Thermochemistry of the Dimer Lithium Hydride Molecule Li2 H2 (g)

18 Thermochemistry of the Dimer Lithium Hydride Molecule Li H (g) 2

C. H. WU

2

and H. R. IHLE

Downloaded by GEORGETOWN UNIV on August 19, 2015 | http://pubs.acs.org Publication Date: March 8, 1982 | doi: 10.1021/bk-1982-0179.ch018

Kernforschungsanlage Jülich GmbH, Institut für Chemie, D-5170 Jülich, West Germany

A s t a b l e molecule Li H has been i d e n t i f i e d experimentally and its stability determined. The gas species over s o l u t i o n s of hydrogen in l i q u i d l i t h i u m were detected by mass spectrometric a n a l y s i s of the s a t u r a t e d vapor e f f u s i n g from a Knudsen cell. From the measurements of the gaseous equilibria 2

2

Li (g)

= 2Li H(g),

Li H (g) + Li(g)

= LiH (g) +

Li H (g) +

=

Li H (g) + 2

2

2

2

2

2

2

Li (g) 2

2

Li (g),

2

Li (g)

2

+ L i H ( g ) and

3

2

L i H ( g ) + LiH(g) = L i H ( g ) + L i H ( g ) , 2

2

2

2

an atomization energy D°O (Li H )= 164.3 ± 10 kcal/ mol and a heat of d i m e r i z a t i o n ΔH°O = -(52.6 ± 10) kcal/mol was obtained. 2

2

Much t h e o r e t i c a l work has been c a r r i e d out on the l i t h i u m hydride molecule, which has become the workbench of the theoret i c a l chemist C O , Browne 0 2 ) , and Fraga and R a n s i l (3) have given the binding energy f o r the L i H i o n by ab i n i t i o c a l c u l a t i o n ; Comp a n i o n ^ ) has a p p l i e d the diatomic-in-molecule theory to the LiJA and L i H molecules and p r e d i c t e d the s t a b i l i t i e s of these molecul e s . We have i n t e n s i v e l y studied the L i - H system by means of Knudsen e f f u s i o n mass spectrometry, and i d e n t i f i e d a l l p r e d i c t e d molecules and ions as c i t e d above(5), and reported the thermochemical p r o p e r t i e s of these gaseous species (6, 7^, 8 ) . The e x i s t e n c e of a s t a b l e molecule L i H has not been demons t r a t e d experimentally p r i o r to t h i s i n v e s t i g a t i o n , T y n d a l l and Companion(9) have studied the s t a b i l i t y of ^n^2 ^ a p p l i c a t i o n of diatomics-in-molecules theory and given f o l l o w i n g heats of reaction: 2LiH( Z ) -> L i H ( B, ) AH = -28.4 kcal/mol 2 2 lg 0 +

2

2

2

0

0

n

0097-6156/82/0179-0265$05.00/0 © 1982 A m e r i c a n Chemical Society

In Metal Bonding and Interactions in High Temperature Systems; Gole, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

266

METAL BONDING AND INTERACTIONS

P r e v i o u s l y we have reported the mass spectrometric determinat i o n of the i o n i z a t i o n p o t e n t i a l s and d i s s o c i a t i o n energies of the molecules LiH(6) , L i H(7), LiU^W together with the b i n d i n g energies of t h e i r i o n s . In c o n t i n u a t i o n of our study on the s y s tem L i - H , the e q u i l i b r i u m constants of four gas r e a t i o n s i n v o l v ing t h i s molecule were measured, from which i t s a t o m i z a t i o n energy has been deduced.


E xp e r i me n t a1 The apparatus used f o r t h i s work has been d e s c r i b e d i n det a i l e a r l i e r ( 6 ) . B r i e f l y , i t c o n s i s t s of a quadrupole mass spectrometer by which the e f f u s a t e from a heated Mo-Knudsen c e l l cont a i n i n g s o l u t i o n s of hydrogen i n l i t h i u m i s analyzed, and a h i g h l y accurate gas d e l i v e r y system permits the admission of e.g. 2x10~9 moles with an accuracy of ± 1%. In the temperature range of 800 to 1000 K and at a concent r a t i o n of about 1000 ppm hydrogen i n l i t h i u m , the f o l l o w i n g gas e q u i l i b r i a have been measured: Li H (g) + Li (g)

2Li H(g)

Li H (g) + Li(g)

LiH (g) + L i ( g )

(2)

