HANDLING AND USES OF THE ALKALI METALS

The Binary System Sodium-Lithium W . H . H O W L A N D a n d L. F. EPSTEIN

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on June 2, 2015 | http://pubs.acs.org Publication Date: January 1, 1957 | doi: 10.1021/ba-1957-0019.ch005

Knolls Atomic Power Laboratory, G e n e r a l Schenectady, N . Y .

Electric

Co.,

The sodium-lithium phase system has been studied by thermal analysis in the liquid and solid regions to temperatures in excess of 400°C. Two liquid phases separate at 170.6°C. with compositions of 3.4 and 91.6 atom % sodium. The critical solution temperature is 442° ± 10°C. at a composition of 40.3 atom % sodium. The freezing point of pure lithium is depressed from 180.5°C. to 170.6°C. by the addition of 3.4 atom % sodium, and the freezing point of pure sodium is depressed from 97.8° to 92.2°C. by the addition of 3.8 atom % lithium. From 170.6° to 92.2°C. one liquid phase exists in equilibrium with pure lithium. Regardless of the similarity in the properties of the pure liquid metals, the binary system deviates markedly from simple nonideal behavior even in the very dilute solutions. Correlation of the experimentally observed data with the Scatchard-Hildebrand regular solution model using the Flory-Huggins entropy correction is discussed.

U N T I L recent years, the study of nonaqueous solutions has dealt p r i n c i p a l l y w i t h systems of polyatomic organic compounds. W i t h these compounds, there are m a n y cases w h e r e properties of the components differ greatly enough to cause l i q u i d phase separations. B i n a r y systems of fused salts a n d l i q u i d metals have not r e ceived the extensive scrutiny that has been devoted to organic systems. T h i s has not been for lack of interesting w o r k i n g materials. A m o n g the metals, at least 50 b i n a r y combinations have been f o u n d w h i c h exhibit large enough deviations f r o m ideality to cause l i q u i d phase separation. T h e components of the system studied here are two of the simplest i n atomic structure that exhibit this phenomenon, a n d no extensive systematic study of the i m m i s c i b i l i t y region has been reported. P r e vious investigations have been made (1, 4, 7) i n the temperature range below 237 °C. S a l m o n a n d A h m a n n (9) extrapolated their l o w temperature data a n d obtained a critical solution temperature of 379°C. at a composition of 35 atom % sodium. N o t only are the e x p e r i m e n t a l data of interest, b u t the relative s i m p l i c i t y of the components of this system provides a rather i n t r i g u i n g basis f o r comparison of observations a n d the results of m o d e r n n o n i d e a l solution theories.

Experimental INERT ATMOSPHERE. Because the a l k a l i metals react v o r a c i o u s l y w i t h a i r a n d moisture, extreme care must be e m p l o y e d i n h a n d l i n g t h e m after they have been purified. T h e use of a purified h e l i u m - a t m o s p h e r e d r y b o x facilitated the p r e p aration of the solutions for t h e r m a l analysis. W e l d i n g grade h e l i u m w a s purified 34

In HANDLING AND USES OF THE ALKALI METALS; Advances in Chemistry; American Chemical Society: Washington, DC, 1957.

HOWLAND AND EPSTEIN—-BINARY SYSTEM SODIUM-LITHIUM

35


b y passing it over heated c a l c i u m before a d m i t t i n g it into the d r y b o x . T h e r e s i d u a l o x y g e n content i n the d r y b o x atmosphere measured b y the m e t h o d of P e p k o witz a n d S h i r l e y (8) was less t h a n 10 p.p.m. PREPARATION OF REAGENTS. B a k e r ' s analyzed CP. l u m p s o d i u m (oil-free) was triple d i s t i l l e d i n glass at about 300 ° C . T a b l e I shows the composition g i v e n b y the m a n u f a c t u r e r a n d the composition after distillation. C h e m i c a l analysis of the distillate was c a r r i e d out i n this l a b o r a t o r y according to the methods described b y G i n n i n g s , Douglas, a n d B a l l (3). L i t h i u m was obtained f r o m the M a y w o o d C h e m ical W o r k s sealed i n cans u n d e r h e l i u m . T h e s u p p l i e r submitted the analysis s h o w n i n T a b l e II. H o w e v e r , no o x y g e n analysis was g i v e n for l i t h i u m , a n d because of the lack of i n f o r m a t i o n o n s o l u b i l i t y - t e m p e r a t u r e studies, it was not possible to estimate the o x y g e n content as i n the case of s o d i u m , b u t it is p r o b a b l y of the same order of magnitude. F o r f u r t h e r purification, the r a w l i t h i u m was filtered near 200 ° C . t h r o u g h a stainless steel m i c r o m e t a l l i c filter of 2 5 - m i c r o n pore size to r e m o v e a n y insoluble oxide a n d n i t r i d e particles.

