The Chemical Fractionation of Boron Isotopes - Advances in

3

The Chemical Fractionation of Boron

Isotopes

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A. A .

PALKO

a n d J . S. D R U R Y

Chemistry Division, O a k Ridge National Laboratory, O a k Ridge, T e n n .

This review

deals with studies

National

Laboratory

of boron

isotopes

compounds.

process

viously

employed.

nation

of the

anomalous

equilibrium

3

exchange

reaction

addition of a

to methods

which

for

of the

of different

isotopic

It also

accounted

preexpla-

in the molecular

variations

as a function

reaction

data.

which

of boron-10

maximum

exchange

other boron

its molecular in the development

was superior

and the observed

constants

experimental

and

Ridge

fractionation

The work also led to a theoretical

predicted

for the

BF

at the Oak

the chemical

resulted

which

concentration

tion compound,

model

between

This research

new separation

performed

concerning

isotopic

donors.

equilibrium

were

the

The

constants

consistent

predicted

the addi-

with

the

of

the

behavior

halides.

" T ^ T a t u r a l l y o c c u r r i n g b o r o n contains 1 9 . 8 % boron-10 a n d 8 0 . 2 % ^

boron-

11. T h e a b s o r p t i o n cross section of the n a t u r a l p r o d u c t f o r t h e r m a l

neutrons is 752 b a r n s ; f o r p u r e boron-10 a n d b o r o n - 1 1 , t h e c o r r e s p o n d i n g values

( 8 ) a r e 3837 a n d 0.005 b a r n s , respectively.

p u r e boron-10

is five times m o r e

effective

natural boron.

I n v i e w of this difference,

Thus, isotopically

as a n e u t r o n s h i e l d t h a n i t is n o t s u r p r i s i n g that a

d e m a n d arose, v e r y early i n t h e n u c l e a r era, for separated b o r o n isotopes. T h e search f o r a m e t h o d b y w h i c h b o r o n isotopes m i g h t b e separated began

as a classified p r o g r a m of t h e M a n h a t t a n Project i n 1943, at

C o l u m b i a U n i v e r s i t y . S e v e n separation schemes w e r e c o n s i d e r e d : t h e r mal

diffusion

of B F a n d d i s t i l l a t i o n 3

of B F , ( C H 0 ) B , 3

3

3

H B0 , 3

3

( C H ) 0 • B F , ( C H ) 0 • B F , a n d ( C H O ) B • 2 B F . T h e distillation 2

5

2

3

3

2

3

2

s

3

3

of ( C H ) 0 • B F w a s selected as t h e most p r o m i s i n g separation m e t h o d . 3

2

3

A l t h o u g h t h e selected isotope separation process w a s d e e m e d

supe-

r i o r to a n y other separation m e t h o d t h e n k n o w n , i t h a d c e r t a i n deficien40

In Isotope Effects in Chemical Processes; Spindel, W.; Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

3.

Chemical

PALKO A N D DRURY

41

Fractionation

cies. U n d e r e q u i l i b r i u m c o n d i t i o n s , o n l y 6 0 % of the M e 0 • B F 2

3

complex

present i n the v a p o r phase of the d i s t i l l a t i o n c o l u m n s w a s dissociated i n t o B F a n d M e 0 . T h e presence of u n d i s s o c i a t e d c o m p l e x i n the v a p o r 3

2

phase s u b s t a n t i a l l y r e d u c e d the single-stage isotopic f r a c t i o n a t i o n factor for the process, a n d i n c r e a s e d b o t h the c a p i t a l i n v e s t m e n t for the p l a n t a n d the u n i t cost of the p r o d u c t . A l s o , a p p r e c i a b l e i r r e v e r s i b l e d e c o m p o s i t i o n of the M e 0 • B F 2

boron-10 as w e l l as B F

3

c o m p l e x o c c u r r e d , w i t h a n a t t e n d a n t loss of

3

a n d M e 0 . T o m i n i m i z e this d e c o m p o s i t i o n , it 2


w a s necessary to operate the d i s t i l l a t i o n e q u i p m e n t at r e d u c e d pressure. T h i s r e s t r i c t i o n r e d u c e d the c a p a c i t y of the separation p l a n t a n d s u b stantially i n c r e a s e d the cost of the p r o d u c t .

Furthermore, i n the opera-

t i o n a l p r o c e d u r e s c u r r e n t i n 1954, difficulties w e r e e n c o u n t e r e d i n recove r i n g p r o d u c t B F f r o m the M e 0 • B F 3

2

3

complex.

T h e d o m a i n of the search for a n i m p r o v e d separation process w a s defined b y c e r t a i n c r i t e r i a : ( a ) i s o t o p i c f r a c t i o n a t i o n s h o u l d b e a c h i e v e d b y means of a two-phase, c h e m i c a l exchange r e a c t i o n w h i c h w a s a m e n a b l e to e o u n t e r c u r r e n t o p e r a t i o n i n a m u l t i s t a g e contactor at a m b i e n t t e m p e r a t u r e a n d pressure;

(b)

the single-stage isotopic f r a c t i o n a t i o n

factor for the r e a c t i o n s h o u l d b e a p p r e c i a b l y larger t h a n that for the d i s t i l l a t i o n of M e 0 • B F ; ( c ) 2

3

the m o l e c u l a r species

i n e a c h process

stream s h o u l d be t h e r m a l l y refluxable—i.e., c o n v e r t i b l e f r o m one

species

to the o t h e r b y the a d d i t i o n or r e m o v a l of heat alone; ( d ) process m a t e rials s h o u l d b e m o r e stable w i t h respect to i r r e v e r s i b l e d e c o m p o s i t i o n t h a n those u s e d i n the ( C H ) 0 process; a n d ( e ) 3

2

the c h e m i c a l f o r m of

the p r o d u c t s h o u l d p e r m i t a r e a d y , q u a n t i t a t i v e c o n v e r s i o n of the separ a t e d isotopes to the e l e m e n t a l state. Criteria (a)

and (c)

l i m i t e d research l a r g e l y to a class of i s o t o p i c

exchange reactions r e p r e s e n t e d b y E q u a t i o n 1: D • »BX (1) + 8

1 0

B X ( g ) = D • ™BX (1) + 3

3

1 1

BX (g)

(1)

3

w h e r e D • B X was a m o l e c u l a r a d d i t i o n c o m p o u n d , D was a L e w i s base 3

c o n t a i n i n g F , O , S, Se, N , P , A s , or C , a n d X w a s H , C H , or a h a l o g e n . 3

C r i t e r i a ( b ) a n d ( d ) g e n e r a l l y l i m i t e d the L e w i s base to those c o n t a i n i n g N , O , or S donors.