Li H (g) + Li (g)

Li (g)

(3)

L i H ( g ) + LiH(g)

Li H(g) + LiH (g)

2

2

2

2

2

2

2

2

2

(1)

2

2

3

2

2

2

+ LiH (g) 2

(4)

2

I d e n t i f i c a t i o n of the ions was accomplished from t h e i r massto-charge r a t i o , s h u t t e r a b i l i t y , appearance p o t e n t i a l and i s o t o p e abundance. Results and D i s c u s s i o n When a d i l u t e s o l u t i o n of hydrogen i n l i t h i u m , with a concent r a t i o n of 1000 ppm, i s heated i n a molybdenum c e l l i n the temper a t u r e range of 830 K to 1000 K, the ions L i , L i + , L i , L i H , L i H , L i H and L i H are observed and the appearance p o t e n t i a l s f o r these ions were found to be 5.5, 5, 4.5, 8, 6.5, 5 and 6 eV. r e s p e c t i v e l y by the l i n e a r e x t r a p o l a t i o n method, with an uncert a i n t y of ± 0.5 eV. These agree with the known i o n i z a t i o n potentials of the corresponding n e u t r a l gaseous species given i n the literature0£, JJ^, J5, 7_ 8 ) ; thus, the appearance p o t e n t i a l s suggest, that the ions observed are produced by i o n i z a t i o n of the corresponding n e u t r a l s . To minimize fragmentation an i o n i z i n g e l e c t r o n energy of 2.5 eV above the r e s p e c t i v e appearance potent i a l s was used during the measurements, +

+

2

+

2

+

3

+

2

2

2

9

A t y p i c a l set of r e l a t i v e i o n c u r r e n t s measured at 936 K i s given by:


18.

AND IHLE

wu

Li LiH and

+

+

Lithium

7

= 3.25

= 2.60 + Li 2 H

x 10 ,

Li

2

+

x 10 , =

2

,

4

Li H

X

1 0

2

Hydride

+

5

= 6.90

2

= 3,60

267

Molecule

x 10 , 2

x 10 ,

LiH

Li +

+ 3

= 2.95

= 1.95

x

x

2

10 ,

10

*

E q u i l i b r i u m Measurements and Atomization Energy of Li^H^(g)


The measurements of the gaseous isomolecular exchange e q u i l i b r i a (1-4) were c a r r i e d out at temperatures between 830 and 1000 K , and the t h i r d law e n t h a l p i e s of r e a c t i o n s (1-4) were c a l c u l a t e d from the r e l a t i o n AH° = -RT

l n K - TAC(G° - H°)/T]

(5)

o o where K , R and A C ( G - H Q ) / T ] represent the e q u i l i b r i u m constant, the gas constant, and the change i n the f r e e energy f u n c t i o n f o r the corresponding r e a c t i o n s . The e q u i l i b r i u m constants f o r the r e a c t i o n s were c a l c u l a t e d from the measured i o n c u r r e n t s , using the r e l a t i o n s T

+

2

KLi H ) £ I(Li )I(Li H 9

=

K p

l

(6)

+

2

+

2

2

)

+

K

= P

Z

I(LiH*)I(Li ) ~2 2— I (Li ) I ( L i H ) 2

+

I(Li

K P

J

+

)I(LiH ) = i j £ — I(Li )I(Li H ) 9

2

K

= P

*

2

(8)

2

+

I(Li and

(7)

2

+

H )I(LiH

) (9)

~

—

I(LiH ) I ( L i H 2

2

)

where I i s the r e l a t i v e i o n i n t e n s i t y . The experimental values f o r the i o n i z a t i o n cross s e c t i o n s and m u l t i p l i e r gains, which are necessary f o r the e v a l u a t i o n of the e q u i l i b r i u m constants of gas r e a c t i o n s from measured i o n i n t e n s i t i e s , are not a v a i l a b l e . Therefore an assumption, that the i o n i z a t i o n cross s e c t i o n s and m u l t i p l i e r gains f o r isomolecular r e a c t i o n s can cancel each other out has been made. By using the estimated molecular parameters given by T y n d a l l and Companion f o r the diamond-shaped and C dimer of L i H , one obtains the f r e e energy f u n c t i o n f o r the L i A ( g ) molecule by the s a t i s t i c a l mechanical method and the r e s u l t i n g numerical values of the f r e e energy f u n c t i o n s at 800, 900 and 1000 K f o r dimer are 56.11, 57.74 and 59.25; and those f o r C dimer are 54.63, 56.29 and 57.82 c a l mol" respectively. 2 v