Table I. Impurity Fe Ca CI PO4 H e a v y metals SO4 Ν O a

Composition of Sodium Raw Sodium, Wt. % 0.000 0.05 0.001 0.0005 0.0005 0.002 0.001 0.0030

Distilled S o d i u m , Wt. % 0.0005 0.0013 0.0010 0.0062 0.0002 0.0015 0.0000 0.0030

0.0137 Total 0.0580 S o d i u m , % (min.) 99.94 99.99 " A s s u m e d to be e q u i l b r i u m solubility a little above m e l t i n g point of sodium.

Table II.

Composition of Lithium

Impurity Si F e a n d A l , calcd. as F e Ca Na H e a v y metals, c a l c d . as N i Ν Cl, maximum Total Li, minimum

Composition, W t . % 0.015 0.03 0.06 0.02 0.09 0.03 0.003 0.248 99.75

PROCEDURE. A t h r e e - j u n c t i o n i r o n - c o n s t a n t a n thermocouple was calibrated against the freezing points of sodium, l i t h i u m , t i n , lead, a n d zinc to ± 0.05 ° C . a n d inserted into the stainless steel protection tube shown i n F i g u r e 1. T h e purified metals were w e i g h e d to ± 0.01 g r a m i n the d r y b o x for the p r e p aration of the starting solution. W e i g h e d c h u n k s of s o d i u m or l i t h i u m w e r e h u n g f r o m each of the four glass hooks (two of w h i c h are shown) b y stainless steel wires. B y rotating one of the ground-glass joints, the weighed m e t a l sample could be dropped into the beaker to change the composition of the solution b y a p r e d e t e r m i n e d amount. Before heating the solution, the system was evacuated to less t h a n 0.1 m i c r o n a n d purified h e l i u m at less t h a n 1 atm. pressure was admitted to reduce the e v a p oration rate of the metals. B y i n d u c t i o n heating, a n d the a i d of a blower, it was possible to keep the glass parts of the system a n d stopcock grease r e l a t i v e l y cool, a n d at the same time to transfer the heat effectively to the conducting metals i n the system. C o o l i n g rates were controlled b y r e d u c i n g the R . F . current after the desired m a x i m u m temperature h a d been attained. T r a n s i t i o n temperatures were d e t e r m i n e d f r o m a differential type plot of the rate of change of e.m.f. as a f u n c t i o n of the e.m.f. It was observed that this type of c u r v e has a more a b r u p t change i n slope at the transition temperatures t h a n does the linear type (e.m.f. vs. t i m e ) , especially i n the h i g h - t e m p e r a t u r e region. T h e e x p e r i m e n t a l results are s h o w n i n T a b l e III a n d F i g u r e 2, w h e r e χ is the mole fraction of s o d i u m a n d the superscript p r i m e a n d double p r i m e refer to t h e l i t h i u m - r i c h a n d s o d i u m - r i c h l i q u i d phases, respectively.