T h e same c r i t e r i a r e s t r i c t e d X , for the most p a r t , to

t h e first m e m b e r of the h a l o g e n f a m i l y . O u r research thus dealt m a i n l y w i t h B F complexes of ethers ( d i m e t h y l , d i e t h y l , d i p h e n y l , a n d m e t h y l 3

p h e n y l ) , thioethers ( d i m e t h y l , d i e t h y l , d i - n - b u t y l , a n d d i p h e n y l ) , m e r captans

( e t h y l a n d b u t y l ) , amines

( t r i e t h y l , JV-methyl d i p h e n y l , a n d

N , N ' - d i m e t h y l p h e n y l ) , and a small group hydrofuran,

of other molecules

phenol, thiophenol, nitrobenzene,

(tetra-

methyl isocyanide,

di-

m e t h y l selenide, a n d d i m e t h y l t e l l u r i d e ) . I n a d d i t i o n , b r i e f studies w e r e m a d e of B C 1 complexes of d i p h e n y l ether, d i p h e n y l t h i o e t h e r , t h i o p h e n o l , 3

and acetyl chloride.


42

ISOTOPE E F F E C T S IN C H E M I C A L

PROCESSES

D o n o r s w e r e screened first o n the basis of d i s s o l v i n g sufficient L e w i s acid.

A L e w i s a c i d : d o n o r r a t i o of 1.0 was d e s i r e d .

If w a r r a n t e d , the

e q u i l i b r i u m constant for R e a c t i o n 1 w a s t h e n d e t e r m i n e d .

Attractive

donors w e r e tested for r e v e r s i b l e d i s s o c i a t i o n of the m o l e c u l a r a d d i t i o n compound.

T h o s e s u r v i v i n g this test w e r e u s u a l l y g i v e n c o m p l e t e e x a m i -

nations w i t h respect to the k i n e t i c s of exchange, c h e m i c a l s t a b i l i t y , c o r r o sion

characteristics, a n d p h y s i c a l properties

of

engineering

interest.

F i n a l l y , bench-scale e q u i p m e n t w a s set u p i n w h i c h the selected exchange Downloaded by UNIV OF TEXAS EL PASO on December 28, 2014 | http://pubs.acs.org Publication Date: June 1, 1969 | doi: 10.1021/ba-1969-0089.ch003

r e a c t i o n was i n t e g r a t e d w i t h the reflux reactions a n d p u r i f i c a t i o n steps, a n d the entire process w a s o p e r a t e d for weeks or m o n t h s to demonstrate the f e a s i b i l i t y of the process. D u r i n g the latter stages of the i n v e s t i g a t i o n , R a m a n a n d i n f r a r e d spectroscopic studies w e r e m a d e of c e r t a i n i s o t o p i cally substituted molecular addition compounds.

T h e s e studies e n a b l e d

i s o t o p i c e q u i l i b r i u m constants to b e c a l c u l a t e d for c o m p a r i s o n w i t h those o b t a i n e d e x p e r i m e n t a l l y . C o n s i d e r a t i o n of a l l i n f o r m a t i o n g e n e r a t e d b y t h e p r o g r a m l e d to the d e v e l o p m e n t of a t h e o r e t i c a l m o d e l of the exchange r e a c t i o n w h i c h satisfactorily a c c o u n t e d

for

the

k n o w n chemistry

of

R e a c t i o n 1.

Physical Properties of the Molecular

Addition

Compounds of BF

3

A d d u c t s f o r m e d f r o m v e r y w e a k L e w i s bases w e r e e x c l u d e d because of u n a t t r a c t i v e B F / d o n o r ratios. C o n v e r s e l y , a d d u c t s f o r m e d f r o m v e r y 3

strong donors w e r e solids w h i c h w e r e not a m e n a b l e to c o u n t e r - c u r r e n t processing unless d i s s o l v e d i n an a p p r o p r i a t e solvent. T h e necessity for t h e solvent to b e u n r e a c t i v e w i t h gaseous B F c o m p l i c a t i o n s l i k e l y to be u n e c o n o m i c . of B F

3

3

introduced operational

I n a d d i t i o n , the rate of

w i t h a d d u c t s of v e r y strong donors p r o v e d to be

exchange

unacceptably

slow. T h u s , i n g e n e r a l , w e sought donors of i n t e r m e d i a t e b a s i c i t y w h i c h f o r m e d l i q u i d complexes at a m b i e n t temperatures. T y p i c a l l y , the heats of association of s u c h a d d u c t s r a n g e d f r o m a b o u t 5 to 20 k i l o c a l o r i e s per mole. P o t e n t i a l l y i n t e r e s t i n g donors w e r e first screened o n the basis of the s a t u r a t i o n pressure of the a d d u c t .

( T h e t e r m " s a t u r a t i o n p r e s s u r e " refers

to the t o t a l pressure of v a p o r i n e q u i h b r i u m w i t h a s a m p l e of m o l e c u l a r addition compound.

T h e v a p o r m a y consist of free a c i d , base, u n d i s s o -

c i a t e d c o m p l e x , or a c o m b i n a t i o n of a l l of these constituents.)

Measured

q u a n t i t i e s of B F a n d the d o n o r w e r e e q u i l i b r a t e d at a g i v e n t e m p e r a t u r e 3

i n the a p p a r a t u s s h o w n i n R e f e r e n c e 14. M a n o m e t r i c observations ( c o r r e c t e d for the free v o l u m e of the e q u i p m e n t ) w e r e m a d e over t h a t p a r t of the l i q u i d r a n g e w h i c h l a y b e t w e e n r o o m t e m p e r a t u r e a n d t h e f r e e z i n g p o i n t of the c o m p l e x .

E s t i m a t e s of the heat of association of the c o m -

plexes w e r e o b t a i n e d f r o m the t e m p e r a t u r e d e p e n d e n c e of the s a t u r a t i o n


3.

PALKO A N D DRURY

Chemical

43

Fractionation

pressures, o r , i n a f e w instances, f r o m l i q u i d - o r gas-phase c a l o r i m e t r i c measurements. T h e f r e e z i n g p o i n t of e a c h c o m p l e x w a s d e t e r m i n e d f r o m r e c o r d e d c o o l i n g curves, a n d f r o m d i r e c t observations of t h e t e m p e r a t u r e at w h i c h c r y s t a l l i z a t i o n o c c u r r e d .

