .42 .. .. 20 .18 .. .. -22 .43 314 .18 -28.5 .30 219 -30.5 - 34 .. .13 95 -43 .. .02 15 .. .. -51 .02 a Poor annealing of the glass led to cracks a t liquid nitrogen temperature and not all the runs could be completed. I, Here the Na*J resonance shows two absorption lines. Although the temperature is above the critical value, the cause may be a different phase adsorbed on the surface of the sample tube. The Ni4absorption gave a single line at thls temperature. Here t,he N14 resonance shows two absorption lines. Shaking the sample produced no effect; however, upon refreezing and warming up to 0" only one absorption wm observed. The Na2a absorption was a single line a t this temperature. Measured for the dilute phases in the twophase region. - 63
37
..
.
-29 -44 -46
68.07
3.62 3.46 2.78
.52 .31 .55
-24
lop
.48
..
- 17
a
133
.34
0
R~C(N)
..
..
22
- 7
2.55
..
.I3
..
I
5.58
.68
.29 .16 .06
450
k(N
.61 .56 .51
..
-52 14
1695
H,
=
(i
?r
- a ) M + qM
Here the Loreiitz cavity field, (4~/3)M,arises from the induced dipoles on the surface of a, microscopic hypothetical sphere which contains the nucleus, a! is the bulk diamagnetic correction factor, a! = 47/3 or Zn, respectively, for a sample shaped as a sphere or an infinite cylinder. For x E;: 10-7,4 and infinite cylinder sample shape, the first term is of the order of 0.1 p.p.m. p is a steric factor which depends on the anisotropy oi the electronic g factor of any paramagnetic species present in solution. =
(QL2 - g t ) (16n/45)(b/~)~ Q2
(15) N. Bloembergen and W. C. Dickinson, Phya. Rea., 79, 179 (1950). (16) W. C. Diokinson, ibid., 81,717 (1951).
J. V. ACEIVOS AND K. S.PITZER
1696
where b is the radius of the paramagnetic species and a is its distance from the nucleus under observation, 91’ and g l are, respectively, the g-factors in the directions parallel and perpendicular to the applied field. The g-factor for the Ka-KH3 solutions is g = 2.0012, which is lower than the free electron value of 2.0025. Since g2 = (1/3)(2g~* gl12) in solution, if one assunies g l = 2.0025, the anisotropy in the g factor gives a negligible contribution, pM 0.003 p . p m Hd is the field due to the orbital motion of the electrons in the iiidividual species. For n’a+(am) it may be assumed that Hd is constant and independent of the anion as is the case for aqueous solutions of different sodium ~ a 1 t s . l ~However, the diamagnetic correction for Naz(am) and Sa(am) is likely to be different from that for Sa+(am) and the estimate of this value is probably the largest source of error. The diamagnetic contribution from the electrons in expanded orbitals in the Na(arn) and Na2(am) species is thus (see for instance Pople, Bernstein, and Schneiderlg)
+
where ki and xi are the mole fraction and KS of the corresponding species. Chemical Equilibria In the concentration range where the chemical equilibria 1 and 2 are valid, R 2 150, the observed KS obey the relationships
k(Na27 = zoku
-
H d
e2
P1
cvhere /co is the KS for N a 2 3 in ?Ja(am), and ko’ and kl‘ are the KS for X14 in the individual species Sa(am) and e-(am), respectively. The mole fractions of Na(am), e-(am), and Xas(am) within the solute are, respectively, xo, xl, and 5 2 . The volumetric and optical spectral properties of Ka(am) and of Na+(am) e-(am) are practically identical. Gold, Jolly, and PitzerZ2 concluded from these facts that n’a(am) probably consisted of ion pairs of solvated sodium ions and electrons. From this model one would expect the KS for K14 to be substantially unchanged by this ion pair association and we shall hereafter assume k ~ ’= h’. The room temperature value of k1‘ is obtained by ] to infinite dilution: see extrapolating [E X k(S) Fig. 3.
+
f - dr IiTo 3mc2 er where p1 is the electron density and E the dielectric constant, which is larger than unity but smaller than the value for the bulk material. If ((ller)) O.lao-l, the diamagnetic shift at the central atom is of the order 2 p.p.m. for each electron, and zero at the coordinated NH3 molecules. H,is the field at the nucleus due to the Fermi contact termlg or in the paramagnetic species. Thus
-
where
Vol. 66
Ez 500
x
10-4
when the Curie temperature dependence of the susceptibility is introduced. I n order to determine k o , the functional dependence of k(Sa) with respect to nz must be known. Thus, if the solutions obey the equilibrium relationships given by eq. 1 and 2
$o is the unpaired electron t m ~ ‘ functiork e arid iV0 is Avogadro’s number. This term is now assumed to give the leading cont,ribution to He in addition to H,. Thus, the field shift with respect to KaCl in
“3
2,
+ + 2x2 r1
=
1
(9)
it follows that
is the KSZO and in the case where the chemical species containing the nucleus, n, under observation undergoes fast chemical exchange it can be shown thatzl (17) J. E. Wertz and 0. Jardetzky, J . Chem. Phys., 26, 357 (1956). (18) J. A. Pople. W. G. Sohneider, a n d H. J. Bernstein. “High Resolution Nuclear Magnetio Resonance,” &IcGraw-Hill Book Co.. Inc., New York, N. Y., 1959, p. 175. (19) E. Fermi, Z. Physik, 60, 320 (1930). (20) C. H. Townes, C . Herring, and U‘.D. Knight, Phys. IZrz., 72, 852 (1950). (21) H. S. Cutowskv. ” . D. TV. 21cCall. and C . P.Pliohter. J . Chem. Phva,, 21, 279 (1953).
where yA is the actiyity coefficient for the charged species. Hence, if one assumes that the value of (22) M.Gold. W. L. Jollv. and K. 84, 2264 (1962).
S. Pitzer. J . Am. Cttem.
Soc.,
TEMPERATURE I]EPENDENCE
Sept., 1962
OF
KNIGHT SHIFT O F SODIUM-1IRIMONIA
1697
SYSTEM
the activity coefficient will not vary appreciably with concentration, the value of lco may be deterniined \&en /