A D V A N C E S IN CHEMISTRY SERIES

Table III. Experimental Data Base of I m m i s c i b i l i t y L o o p

Two-Liquid-Phase Region


x'

t,°C.

x"

t,°C 170.50 î 0 8 8 i .41

t,°C. «c 0.0235 0.0235 0.0358 0.0358

0.043 0.052 0.055 0.059 0.063 0.063 0.068 0.068 0.076 0.085 0.095 0.112 0.112 0.132 0.148 0.178 0.178 0.178

194.4 206.9 220.6 227.2 0.903 183.1 231.9 0.867 206.9 238.7 0.838 250.9 293.2 0.785 312.0 301.0 0.754 329.3 310.8 0.734 353 342.2 0.706 377 375 0.706 377 373 0.672 416 374 0.604 424 393 403 400 396 413 F r e e z i n g P o i n t Depression Sodium Lithium t,°C. t,°C. X X 1.0000 0.0000 180.54 97.81 0.9944 97.05 0.0066 178.29 0.9881 96.20 0.0066 178.56 0.9750 93.95 0.0129 176.61 0.9690 93.17 0.0129 176.77 0.9612 92.91 0.0235 173.58 0.0235 173.66

X

7 0 5

1 7 0 > 5

1 7 0 < 5 70

0.0471 0.0642 0.0642 0.0941 0.1479 0.7540 Mean

L 7 0 I 5 8

y 2 ^0.82 3 UQ.38 170.6 ^0.1 0 > 2

1 7 0 9

Îc4 0.954 0.940 0.924

0 0

0.0642 0.0941 0.1479 0.7540 °- °Mean 754

Π1· .2

7

148

92.25 7 2.72 .35 7 92.17 ±0.44 9 2 > 8

9

91

9 1 > 6

Figure 1. Apparatus for determination of cooling curves in sodium-lithium system



HOWLAND AND EPSTEIN—BINARY SYSTEM SODIUM-LITHIUM

Figure 2. B i n a r y

system

37

sodium-lithium

Results and Discussion LIQUID-LIQUID CURVE AND CRITICAL SOLUTION POINT. I n the n o w classical theory of r e g u l a r solutions developed b y S c a t c h a r d (10) a n d H i l d e b r a n d (5) w i t h t h e n o n i d e a l entropy correction g i v e n b y F l o r y a n d H u g g i n s (5), the activities of t h e components of a b i n a r y system are g i v e n b y In a* =

In i +

In a, =

In (1 - 0 ) +

(1 - α) (1 - 0 ) + β/Τ (1 - φι)

(la)

9

4

t

[(1 - a ) / a ] i + β/(αΤ)

\

(lb)

w h e r e φχ is the v o l u m e fraction of the i ' t h component a n d α = Vi/V where the Vi's are m o l a l volumes. Subscripts 1 a n d 2 refer to s o d i u m a n d l i t h i u m , respective ly, throughout this report, β is a parameter essentially independent of t e m p e r a ture a n d composition, a n d characteristic of the nature of the components of the system. If the f u r t h e r assumption is made that the interaction force between u n l i k e species is the geometric m e a n of the values for l i k e molecules, a postulate that has been extensively e x p l o r e d b y S c a t c h a r d (10) a n d H i l d e b r a n d (5), it f o l lows ftiat β should be given b y t

/3=

T h e solubility parameter, b systems b y the r e l a t i o n

h

(«ι - δ ) VJR 2

(2)

2

has been f o u n d to be a p p r o x i m a t e d w e l l i n m a n y d\=E\/Vi

(3)

w h e r e E \ is the energy of v a p o r i z a t i o n of the i ' t h component. I n this theory, the v o l u m e changes o n m i x i n g are considered n e g l i g i b l y s m a l l . A t the c r i t i c a l point, Id In cu/3 In 0 « ] = [3 In a /d

(In 0 i ) ]

2

c

2

t

c

= 0

(4)

a n d the critical solution temperature a n d composition are g i v e n b y

xc = 1/ (1 + a c ) _

(5a)

8/2

Το = 2β / (1 + V a ) ΰ

c

2


(5b)