T h e results of these studies are s u m -

marized i n Table I and Table II.


Table I. Saturation Pressures of Some 1:1 Molecular Addition Compounds from the Freezing Point to Room Temperature LogP Freezing Point °C.

Adduct

±

=

a-(b/T)

a std. error

b ^^•association ± std. error (kcal/mole) Ref.

19,6 — — 35.7 — Donor decomposed by B F 92 Adduct dissociates irreversibly upon melting (C H ) NMe • B F , 100 Adduct dissociates irreversibly upon melting Me 0 • BF -12 9.806 2775 13.6" Et 0 • BF - 5 9 10.082 2879 11.9* Bu 0 • B F — -30 5 5.65 ± 0.05 1010 ± 15 HCOOEt • B F — -8 5.70 ± 0.05 1330 ± 20 6" MeCOOEt • B F 8.5 7.20 1870 EtCOOEt • B F , 12.6 9.83 2726 (CH ) 0 • B F 12 9.734 3126 16.8* C H O H • 0.8BF 8.7* -15 9.94 ± 0.008 1900 ± 16 C H O M e • 0.9BF 12.4 — 2 10.1 ± 0.1 2140 ± 33 C H OEt • BF 10.9 2575 11.8" (C H ) 0 • B F Does not form at - 4 0 ° C . — — C H N0 • BF — 0 9.2 C H OBu • BF 12.1" 12.04 2650 Me S • B F 10.2 - 2 0 10.164 ± 0.001 2209 ± 70 Et S • B F - 6 2 10.030 ± 0.004 2111 ± 21 9.6 Bu S • B F 12.8 2174 ± 19 < - 6 0 10.39 ± 0.06 CgfLjSH • B F , Does not form at - 4 0 ° C . (C H ) S • B F Does not form at - 4 0 ° C . Me Se • B F 8.3° -43 9.945 ± 0.005 1824 ± 25 Me Te • B F , Does not form at - 3 0 ° C . — — M e C O C l • BC1, — -60 — — 5.3 — 4 (C H ) 0 • BCi C^rL^SF! • BC1 Adduct completely dissociated at 25°C. 8.8 (CeH ) S • BC1 42 — —

Et N • B F MeNC • B F C H NMe • BF 3

3

3

6

5

3

2

6

5

3

2

2

3

2

3

2

a

3

3

a

3

a

2

6

5

6

5

6

5

4

3

3

3

6

5

6

3

2

5

6

r

3

5

3

2

a

3

a

3

2

6

a

3

5

2

3

2

3

2

6

5

2

a

s

3

5

(18) JT4) (14) (19) (19) (9) (9) (15) (20) (21) (11)

3

2

2

(1) (18) (18)

2

a

3

(4) (10) (19, 22) (23) (24) (18) (18) (19) (19) (6) (6,13) (18) (18)

Estimate was based on the relationship, A H = 2.303 Rb, where R is the gas constant and b is the coefficient of the temperature term in the equation, log P =

0

a 8 S O C l a t i o n

a b

c

(b/T).

This value was obtained from gas-phase dissociation measurements. Datum is from measurements made in nitrobenzene solutions.


44

ISOTOPE E F F E C T IN C H E M I C A L

Table II.

Solubility of B F , in Donor (moles B F / m o l e Donor) 3

Temp. (°C.)

Donor Me 0

-19.0 -16.5 -9.0 -8.1 5.5 6.0 22.0 30.0 31.0 -20.0 -19.0


2

Et 0 2

-10.0 -9.5 -8.5 5.5 22.0 (CH ) 0 2

4

Et S 2

EtSH

C H N0 6

5

PROCESSES

2

8.0 14.0 22 -25.0 -17.0 -16.0 -8.0 -6.0 10.5 22.5 31.0 31.5 -78 -50 0 25 -4.0 1.1 7.0 11.0 14.0 21.0 25.0

Pressure 400 Torr

1.103 1.082 — — 1.051 1.034 — 1.027 — 1.161 1.159 1.111 — 1.106 1.069 1.043 1.043 1.021 1.011 1.005 1.116 1.085 — 1.052 — 0.997 0.936 — 0.857 — — — — 0.2134 0.0792 — 0.0538 0.0458 0.0318 0.0253

760 Ton 1.201 — — 1.133 1.085 — 1.050 1.038 — 1.276 1.271 — — 1.185 1.182 1.116 1.070 1.062 1.048 1.032 — — 1.138 — 1.092 1.032 0.996 0.950 — 3.425 2.402 0.0324 0.000 0.765 — 0.1146 0.0948 0.0838 0.0597 0.0506

T h e i n d e x of s t a b i l i t y o b t a i n e d b y d i r e c t l y c o m p a r i n g the s a t u r a t i o n pressures of t w o c o m p l e x e s w a s b i a s e d b y the v o l a t i l i t y of t h e free d o n o r


3.

Chemical

PALKO A N D DRURY

45

Fractionation

i f the b o i l i n g p o i n t of the latter w a s r e l a t i v e l y l o w . B e t t e r estimates

(2)

of s t a b i l i t y w e r e o b t a i n e d b y c o m p a r i n g the t h e r m a l d e p e n d e n c e of the saturation pressures. T h i s p r o c e d u r e was e q u i v a l e n t to a c o m p a r i s o n of t h e enthalpies of f o r m a t i o n of the a d d u c t s f r o m t h e i r constituent m o l e cules.

S u c h comparisons w e r e u s u a l l y consistent w i t h the o r d e r of sta-

b i l i t y d e t e r m i n e d b y other c r i t e r i a .

H o w e v e r , for s t r u c t u r a l l y diverse

complexes, these comparisons w e r e not a l w a y s d e p e n d a b l e since, i n some cases, e n t r o p y effects strongly i n f l u e n c e d the t h e r m a l d e p e n d e n c e of the Downloaded by UNIV OF TEXAS EL PASO on December 28, 2014 | http://pubs.acs.org Publication Date: June 1, 1969 | doi: 10.1021/ba-1969-0089.ch003

saturation pressures. I n g e n e r a l , w e f o u n d that the s t a b i l i t y of s i m i l a r B F a d d u c t s v a r i e d 3

w i t h different d o n o r atoms, d e c r e a s i n g i n the o r d e r

N > 0 > S > S e >

T e . T h u s , M e 0 • B F w a s m o r e stable t h a n M e S • B F 2

3

2

or M e S e • B F .