1



268

The f r e e energy f u n c t i o n s f o r L i ( g ) and L i (g) were taken from the JANAF Tables, those f o r L i ^ g ) , L i H ( g J and L i H ( g ) were taken from our previous work ( H , 7, 8 ) . The measured e q u i l i b r i u m constants as f u n c t i o n s of temperature are shown i n Figure 1 and the t h i r d law r e s u l t s of r e a c t i o n s (1), (2), (3) and (4) are given i n Tables I , I I , I I I , IV. The t h i r d law values of r e a c t i o n s (1), (2), (3) and (4) were combined with the f o l l o w i n g atomization e n e r g i e s : 2

D°(Li )=25.5 ± 1.5 k c a l / m o l ( l l )

D°(Li H)=89.7 ± 5.0 kcal/mol(7)

D°(Li )=45.5 ± 4.0 k c a l / m o l ( l l )

D°(LiH) =55.86 kcal/mol(12)

2

2

3


2

D°(LiH ) = 127.0 ± 7.0 kcal/mol(8) 2

This y i e l d s the corresponding heats of atomization: D ° ( L i H ) = 162.0 ± 5.2 kcal/mol U 2 z 0

D

0

( L 1

( D Dimer) zn

0

H

2 2

)

=

1

6

3

,

4±

5

,

2

k

c

a

l

/

m

o

1

( C

o u

2v

D i m e r )

>

from r e a c t i o n (1) D°(Li H ) = 164.5 ± 7.i kcal/mol U z z D

0

( L i

H

2 2

)

=

1

6

5

,

9±

7

,

1

k

c

a

l

/

m

o

1

(

C 2

(D_ Dimer) zn v

D i m e r )

>

from r e a c t i o n (2) D°(Li H ) = 165.9 ± 8.2 kcal/mol U z z

( D Dimer) zn

D ° ( L i H ) = 167.2 ± 8.2 kcal/mol

(C

2

o u

2

from r e a c t i o n

Dimer),

(3) and

D ° ( L i H ) = 161.9 ± 8.5 kcal/mol U 2 2

( D Dimer) zn

D ( L i H ) = 163.2 ± 8.5 kcal/mol

(C

0

Q

2

0

o u

2

Dimer),

from r e a c t i o n (4). The second law values of the jjeat of r e a c t i o n f o r the r e a c t i o n s (1), (2), (3) and v(4) are AH = 4.8 ± 3.0 kcal/mol, AH° = 15.6 ± 2.2 kcal/mol, AH° = 12.6 ± 1 1 . 4 kcal/mol and AH = 2.1 ± 1.5 kcal/mol r e s p e c t i v e l y . These values agree w e l l with the t h i r d law values w i t h i n the l i m i t s of e r r o r . However, the t h i r d law values are much more r e l i a b l e than those from the second law. Therefore only the t h i r d law values have been used f o r the e v a l u a t i o n of the atomization energy of L i H . 0

2

2


w u AND IHLE

Lithium

Hydride

Li H (g)*LiH(g) =


2

1,00

1,05

269

Molecule

2

1.10

Li H(g)*LiH (g) 2

2

1.15

1.20

10 /T 3

Figure 1.

Equilibrium

constants of reactions involving Li H temperature. 2

2

as a function of


270


I t i s seen that the agreement between the atomization energies derived from four independent isomolecular exchange r e a c t i o n s i s e x c e l l e n t . This suggests that the measurements were conducted under e q u i l i b r i u m c o n d i t i o n s i n the Knudsen c e l l , and that there i s no serious e r r o r i n the f r e e energy f u n c t i o n f o r L i ^ H (g) and i n the p r e v i o u s l y determined atomization energies of L J ^ H ( g ) ( 7 ) , L i H (g)(8) and L i (g)(11). The average value of the atomization energy f o r L i ^ H (g) i s D ( L i ^ ) = 164.3 kcal/mol. By u s i n g the same e r r o r treatment as mentioned i n e a r l i e r works (7^, 21), an estimated u n c e r t a i n t y of ±10 kcal/mol i s obtained f o r the atomi z a t i o n energy of L i H ( g ) . F i n a l l y , combining the atomization energy gf L i H ( g ) , A H ( L i H ) = 164.3 ± 10 kcal/mol and L i H ( g ) , AH (LiHJ = 55.86 k c a l / m o l ; with the heat of formation o f L i ( g ) , HH° = 38.5 ± 0.1 kcal/mol, and the d i s s o c i a t i o n energy D (H ) = 103.25 kcal/mol, y i e l d s the heat of formation AH^Li^H^) = T6.0 ± 10 kcal/mol, and the heat of d i m e r i z a t i o n 2

2


0

9

Q

Q

n

2LiH + L i H 2

AH° = -(52.6 ± 10)

2

kcal/mol.