38

A p p l y i n g this theory to the l i t h i u m - s o d i u m system, c o m p u t i n g the 5 's a n d W s f r o m k n o w n heat of v a p o r i z a t i o n a n d l i q u i d density data, a = 1.908 (6a) βο = 5790 (6b) W i t h these constants, x — 0.275 mole fraction s o d i u m (7a) U = 1769°C. (7b) T h e c r i t i c a l solution temperature thus obtained is e x t r e m e l y h i g h c o m p a r e d w i t h the measured v a l u e . T h e v a l i d i t y of the geometric m e a n assumption appears to be as questionable i n this system as it m a y be for most metallic solutions. (

c

c

If E q u a t i o n l a is extended to the next h i g h e r power of the composition—i.e., In α = In φ + 1

α

(1 - φ,) +

(1 - α)

(β/Τ)

(1 - 0 θ

2

+

( Γ / Τ ) (1 - 0 ι )

3

(8a)


b y the G i b b s - D u h e m r e l a t i o n 1 η α , = 1η(1 - ( 1 / α ) ( α - 1 ) φ + [(2/3 + 3 Γ) / (2 α Τ ) ] φ\ - ( Γ / α Τ ) ^ (8b) T o calculate the l i q u i d - l i q u i d c u r v e for this system, β a n d Γ w e r e treated as parameters dependent o n temperature but independent of composition, a n d fitted to the equations β = + 6199.0 11.458 Τ + 0.010282 Τ (9a) Γ = - 9461.9 + 29.637 Τ - 0.02613 Τ (9b) F r o m E q u a t i o n s 4 a n d 5 the c r i t i c a l solution temperature a n d composition are given by l / 0 c = ( 1 / T c ) [2 βο + 6 r (1 - * , ) ] (10a) T = 2 0% [ ( j 8 , - 3 I \ . ) - 3 Γ , 0 , ] (10b) and simultaneous solution of these equations, along w i t h the values (6) βο = 3263 a n d T — —1628 yields Xc = 0.403 ± mole fraction s o d i u m (11a) U = 442° ± 1 0 C . (lib) i n good agreement w i t h a r e l a t i v e l y short v i s u a l extrapolation of the e x p e r i m e n t a l data. (Unless otherwise indicated, φ a n d χ refer to s o d i u m — i . e . , φ=φχ , x=Xi t is i n degrees centigrade, Τ i n degrees K e l v i n . ) T h e probable e r r o r i n the c o m position g i v e n here was d e t e r m i n e d f r o m a n e x a m i n a t i o n of the fit of the x' - x" 8

1

2

c

c

c

C

f

)

°C. 40. 3%

LIQU

LIQUID Π

j 2

— EXPERI CENTAL

\

/

LIQUID I

EMPIRICAL

+ LIQUID Π

+ \\

J

170.6 C. e

\91.6 %

3.4%

\

j 10

20

30

40 50 ATOMIC PERCENT SODIUM

+

60

70

Figure 3. O b s e r v e d a n d c a l c u l a t e d curves f o r l i q u i d u s

80 region


100

HOWLAND A N D EPSTEIN—BINARY SYSTEM

39

SODIUM-LITHIUM

Τ data to these equations (see below) ; a n d the e r r o r A t i n the critical temperature f r o m the corresponding error i n the composition A and the relation c

c

Ate = 2φο [2 (βο - 3 Tc) - 9 r 0c] Δ 0c (9) A t e q u i l i b r i u m , the activity of the i ' t h component is the same i n a l l phases, so that the above equations y i e l d the expressions c

In

(070")-(1-a) +

(Γ /T)

(0'-0")_(/3/T) [3 (0' - 0") - 3

1η [ ( 1 - . 0 θ / ( 1 - 0 " ) ] - ( 1 - α )


+

( 0 ' ~ 0 " ) [2—(0 +

(0' - 0" ) + 2

(1/α

2

3

2

3

(12a)

(φ'-φ")

(2 β + 3 Γ) (ι/ α Τ ) ( 0 ' _ . 0 ' < ) _ ( Γ / α Τ ) 2

0")]

(0' - 0" ) ] = 0 (0' —0" )=Ο

2

3

3

(12b)

w h e r e φ' a n d φ" are the v o l u m e fractions of s o d i u m i n the l i t h i u m - r i c h a n d s o d i u m r i c h phases, respectively. F r o m E q u a t i o n s 6 a n d 10 the e m p i r i c a l l i q u i d u s c u r v e as a function of temperature m a y be calculated b y successive approximations. T h e calculated compositions are s h o w n at r o u n d e d temperatures i n T a b l e I V , a n d g r a p h i c a l l y i n F i g u r e 3.