3

2

3

T h e s t a b i l i t y of B F a d d u c t s c o n t a i n i n g the same d o n o r a t o m , b u t differ3

ent substituents i n the d o n o r m o l e c u l e , also v a r i e d . T h e presence of a n e l e c t r o p h i l i c g r o u p i n the d o n o r m o l e c u l e decreased the b a s i c i t y of the d o n o r a n d w e a k e n e d the a d d u c t . and C H O M e • B F 6

5

3

Thus, ( C H ) O B F 6

5

2

3

was less stable t h a n M e 0 • B F . 2

d i d not f o r m , C o n v e r s e l y , the

3

presence of a s m a l l n u c l e o p h i l i c substituent i n the d o n o r m o l e c u l e t e n d e d to s t a b i l i z e the r e s u l t i n g a d d u c t . H o w e v e r , i f the n u c l e o p h i l i c substituent w e r e sufficiently l a r g e a w e a k e n e d a d d u c t c o u l d result, o w i n g to steric interference b e t w e e n the substituent a n d the b o r o n t r i h a l i d e ( 3 ) .

Thus,

M e S • B F w a s s o m e w h a t m o r e stable t h a n E t S • B F . H e r e , the ^ - c a r b o n 2

3

2

3

atoms i n the e t h y l groups of the latter c o m p o u n d interfere w i t h the n o r m a l p o s i t i o n i n g of the fluorine atoms i n the a d d u c t . A s i m i l a r degree of steric interference existed b e t w e e n the /3-carbon atoms a n d the

fluorine

atoms

of the B u S a d d u c t , b u t this c o m p l e x was s o m e w h a t m o r e stable t h a n 2

the e t h y l c o m p o u n d , p r e s u m a b l y because the b u t y l groups c o n t r i b u t e a greater i n d u c t i v e effect t h a n the e t h y l groups. T h i s d o m i n a n c e of i n d u c t i v e effect over steric interference i n the B u S a d d u c t w o u l d not 2

be

e x p e c t e d i n the B u 0 • B F m o l e c u l e . H e r e , the s m a l l e r size of the d o n o r 2

3

a t o m l e d to severe steric interference b e t w e e n the a l k y l groups a n d the fluorine

atoms

(3).

A f u r t h e r e x a m p l e of the influence of steric interference i n ether a d d u c t s of

BF

(C H ) 0-BF 2

5

2

3

3

was provided by and ( C H ) O B F . 2

4

3

a comparison

of

the stabilities of

A l t h o u g h the a t o m i c

compositions

of these m o l e c u l e s differed o n l y b y t w o protons, the e n t h a l p y of associat i o n of the latter m o l e c u l e e x c e e d e d that of the f o r m e r b y m o r e t h a n 40%.

It seems clear that the increase i n s t a b i l i t y of the t e t r a h y d r o f u r a n

c o m p l e x m u s t b e a t t r i b u t e d to the r i n g s t r u c t u r e of the d o n o r w h i c h locks the i n t e r f e r i n g e t h y l groups out of the w a y of the fluorine atoms, thus e l i m i n a t i n g , or at least r e d u c i n g , steric interference ( 3 ,

17).


46

ISOTOPE E F F E C T S IN C H E M I C A L PROCESSES

Table III.

Equilibrium Constants and Related + Donor • BF (l)

BF (g)

10

Donor


2

2

4

5

6

5

6

5

6

3

= BF (g) n

+

3

-AH° (cal. mole' )

b std. error

±

K

0.018 ± 0.005 0.010 ± 0.005 (0.006)

2

2

6

a std error

±

Me 0 Et 0 Bu 0 HCOOEt MeCOOEt EtCOOEt (CH ) 0 C H OH C H OMe C H OEt C H OBu Me S Et S Bu S Me Se Et N

n

3

1

40 33 (7)

8.8 ± 1.5 7.1 ± 1.3 (1.6)

0.094

32.5

0.0089 ± 0.006 0.023 ± 0.001 0.022 ± 0.006 0.026

6.0 ± 1.8 10.1 ± 0.3 10.5 ± 1.8 12.9

28 46 48 59

0.020 0.012 0.018 0.013 0.012

10.7 8.5 9.6 8.1 6.4

49 39 44 37 30

148.5

5

2

2

2

2

8

± ± ± ± ±

The Isotopic Exchange

0.004 0.002 0.005 0.001 0.002

± ± ± ± ±

1.1 0.6 1.2 0.4 0.5

Reaction

A f t e r p r e l i m i n a r y s c r e e n i n g o n the basis of v a p o r pressure m e a s u r e ments, a t t r a c t i v e donors w e r e screened

f u r t h e r o n the basis of t h e i r

e q u i l i b r i u m constants for the isotopic exchange r e a c t i o n : Donor • B F ( l ) + n

8

1 0

B F ( g ) = Donor • 3

1 0

BF (1) +

n

8

BF (g).

(2)

8

T h e e q u i l i b r i u m constants for a p a r t i c u l a r d o n o r w e r e d e t e r m i n e d b y s t i r r i n g a p p r o p r i a t e q u a n t i t i e s of the d o n o r a n d B F for several hours i n 8

a s u i t a b l e r e a c t i o n vessel (24).

R e p l i c a t e a l i q u o t s of B F b e f o r e a n d after 8

e q u i l i b r a t i o n w e r e a n a l y z e d for b o r o n - 1 0 b y means of a 6 - i n c h , 60°-sector r a t i o mass spectrometer.

I n o u r experiments the a m o u n t of b o r o n t r i -

fluoride i n the gas phase w a s d e l i b e r a t e l y k e p t s m a l l , c o m p a r e d w i t h the a m o u n t of b o r o n t r i f l u o r i d e i n the l i q u i d phase.

F o r this c o n d i t i o n , the

r a t i o of b o r o n - 1 0 to b o r o n - 1 1 i n the gas before a n d after e q u i l i b r a t i o n a p p r o x i m a t e d the t r u e single-stage f r a c t i o n a t i o n factor, 1 0

B/ B(gas).