Kollman, Bender and Tothenberg(13) have p r e d i c t e d a heat of dimer i z a t i o n A H Q = -47.2 kcal/mol by e l e c t r o n i c s t r u c t u r e c a l c u l a t i o n . Milne and C u b i c c i o t t i ( 1 4 ) have a p p l i e d i o n i c models to c a l c u l a t e the heats of d i m e r i z a t i o n f o r gaseous a l k a l i h a l i d e dimer molecules, and the r e s u l t s are as f o l l o w s : 2LiF + L i F 2

2

2LiCl

A H

Li Cl 2

2LiBr + L i B r 2

2LiI

AH° = -57.6

2

L i

I 2

2

=

0

*"

5 4 , 7

AH° = -52.3

2

A H

0

=

~

4 8

-

9

kcal/mol k

c

a

l

/

m

o

1

kcal/mol kcal/mol

The c a l c u l a t e d s t a b i l i t y of L i H (13) agrees w e l l with our experimental r e s u l t s , which place t h e ^ d i m e r i z a t i o n energy of L i H c l o s e to that of L i B r given above. This supports the statement that the L i H dimer i s s i m i l a r to the a l k a l i halide(9) .


18.

wu

AND IHLE

Table I:

Lithium

Hydride

Molecule

T h i r d law e n t h a l p i e s

211

f o r the r e a c t i o n

L i X ( g ) + L i ( g ) = 2 L i H(g) o o 0

z

T

K

,xl0 Pi

J


(K)

836 869 890 850 908 924 936 946 962 967 840 855 968 978 998

z

z

( c a l mol

K C

)

0

2v -0.63 -0.70 -0.72 -0.66 -0.78 -0.81 -0.82 -0.84 -0.87 -0.88 -0.63 -0.68 -0.88 -0.90 -0.93

T

f o r the r e a c t i o n L

0

( c a l mol

(K)

836 869 890 850 908 924 936 946 962 967 840 855 968 978 998

L

2

0.835 1 .61 1.23 1.05 1.46 2.20 3.35 3.00 4.20 2.43 0.844 3.41 3.55 3.70 3.53

D__ Dimer zn 5.60 5.61 5.59 5.59 5.61 5.59 5.59 5.59 5.57 5.57 5.60 5.61 5.57 5.57 5.53

1

C

K

2v 7.07 7.06 7.05 7.06 7.06 7.03 7.03 7.03 7.01 7.00 7.07 7.08 7.01 7.01 6.99

Dimer 2v 9.29 9.48 10.66 9.54 9.22 10.46 9.48 9.91 10.27 10.04 8.12 6.67 9.53 9.30 10.06 9.47±0.98 n

zn 8.07 8.22 9.35 8.29 7.91 9.13 8.14 8.54 8.89 8.66 6.88 5.40 8.13 7.89 8.61 Av. 8.14±0.96

Z

o AH

Q

(kcal mol

)

D_, Dimer zn 12.63 12.01 12.75 12.45 12.72 12.17 11.55 11.88 11.42 12.53 12.67 10.54 11.81 11.85 12. 15 Av. 12.08±0.60

Dimer

)

C

Dimer

L i H_(g) + L i ( g ) = L i H (g) + L i , ( g ) ^ o o K xl0 -A[G -H )/T] •y

^

Q

( k c a l mol D

Dimer

Table I I : T h i r d law e n t h a l p i e s

T

o AH

T

D_, Dimer Zn -2.10 -2. 15 -2.18 -2. 13 -2.23 -2.25 -2.26 -2.28 -2.31 -2.31 -2. 10 -2.15 -2.32 -2.34 -2.39

2.70 2,90 1,68 2,52 4.07 2.23 4.03 3.37 2.99 3.45 5.62 1.41 4.53 5.30 3.91

z

-A[(G -iy/T]

)