Table IV.

x' and x" at Rounded Temperatures

t,°c. 170.6

x' 0.0340

x" 0.9160

180.0 190.0

0.0342 0.0346

0.9103 0.9039

200.0 210.0 220.0 230.0 240.0

0.0353 0.0362 0.0372 0.0388 0.0405

0.8973 0.8903 0.8830 0.8753 0.8673

250.0 260.0 270.0 280.0 290.0

0.0426 0.0450 0.0478 0.0511 0.0549

0.8588 0.8500 0.8406 0.8307 0.8203

300.0 310.0 320.0 330.0 340.0

0.0593 0.0644 0.0702 0.0771 0.0850

0.8093 0.7975 0.7850 0.7717 0.7573

350.0 360.0 370.0 380.0 390.0

0.0943 0.1051 0.1178 0.1328 0.1505

0.7419 0.7252 0.7069 0.6869 0.6646

400.0 410.0 420.0 430.0 440.0

0.1719 0.1978 0.2304 0.2744 0.3528

0.6395 0.6106 0.5760 0.5311 0.4529

441.8

0.4030

0.4030

T h e extended expressions for the activities (8), using the F l o r y - H u g g i n s e n t r o p y correction a n d the a d d i t i o n a l t e r m ( Γ / Τ ) (1 - 0 i ) , y i e l d adequate agreement w i t h observation, p r o v i d i n g that the e m p i r i c a l β a n d Γ values of E q u a t i o n 6 are used. T h e value of βο observed is v e r y l o w c o m p a r e d w i t h the constant obtained f r o m the energies of v a p o r i z a t i o n a n d m o l a l v o l u m e data; the reasons f o r this are somewhat obscure. It m a y be that the v o l u m e change on m i x i n g t e r m is not zero, as is assumed above, b u t quite large. A plausible explanation is that the l i q u i d is considerably more complex t h a n was assumed i n the theoretical analysis. I n stead of a simple solution containing only the species l i t h i u m a n d sodium, it seems l i k e l y that there m a y be some c h e m i c a l combination. It has been established (3) that i n the b i n a r y systems of s o d i u m w i t h cesium, r u b i d i u m , a n d potassium, c o m pounds of the f o r m N a K exist; a n d it is perhaps not excessively speculative to assume that the c o m p o u n d N a L i m a y be present i n the system u n d e r i n v e s t i g a tion. W h i l e the quantitative relations for the c r i t i c a l solution temperature of such a t e r n a r y m i x t u r e have not been developed, it seems l i k e l y that the i n c l u s i o n of a t h i r d species w o u l d result i n the l o w e r i n g of t , a n d thus a n apparent gross failure of the geometric m e a n relation, as w e l l as a large temperature coefficient for β. 3

2

2

c



40

FREEZING POINT DEPRESSIONS. T h e a p p l i c a t i o n of the f u n d a m e n t a l laws of t h e r m o d y n a m i c s to the freezing point depressions, o n the assumption that the solid species c o m i n g out of solution is the p u r e component, leads to expressions f o r t h e activity coefficients along the freezing point c u r v e In i = - In χι + ( Δ Η ° < / K ) ( 1 / T ° 7


+

0/R)£

e

t

- 1/T)

[Cp ( 1 ) - C

P

( T - T ° i ) dT

( s ) ] * (1/T«)

(13)

w h e r e Δ Η ° , is the heat of fusion a n d T % is the absolute m e l t i n g point of the i ' t h component. T h e values of these quantities, a n d the constant pressure heat c a p a c i ties of both solid a n d l i q u i d , are v e r y w e l l k n o w n f r o m the w o r k of Douglas, G a i nings, a n d associates (2,3) f o r l i t h i u m a n d s o d i u m . T h e i r use permits the c o m p u t a tation of the apparent activity coefficients a l o n g the t w o freezing point curves. It is f o u n d u s i n g these data that In i = - In + Ai+ B ( 1 / T ) + C* In Τ + Di Τ + Et Τ + F w i t h the f o l l o w i n g values for the constants: X