W h e n c o r r e c t e d for the B F

n

3

1 0

B/

1 1

B(liquid)/

present i n the l i q u i d phase

i n excess of the 1 : 1 m o l e r a t i o r e q u i r e d b y the m o l e c u l a r a d d i t i o n c o m pound

( T a b l e I I ) , these single-stage f r a c t i o n a t i o n factors

represented

the isotopic e q u i l i b r i u m constants for R e a c t i o n 2. E q u i l i b r i u m constants for the exchange of b o r o n b e t w e e n B F p o u n d s of B F

3

8

gas a n d fifteen a d d i t i o n c o m -

are s h o w n i n T a b l e I I I . C u r v e s of t h e f o r m , l o g K

eq

=

(b/T)

— a, w e r e fitted to the d a t a b y means of the least squares t e c h -

nique.

F r o m the slopes of these curves a n d the values of the i s o t o p i c


3.

Chemical

PALKO A N D DRURY

47

Fractionation

Thermodynamic Functions for the Isotopic Exchange Reaction Donor • BF (l); 10

3

Log K

K

-AS (e.u.)

AF° mole' )

0Q

0

1

15 19


= (b/T) - a

eq

0.08 0.05

15 14 18 26

0.04 0.11 0.10 0.10

22 22 19 19 13

0.09 0.06 0.08 0.06 0.05

30°C. 1.026 1.031 1.029 1.033 1.019 1.026 1.024 1.030 1.042 1.026 1.037 1.037 1.032 1.032 1.022

0°C.

Ref.

1.033 1.037

(19) (23) (19) (29) (9) (9) (18) (20) (21) (U) (10) (19) (23) (24) (19) (23)

(20°C.) (28°C.) (45°C.) 1.031 1.040 1.039 (25°C.) (25°C.) 1.046 1.043 1.040 1.039 1.028

e q u i l i b r i u m constants, the t h e r m o d y n a m i c q u a n t i t i e s , A F ° ,

Ai/°,

and

A S ° , w e r e c o m p u t e d for the i s o t o p i c exchange r e a c t i o n . It m a y b e seen f r o m F i g u r e 1 that the e q u i l i b r i u m constants for R e a c t i o n 2 v a r i e d w i t h d o n o r , d o n o r substituents, a n d w i t h t e m p e r a t u r e . A t 30 ° C . the f o l l o w i n g d o n o r o r d e r w a s o b s e r v e d : d i e t h y l sulfide > d i m e t h y l sulfide > d i m e t h y l selenide >

d i b u t y l sulfide >

d i m e t h y l ether >

d i e t h y l ether >

tetrahydrofuran >

phenol >

m e t h y l p h e n y l ether

>

triethyl amine. In gen-

eral, the isotopic e q u i l i b r i u m constants for donors c o n t a i n i n g s u l f u r w e r e greater t h a n those for s i m i l a r donors c o n t a i n i n g oxygen.

Equilibrium

constants for donors c o n t a i n i n g o x y g e n w e r e greater t h a n those for c o r r e s p o n d i n g bases c o n t a i n i n g n i t r o g e n . F o r m o l e c u l a r a d d i t i o n c o m p o u n d s i n w h i c h the d o n o r a t o m w a s s u l f u r , the v a l u e of the isotopic e q u i l i b r i u m constant at 3 0 ° C . v a r i e d w i t h substituents i n the f o l l o w i n g o r d e r : e t h y l > methyl > >

butyl.

A t l o w e r temperatures this o r d e r w a s m e t h y l >

b u t y l , o w i n g to differences i n e n t h a l p y of the respective

reactions. F o r oxygen donors, the o r d e r at 3 0 ° C . was e t h y l > tetrahydrofuran > acetate

>

formate

butyl > >

methyl ^

O H . W i t h esters, the o r d e r at 3 0 ° C .

propionate.

ethyl

exchange

I n g e n e r a l , it w a s o b s e r v e d

was that

w e a k e r m o l e c u l a r a d d i t i o n c o m p o u n d s r e s u l t e d i n larger i s o t o p i c e q u i l i b r i u m constants.

A d e t a i l e d d i s c u s s i o n of the t h e o r y of i s o t o p i c f r a c -

t i o n a t i o n b y means of R e a c t i o n 1 w i l l b e p r e s e n t e d later i n this p a p e r . T h e rate of exchange of b o r o n b e t w e e n the m o l e c u l e s p a r t i c i p a t i n g i n R e a c t i o n 1 is i m p o r t a n t i n p r a c t i c a l a p p l i c a t i o n s . If the r e a c t i o n is to Library American Chemical Socfe^f In Isotope Effects in Chemical Processes; Spindel, W.; Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

48

ISOTOPE E F F E C T S IN C H E M I C A L PROCESSES

b e u s e d i n p a c k e d c o l u m n s , the h a l f - t i m e of the exchange r e a c t i o n s h o u l d b e of the order of seconds, otherwise the effective stage l e n g t h w i l l be excessive.

Q u a l i t a t i v e observations

made

d u r i n g e q u i l i b r i u m constant

d e t e r m i n a t i o n s i n d i c a t e d that the rate of exchange of b o r o n b e t w e e n B F a n d the m o l e c u l a r a d d i t i o n c o m p o u n d was p r o b a b l y r a p i d for

3

adducts

w h i c h w e r e h i g h l y d i s s o c i a t e d i n the v a p o r phase, s u c h as the anisole c o m p l e x , b u t w a s c o n s i d e r a b l y slower for stronger m o l e c u l a r a d d i t i o n compounds

s u c h as the t r i e t h y l a m i n e c o m p l e x .


of these t w o complexes

with B F

were

3

T h e rates of

exchange

determined quantitatively by

c o n t a c t i n g the n o r m a l B F c o m p l e x w i t h boron-10 e n r i c h e d gas. A n a l y s i s 3

of the gas before a n d after e q u i l i b r a t i o n s h o w e d h o w m u c h

exchange

occurred.

was

F o r the anisole system, the h a l f - t i m e of exchange

less

t h a n f o u r seconds. A h a l f - t i m e of a b o u t fifty m i n u t e s w a s estimated for the t r i e t h y l a m i n e system ( T a b l e I V ) . .0261

1

1

,

,

,

!

1

1

,

1

T Figure 1.