C

Dimer 2v 13.86 13.27 14.05 13.69 14.04 13.50 12.89 13.24 12.80 13.91 13.91 11.80 13.21 13.26 13.61 13.40±0.60


272


T h i r d law enthalpies

Table I I I :

T

4 K ~xl0 P3

L i H (g) + L i (g) = L i . ( g ) + L i H (g) o± o " A [ ( G - Hp)/T] z

z

J

( c a l mol ~^ D Dimer 2h 8.32 8.35 8.37 8.33 8.37 8.38 8.38 8.39 8.40 8.33 8.33 8.39 8.40 8.40


rtt

0.756 2. 10 1.31 1.37 1 .22 2.30 3.47 2.84 2.75 1.26 8.79 2.22 2.99 2.64

Table IV:

K . p4

]

C„ Dimer 2v 9.99 9.80 9.83 9.80 9.82 9.82 9.82 9.83 9.83 9.80 9.80 9.83 9.84 9.84 Av.

T h i r d law e n t h a l p i e s

Dimer 2h 1.09 1 .08 1.06 1 .08 1.05 1.03 1.02 1.01 0.99 0.99 1. 10 1.08 0.99 0.98 0.94 D

1.16 0.836 0.667 0.875 1.09 0.687 1 .12 0.993 1.35 0.865 0.730 1.08 0.872 1.11 0.822

!

z

K *) C„ Dimer 2v 2.56 2.53 2.52 2.55 2.50 2.47 2.46 2.45 2.43 2.42 2.57 2.55 2.43 2.42 2.40 Av.

Dimer 2v 23.95 23.14 24.56 23.35 25.17 24.45 24.01 24.65 25.26 23.22 20.33 25.70 25.39 26. 16 24.24±1.46 o


z

( c a l mol

C

D., Dimer 2h 22.72 21.88 23.26 22.11 23.86 23.12 22.66 23.29 23.88 21.98 19.08 24.30 23.99 24.77 22.92±1.41

L i H (g) + LiH(g) = Li.H(g) + LiH,(g) 2 o o o -AC^-H^/T] AH

(K)

836 869 890 850 908 924 936 946 962 967 840 855 968 978 998

o

-1 (kcal mol )

K )

z

T

z

T

(K)

836 869 890 850 908 924 936 946 967 940 855 968 978 998


^

Q

(kcal mol D

Dimer 2h 0.66 1.24 1.66 1.14 0.80 1.64 0.74 0.97 0.39 1.25 2.45 0.79 1.23 0.76 1.33 1.07±0.37 O L

)

C

Dimer 2v 1.89 2.51 2.95 2.39 2.11 2.97 2.09 2.33 1.76 2.62 2.68 2.05 2.62 2.16 2.78 2.39±0.37


18.

w u AND IHLE

Lithium

Hydride

273

Molecule

Acknowledgement The authors wish to thank Mr. F. Frbschen f o r t e c h n i c a l


Literature 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14.

help.

Cited

Stawlley, W. C.; Way, K. R. J. Chem. Phys. 1974, 60, 3611. Browne, J . C. J. Chem. Phys. 1964, 41, 3495. Fraga, S.; R a n s i l , B. J. J. Chem. Phys. 1961, 35, 669. Companion, A. L. J. Chem. Phys. 1968, 48, 1186. I h l e , H. R.; Wu, C. H. Adv. Mass Spectrometry 1978, 7A, 636. I h l e , H. R.; Wu, C. H. J. Chem. Phys. 1975, 63, 1605. Wu, C. H.; I h l e , H. R. J. Chem. Phys. 1977, 66, 4356. Wu, C. H. J. Chem. Phys. 1979, 71(2), 783-7. T y n d a l l , J . R.; Companion, A. L. J. Chem. Phys. 1970, 52, 2036. F r a n k l i n , J . L.; Dillard, J . G.; Rosenstock, H. M.; Herron, J . T.; D r a x l , K.; Field, F. H. N a t l . Stand. Ref. Data 1969, Ser. 26. Wu, C. H. J. Chem. Phys. 1976, 65, 3181. Velasco, R. Can. J. Phys. 1957, 35, 1204. Kollman, P.; Bender, C. F.; Rothenberg, S. J. Amer. Chem. Soc. 1972, 94, 8016. M i l n e , T. A.; C u b i c c i o t t i , D. J. Chem. Phys. 1958, 29, 846.

RECEIVED September 25,

1981.


Thermochemistry of the Dimer Lithium Hydride Molecule Li2 H2 (g)

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