7

i

i

(Metal) At Bi Ci Di Et Fi

4

1 (Na) + 23.873 45 — 4.955 91 χ 10+ 4.874 14 + 2.214 40 χ 10— 1.392 46 χ 100

t

Τ

(13a)

2 (Li) + 48.265 56 — 9.953 19 χ 10 — 9.665 41 + 4.239 72 χ 10" — 3.678 02 χ 10+ 1.489 54 χ 10~

2

+2

2

2

5

5 8

V a l u e s of logio7t c o m p u t e d f r o m these e q u a t i o n s a r e g i v e n i n T a b l e V , m a r k e d E q u a t i o n 13. If a l l the assumptions made i n this analysis are v a l i d , it s h o u l d also be possible to compute the activity coefficient of l i t h i u m at the point 1 7 0 . 6 ° C , X i = 0.034 ( w h i c h lies o n both the freezing point a n d l i q u i d - l i q u i d curves) f r o m E q u a t i o n 8b. If this is done, it is f o u n d that logioTa f r o m E q u a t i o n 13 is about + 0.0073; b u t f r o m E q u a t i o n 8b, the v a l u e of logi72 f o u n d is - 0.023. T h e scatter i n the points g i v e n i n T a b l e V is d u e to the fact that e x p e r i m e n t a l values of χ ι a n d T t w e r e inserted i n E q u a t i o n 13a; a n d the l a c k of monotonie b e h a v i o r i n the calculated values of log™ y ι is a direct consequence of the errors of observation.

Table V.

Calculated Activity Coefficients along the Freezing Point Curves Lithium logio 72 E q u a t i o n 15 E q u a t i o n 13 0 0 0.00137 0.00143 0.00116 0.00143 0.00275 0.00277 0.00263 0.00277 0.00502 0.00498 0.00496 0.00498 0.00733

Sodium t, c. c

97.81 97.05 96.20 93.95 93.17 92.21

t,°C.

logio 72 E q u a t i o n 13 E q u a t i o n 15 0 0 0.00169 0.00156 0.00360 0.00322 0.00714 0.00682 0.00904 0.00849 0.01157 0.01078

180.54 178.56 178.29 176.77 176.61 173.66 173.58 170.60

T h i s rather large discrepancy suggests that the values of 7< c o m p u t e d f r o m E q u a t i o n 13 are not i n fact true activity coefficients, b u t o n l y apparent activity coefficients, o n the assumptions that the solid is p u r e m e t a l a n d the l i q u i d contains only the species l i t h i u m a n d s o d i u m . T h e second of these assumptions is open to some doubt; perhaps the c o m p o u n d N a L i is also present, at a concentration w h i c h decreases m o n o t o n i c a l l y as the temperature goes u p . S o far as the nature of the solid phases is concerned, no evidence of solid solution f o r m a t i o n was observed i n the determination of the cooling curves. P r e l i m i n a r y experiments b y x - r a y e x a m ination a n d other techniques have g i v e n no i n d i c a t i o n of a n y t h i n g b u t p u r e s o d i u m a n d l i t h i u m as the solid separated phases, a l t h o u g h a d m i t t e d l y the presence of a solid solution r e g i o n of no m o r e t h a n a few tenths of a n atom p e r cent w o u l d p r o b a b l y have escaped detection. It is not possible to say whether it is necessary to assume solid solution formation i n order to e x p l a i n the freezing point curves of s o d i u m a n d l i t h i u m , because of the uncertainties noted above about the exact species present i n the l i q u i d . 2

F u r t h e r evidence for the h i d d e n complexities of this system come w h e n a n attempt is made to fit the data for the apparent In y as d e t e r m i n e d f r o m E q u a if


HOWLAND AND EPSTEIN—BINARY SYSTEM SODIUM-LITHIUM

41

tion 13 a n a l y t i c a l l y . It m i g h t be expected that equations of the f o r m of E q u a t i o n 1 w o u l d be v a l i d a n d that, i n terms of the quantities fi =