Variations of the isotopic equilibrium

Donor • H B F ( 1 ) + 8

constants of the

B F ( g ) = Donor • B F ( 1 ) + With donor and temperature 1 0

3

1 0

3

n

reaction

BF (g) 3

F r o m T a b l e I I I i t is a p p a r e n t that a n u m b e r of different donors c o u l d be u s e d to o b t a i n v e r y attractive f r a c t i o n a t i o n factors. I n d e e d , at 3 0 ° C , the isotopic e q u i l i b r i u m constant w a s 1.03, or m o r e , for phenetole, anisole, d i e t h y l ether, e t h y l formate, d i m e t h y l selenide, d i m e t h y l sulfide, a n d d i e t h y l sulfide. H o w e v e r , a l l of these donors w e r e not e q u a l l y satisfactory for our purpose. T h e b o r o n t r i f l u o r i d e complexes of the thioethers, the selenide, a n d the ester h a d a p r o n o u n c e d t e n d e n c y t o w a r d i r r e v e r s i b l e d e c o m p o s i t i o n a n d w e r e too u n s t a b l e to be seriously c o n s i d e r e d for a n


3.

PALKO A N D DRURY

i n d u s t r i a l process.

Chemical

49

Fractionation

D i e t h y l ether, w h i c h h a d b e e n rejected earlier for the

e x c h a n g e - d i s t i l l a t i o n m e t h o d i n the M a n h a t t a n Project studies, was r e jected b y o u r c r i t e r i a also, t h o u g h o n different grounds.

Since t h e B F

3

a d d u c t of this ether w a s p a r t i a l l y associated i n the v a p o r phase, it w a s not a m e n a b l e to t h e r m a l refluxing. T h u s , of a l l the donors l i s t e d i n T a b l e I I I , o n l y anisole a n d phenetole r e m a i n e d for c o n s i d e r a t i o n .

T h e former

c o m p o u n d was a n i n e x p e n s i v e , c o m m e r c i a l l y - a v a i l a b l e solvent; the latter c o m p o u n d w a s expensive, a n d w a s a v a i l a b l e o n l y i n research q u a n t i t i e s . Downloaded by UNIV OF TEXAS EL PASO on December 28, 2014 | http://pubs.acs.org Publication Date: June 1, 1969 | doi: 10.1021/ba-1969-0089.ch003

W e chose anisole as the d o n o r to be f u r t h e r i n v e s t i g a t e d .

If, at some

f u t u r e date, phenetole becomes c o m m e r c i a l l y a v a i l a b l e a n d e c o n o m i c a l l y c o m p e t i t i v e w i t h anisole, it w i l l be a n attractive substitute for anisole since its B F a d d u c t y i e l d s a s o m e w h a t larger s e p a r a t i o n factor t h a n does 3

the B F a d d u c t of anisole. 3

Reflux Studies I n c h e m i c a l exchange

systems,

reflux consists

of

converting

the

c h e m i c a l forms of the i s o t o p i c species f r o m that of one reactant to that of the other.

I n the systems u n d e r c o n s i d e r a t i o n i n this p a p e r ,

these

reactions a r e : heat Donor • B F ( 1 )

-»

3

Donor(l) + B F ( g )

(3)

3

cool Donor(1) + B F ( g ) -> Donor • B F . (4) R e a c t i o n s 3 a n d 4 are t e r m e d the p r o d u c t - e n d reflux a n d the w a s t e - e n d 3

reflux, respectively.

3

I n p r a c t i c a l a p p l i c a t i o n s , the d o n o r r e s u l t i n g f r o m

R e a c t i o n 3 is u s e d as the reactant i n R e a c t i o n 4. T h e B F associated w i t h 3

the d o n o r i n R e a c t i o n 3 is e n r i c h e d i n boron-10.

T h e B F associated w i t h 3

the d o n o r i n R e a c t i o n 4 is d e p l e t e d i n boron-10. r e m i x i n g of separated isotopes

p r o d u c t - e n d reflux r e a c t i o n m u s t b e free of B F c o n t a i n i n g species.

It is o b v i o u s that, i f

is to b e a v o i d e d , the d o n o r f r o m 3

or a n y other

the

boron-

T h e c r u c i a l n a t u r e of R e a c t i o n 3 becomes e v e n m o r e

a p p a r e n t w h e n it is r e a l i z e d that, for systems of interest i n this p a p e r , e a c h m o l e of p r o d u c t m u s t u n d e r g o R e a c t i o n 3 a p p r o x i m a t e l y 200 times. It is also obvious that, for reflux ratios of this m a g n i t u d e , v e r y l i t t l e i r r e v e r s i b l e d e c o m p o s i t i o n of the a d d u c t , or the donor, c a n b e t o l e r a t e d . T h e r e v e r s i b l e d i s s o c i a t i o n of the anisole a d d u c t was first e x a m i n e d u n d e r l a b o r a t o r y c o n d i t i o n s . A q u a n t i t y of the 1 : 1 c o m p l e x w a s p l a c e d i n a r o u n d - b o t t o m flask w h i c h w a s a t t a c h e d to a v a c u u m t r a i n . T h e flask w a s e q u i p p e d w i t h a r e f l u x i n g condenser, a pressure r e g u l a t o r a n d a p o r t for s a m p l i n g the l i q u i d phase. predetermined

T h e flask w a s h e a t e d e l e c t r i c a l l y at a

pressure u n t i l B F

3

no

longer

escaped

from

the


flask.

50


PROCESSES

Table IV. Rate of (Donor • B F ( l ) + B F ( g ) — n

Adduct C H OCH 6

5

3

• 0.87 B F

E t N • 1.0 B F


3

a

3

3

1 0

3

3

Wt. Adduct (g)

Vol. BF (ST? ml.)

Elapsed Time (sec.)

10.523 10.207 10.480 11.296 12.737 12.083

224.5 164.0 128.6 160.3 147.8 126.3

15 7 15 30 300 1800 3600

3

Without isotope effect.

S a m p l e s of the l i q u i d w e r e t h e n o b t a i n e d for analysis, a n d the e x p e r i m e n t w a s r e p e a t e d at a h i g h e r pressure. o n l y 50-60 parts p e r m i l l i o n of B F c o m p l e x w a s h e a t e d to 1 6 0 ° C .

F r o m T a b l e V it m a y b e seen t h a t 3

r e m a i n e d i n the anisole w h e n the

T h i s degree of r e c o v e r y of B F f r o m the 3

c o m p l e x w a s satisfactory e v e n for the p r o d u c t i o n of v e r y h i g h p u r i t y boron-10. Table V .