Τ ] In 7i—In α +

In [1 +

(a-1) X i l - d — a )

f

Τ ] In y

In [1 +

(a-1) x j - ( l - l / a )

s

=

2

+

(1-^>ι) \ 0i

|-

(14a) (14b)

(f/V)i s h o u l d be l i n e a r i n ( 1 — φ ) . It has been f o u n d , o n the c o n t r a r y , that the freezing point data are v e r y w e l l fitted b y the e m p i r i c a l r e l a t i o n


ι

2

(//V)* = K ( 1 - 0 0 (15) i.e., the quantity is linear, rather t h a n quadratic, i n (1 - φι). A l s o most s u r p r i s i n g l y , it w a s f o u n d that the single constant Κ = 17.04 c e , independent of t e m p e r a ture, fitted both the s o d i u m a n d l i t h i u m freezing point curves, as is s h o w n i n F i g u r e 4 a n d T a b l e V . E q u a t i o n 15 w i t h i=l a n d i—2 does not satisfy the G i b b s D u h e m relation, a n d i t must be e m p l o y e d w i t h e x t r e m e caution. T h e curves of ( j V V ) i vs. (1 - φι) are linear, b u t w i t h different slopes i f t h e F l o r y - H u g g i n s e n t r o p y correction is omitted i n E q u a t i o n s 14a a n d 14b; i n c l u s i o n of this t e r m brings the t w o straight lines together. N o e x p l a n a t i o n f o r the astonishingly simple f o r m f o r E q u a t i o n 15 has been f o u n d , a n d the p h y s i c a l basis of this r e l a t i o n must be p r e s u m e d to l i e e m b e d d e d i n the complexities of the l i q u i d a n d solid phases discussed above, as must the e x p l a n a t i o n of the other deviations f r o m simple n o n i d e a l solution theory b e h a v i o r w h i c h have been observed w i t h this system.

(f/V), «17.04(1-^,)

_

0.5|

s

1 ο Να 2 · Li

· 0.02

(Ι-φί)

0.03

Figure 4. Sodium-lithium freezing

point curves

Acknowledgment T h e senior author wishes to express his appreciation to W . M . C a s h i n , w h o served as a thesis sponsor representing S i e n a College at this l a b o r a t o r y , a n d to N a n c y E . F r e n c h f o r h e r assistance w i t h the calculations.

Literature Cited B o h m , B., K l e m m , W . , Z. anorg. Chem. 243, 69 (1939). Douglas, T. B., Epstein, L.F., D e v e r , J.L., H o w l a n d , W . H . , J. Am. Chem. Soc. 77, 2144 (1955). G i n n i n g s , D . C . , Douglas, T . B . , Ball, A. F., J. Research Natl. Bur. Standards 45, 23-33 (1950); Research P a p e r 2110. (4) H e y c o c k , C . T . , N e v i l l e , F.H., J. Chem. Soc. 55, 666 (1889). (5) H i l d e b r a n d , J . H . , Scott, R . L . , " S o l u b i l i t y of N o n e l e c t r o l y t e s , " 3rd ed., p p . 131, 267, R e i n h o l d , N e w Y o r k , 1950. (6) L u k e s h , J . S . , H o w l a n d , W . H . , Epstein, L.F., P o w e r s , M . D . , J. Chem. Phys. 23, 1923 (1955). (7) M a s i n g , G. M., T a m m a n , G . T., Ζ. anorg. Chem. 76, 183 (1910). (8) P e p k o w i t z , L.P., S h i r l e y , E.L., A n a l . Chem. 25, 1718 (1953). (9) S a l m o n , O . N . , A h m a n n , D . H . , J. Phys. Chem. 60, 13 (1956). (10) Scatchard, G . , Chem. Revs. 8, 321 (1931). B a s e d o n a thesis submitted b y W . H. H o w l a n d to the faculty of the Graduate School of Siena College i n partial fulfillment of the requirements f o r the degree of master of science, A p r i l 15, 1955. (1) (2) (3)


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