Reversible Dissociation of the Anisole • B F Complex 3

Pressure of BF (ton)

Moles BF Remaining per 10 Moles of Anisole

800 875 937 999 1060

69 60 42 54 59

3

Temperature (°C.) 157.0 159.8 163.2 165.0 166.2 Integrated Operation

ti

s

of the Anisole System

T o c o n f i r m the f a v o r a b l e results o b t a i n e d for the anisole system u n d e r l a b o r a t o r y c o n d i t i o n s , a bench-scale,

integrated pilot plant was

con-

structed. T h i s u n i t consisted of a p a c k e d exchange c o l u m n , 1 i n c h o.d. X 36 inches l o n g ; a p a c k e d c o l u m n , 1 i n c h o.d. X 22 inches l o n g , i n w h i c h the a d d u c t w a s f o r m e d ( w a s t e - e n d r e f l u x e r ) ; a p a c k e d c o l u m n , 2 i n c h o.d. X 30 inches l o n g , to w h i c h a reservoir w a s a t t a c h e d ( p r o d u c t e n d r e f l u x e r ) ; a n d a solvent p u r i f i c a t i o n still. P u m p s , valves, a n d i n s t r u m e n t a t i o n w e r e s u p p l i e d as n e e d e d to ensure a u t o m a t i c o p e r a t i o n of the equipment.

C o n t i n u o u s r u n s , one as l o n g as 78 d a y s , w e r e m a d e i n this

equipment.

A p p r o p r i a t e samples w e r e t a k e n to measure t h e


isotopic

3.

Chemical

PALKO A N D DRURY

51

Fractionation

Exchange for the Reaction Donor • B F ( 1 ) + B F ( g ) ) 10

n

3

%

3

B

10

Before

After

CaYd. % B at Equilibrium

40.71 40.82 47.19 47.19 25.26 25.26 25.26

23.05 23.96 44.41 44.12 23.55 23.14 22.46

23.2 21.45 21.70 22.03 20.10 20.05 20.05


10

CaYd. %

a

Exchange

100 90 10.9 12.2 33.1 40.7 53.6

f r a c t i o n a t i o n , the solvent d e c o m p o s i t i o n rate, the b o r o n content of the p r o d u c t - e n d refluxer, as w e l l as the c o r r o s i o n rates of v a r i o u s m a t e r i a l s of c o n s t r u c t i o n . T a b l e s V I a n d V I I s u m m a r i z e the results. T h e d a t a of T a b l e V I s h o w that i r r e v e r s i b l e d e c o m p o s i t i o n

of the d o n o r solvent is

a c c e p t a b l y l o w u n d e r realistic o p e r a t i n g c o n d i t i o n s . It m a y also b e seen that corrosion, as m e a s u r e d b y the presence of F e , C r , a n d N i i n the l i q u i d , is a c c e p t a b l y l o w .

T h e d a t a i n T a b l e V I I illustrate the effectiveness

the r e c o m b i n e r i n c o n v e r t i n g B F

3

gas to the 1:1

of

molecular addition

compound. Table V I . Data Relating to Donor and A d d u c t Stability D u r i n g Operation of the Bench-Scale Pilot Plant Run No.

Length of Run (days)

23 29 30 31* 32 33

20 19 50 20 37 78

b

6 e

e f

Donor Recovered,

%

Decomp. Rate, % /Day

93.4 80 92 95 78

0.35 0.40 0.40 0.35 0.28

Metal in Donor, a

B

Fe

Cr

Ni 3

128 470 169 566 315

v.v.m.

6 119 2 2.5

2 3

38 5 1 1.2

Cu 26 59 54 2.4 3.5

° % Working inventory/day. Nickel packing in exchange column, decomposer, and recombiner. Stainless steel packing. Same as Run 30 plus addition of copper. Same as Run 30 plus addition of black iron. Apparatus contained stainless steel packing, transfer lines, and pumps. Valves were Monel, hence copper is in effluent. b

c

d

e f

T h e results of the f o r e g o i n g l a b o r a t o r y investigations of the anisole d o n o r w e r e sufficiently a t t r a c t i v e to w a r r a n t a n e n g i n e e r i n g e v a l u a t i o n of the t e c h n i c a l f e a s i b i l i t y of u s i n g this m e t h o d to separate l a r g e q u a n t i t i e s


52

ISOTOPE E F F E C T S IN C H E M I C A L PROCESSES I

I

1

1

1

1

1

1

1 —

1.050

4

1.045 r 1 . 0 4 0 '— : 1.035 7


1.025

2

= ••EtAc I

" —

2

"

B

u

^^^^ ^ ^ J C 6 H

2

5

-_

S 0 C H

3

^Me Se 2

i i i i I i

1.030

-=

Et S - • - • ^ Me S

• EtPr

Mej^O

^

THF •

—-

" -

C H 0H 6

5

—

1.020

1.015 8.0

1

1 11.0

1

9.0

10.0

1 12.0

1 13.0

1 14.0

HEAT OF ASSOCIATION OF DONOR A N D B F

Figure

2.

Isotopic equilibrium

1 16.0

1 15.0

1 17.0

(kcal./mole)

3

constants for the

reaction

Donor • H B F ( 1 ) + B F ( g ) = Donor • B F ( 1 ) + BF (g) As a function of the enthalpy of association of the adduct 1 0

8

of b o r o n isotopes.

3

1 0

n

3

3

T h i s w o r k was p e r f o r m e d at another U . S. A t o m i c

E n e r g y C o m m i s s i o n i n s t a l l a t i o n b y a n e n g i n e e r i n g research g r o u p r e p o r t e d t h e i r findings i n d e t a i l elsewhere (16). ing

who

After thoroughly study-

the system f r o m the s t a n d p o i n t of H T U i n a 6 - i n c h i . d . c o l u m n ,

flooding

rate for 5 / 8 - i n c h P a l l p a c k i n g , solvent d e g r a d a t i o n , r e v e r s i b l e

d i s s o c i a t i o n of the c o m p l e x , r e c o m b i n a t i o n of the c o m p l e x , s o l v e n t - d r y i n g p r o c e d u r e s , materials of c o n s t r u c t i o n , a n d corrosion, t h e y c o n c l u d e d that the large-scale anisole process w a s t e c h n i c a l l y feasible.

Table VII.

Operation of the Waste-End Refluxer in the Bench-Scale Pilot Plant Mole Ratio BF /Anisole Leaving Recombiner

Temp. rc.)

Pressure (ton)

1.07 1.06 0.92

6 7 20

850 950 875

3

Run No. 16 17 20

Since the anisole process w a s s u p e r i o r to the d i m e t h y l ether process w i t h respect to s e p a r a t i o n factor, t h r o u g h p u t , i r r e v e r s i b l e d e c o m p o s i t i o n , a n d ease of p r o d u c t recovery, i t was expected to b e m o r e e c o n o m i c a l as


3.

Chemical

PALKO A N D DRURY

well.

53

Fractionation

T h i s e x p e c t a t i o n w a s s u b s t a n t i a t e d b y cost analyses of the t w o

processes.

T h e u n i t cost of b o r o n - 1 0 separated b y the anisole process

was e s t i m a t e d to b e a p p r o x i m a t e l y o n e - h a l f that for the d i m e t h y l ether process

(12).

T h e s e c o n d objective of the present i n v e s t i g a t i o n w a s to u n d e r s t a n d the m e c h a n i s m b y w h i c h b o r o n isotopes are f r a c t i o n a t e d i n R e a c t i o n 1. W e w i s h e d to e x p l a i n w h y b o r o n - 1 0 c o n c e n t r a t e d p r e f e r e n t i a l l y i n the m o l e c u l a r a d d i t i o n c o m p o u n d , c o n t r a r y to the u s u a l e x p e c t a t i o n t h a t the Downloaded by UNIV OF TEXAS EL PASO on December 28, 2014 | http://pubs.acs.org Publication Date: June 1, 1969 | doi: 10.1021/ba-1969-0089.ch003

h e a v y isotope s h o u l d b e p r e f e r r e d b y the c o m p l e x e d species.

W e also

w i s h e d to e x p l a i n the v a r i a t i o n s of the i s o t o p i c e q u i l i b r i u m constants for R e a c t i o n 1 for v a r i o u s d o n o r molecules. F u r t h e r , i t w a s d e s i r a b l e to c o m p u t e t h e o r e t i c a l m a x i m a for the isotopic e q u i l i b r i u m constants of R e a c t i o n 1 to serve as guides for the p r a c t i c a l w o r k . F i n a l l y , w e w i s h e d to e v a l u a t e t h e p o t e n t i a l usefulness of other b o r o n t r i h a l i d e s i n the f r a c t i o n a t i o n of b o r o n isotopes b y R e a c t i o n 1. Theory of Isotopic Fractionation BF

3

and Its Molecular

Addition

in the Exchange of Boron Between Compounds

(25)

T h e u n u s u a l i s o t o p i c c h e m i s t r y of R e a c t i o n 2 m a y b e

understood

i n terms of the e l e c t r o n i c configurations a n d s t r u c t u r a l details of B F a n d its constituent atoms.

T h u s , the three v a l e n c e electrons of

h a v e a n o m i n a l 2$ 2p* c o n f i g u r a t i o n . W h e n B F 2

electrons of b o r o n h y b r i d i z e to sp

2

3

3

boron

is f o r m e d , the v a l e n c e

orbitals w h i c h form n o r m a l sigma

b o n d s w i t h the u n p a i r e d p e l e c t r o n of e a c h fluorine a t o m . T h i s results i n a p l a n a r B F m o l e c u l e h a v i n g the u s u a l 120° c e n t r a l v a l e n c e b o n d a n g l e , 3

a n d a left-over e m p t y b o r o n o r b i t a l , w h i c h projects f r o m the p l a n e of the m o l e c u l e at a n angle of 9 0 ° . T h e seven v a l e n c e electrons of have a nominal 2s 2p 2

5

fluorine

c o n f i g u r a t i o n . T h r e e p a i r s of these electrons are

n o n - b o n d i n g . B e c a u s e of the s m a l l size of the fluorine a t o m , these n o n b o n d i n g e l e c t r o n p a i r s are closer i n fluorine t h a n i n a n y other element. T h e r e p u l s i v e forces b e t w e e n t h e m , c o n s e q u e n t l y , are greater t h a n i n other elements. T h e r e p u l s i v e forces are so great that w h e n B F is f o r m e d , 3

one p a i r of these electrons o c c u p i e s the e m p t y p b o r o n o r b i t a l . T h u s , one of the three fluorine atoms i n B F is effectively d o u b l e - b o n d e d to b o r o n 3

w h i l e the other t w o h a v e c o n v e n t i o n a l s i g m a b o n d s . figurations

Three such con-

are possible, a n d resonance occurs b e t w e e n t h e m (27).

Cotton

a n d L e t o ( 5 ) e s t i m a t e d this resonance energy to be 48 k c a l . / m o l e . It is this s u r p r i s i n g l y large energy associated w i t h the ?r-bonding w h i c h is d i r e c t l y responsible for the u n e x p e c t e d e n r i c h m e n t of the h e a v y b o r o n isotope i n the gas phase. W h e n a m o l e c u l a r a d d i t i o n c o m p o u n d is f o r m e d f r o m B F L e w i s base, energy associated w i t h the 7r-bond i n the B F

3

3

and a

m o l e c u l e is

a b s o r b e d , a n d energy associated w i t h the c o o r d i n a t e c o v a l e n t b o n d i n


54


PROCESSES

t h e a d d u c t is released. It is c o n v e n i e n t to v i e w these changes as separate, d i s c r e t e steps, a n d to r e g a r d the e x c h a n g e as p r e c e d i n g t h r o u g h a h y p o t h e t i c a l , i n t e r m e d i a t e m o l e c u l e B F , i n w h i c h no 7r-bonding occurs—i.e., 3

a m o l e c u l e i n w h i c h e a c h fluorine a t o m is a t t a c h e d to the b o r o n w i t h a normal sigma bond.

W e m a y n o w r e g a r d R e a c t i o n 2 as a c o m p o s i t e

of

t w o separate reactions a n d r e w r i t e i t as s h o w n b y E q u a t i o n s 5 a n d 6. 1 0

BF

+ HBF

3

= HBF

3

+

3

D • !°BF + H B F = D •


3

3

1 0

1 1

BF

(5)

3

BF +

1 0

3

BF

(6)

3

It w i l l b e seen that w h e n the reactions are w r i t t e n i n this m a n n e r , the isotopes c o n c e n t r a t e i n the s o - c a l l e d " c o r r e c t " d i r e c t i o n ; that is, the h e a v y isotope is associated i n e a c h case w i t h w h a t is o b v i o u s l y the m o r e s t r o n g l y b o n d e d species.

T h e expressions for the i s o t o p i c e q u i l i b r i u m constants

for these reactions are g i v e n b y E q u a t i o n s 7 a n d 8,

The Chemical Fractionation of Boron Isotopes - Advances in

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