Mass Spectrometry in Inorganic Chemistry - ACS Publications

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3 Mass Spectrometric Study of Ion-Solvent Molecule Interactions in the Gas Phase P.

KEBARLE

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University of Alberta, E d m o n t o n , Alberta, Canada

Important

and

hitherto

-solvent molecule spectrometric Individual

detection solvation

A

reactions systems

+

A

where

+

and

B Cl 2

-

=

NH4 ,

3

of

CH OH2

into this shell while

gas

and S =

solvation

water

and

phase.

(large clusters)

NH

and BCl ,

3

-

-

competi­

at close

it is range

water is taken

ion shows a distinct is taken up

water is taken up

the The

of Cl ,

methanol,

solvating

Ammonia

ion­

for

In a study of the

The ammonium

shell of four solvent molecules. into the outer

+

is more strongly

At larger distances

up preferentially.

Na

+

by

+

3

in the

and entropies

HO,

+

on

from the mass

· n S can be obtained.

by water is described.

tive solvation

entially

clusters

The comparative

found that methanol of the ion.

of ion

step enthalpies +

are described.

information

can be obtained

· (n — 1)S + S = A

HO 2

unavailable

interactions

inner prefer­

preferentially

shell.

Ο t u d i e s of ion-solvent m o l e c u l e interactions i n s o l u t i o n date b a c k to the ^

b e g i n n i n g of p h y s i c a l c h e m i s t r y a n d represent a m a j o r field i n c h e m i ­

c a l r e s e a r c h . I n contrast, the systematic s t u d y of ion-solvent m o l e c u l e interactions i n t h e gas phase is o n l y a f e w years o l d (10,

12).

I n this

p a p e r w e h o p e to s h o w that a great w e a l t h of significant i n f o r m a t i o n o n i o n - s o l v e n t m o l e c u l e i n t e r a c t i o n s c a n b e o b t a i n e d f r o m the s t u d y of i o n - s o l v e n t m o l e c u l e clusters A

+

· n S or B " * nS i n the gas phase. A or B " +

is a n y p o s i t i v e or n e g a t i v e i o n , a n d S is a solvent m o l e c u l e — i . e . , a m o l e ­ cule w i t h a high dipole moment. T h e mass s p e c t r o m e t r i c gas phase studies are b a s e d o n m e a s u r e m e n t of the r e l a t i v e concentrations of the c l u s t e r e d i o n i c species: A A

+

* ( n + l ) S etc.

+

· nS,

T h e m e a s u r e m e n t of the r e l a t i v e concentrations is

o b t a i n e d b y b l e e d i n g a p r o b e of the gas i n t o a n i o n mass analysis system —i.e., a v a c u u m c h a m b e r a t t a c h e d to a mass spectrometer. I n the v a c u u m 24

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

3.

KEBARLE

Gas

25

Phase

c h a m b e r the gas is p u m p e d out w h i l e the ions are c a p t u r e d b y e l e c t r i c fields,

a c c e l e r a t e d , focused,

a n d mass a n a l y z e d b y some c o n v e n t i o n a l

means ( m a g n e t i c s e p a r a t i o n , q u a d r u p o l e filter, etc. ). A f t e r mass analysis, t h e i o n b e a m intensities are d e t e c t e d as e l e c t r i c a l currents. S e v e r a l types of s o l v a t i o n studies c a n b e u n d e r t a k e n i f the r e l a t i v e concentrations of the i o n i c species are k n o w n . Solvation Enthalpies and Entropies of Individual Solvent Molecule Additions Steps. C o n s i d e r the i o n A

p r o d u c e d i n the gas phase b y some

+

f o r m of i o n i z i n g r a d i a t i o n or t h e r m a l means. I f the a t m o s p h e r e s u r r o u n d ­ i n g the i o n contains the v a p o r of a p o l a r m o l e c u l e ( s o l v e n t S ) , a n u m b e r

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of c l u s t e r i n g reactions w i l l o c c u r . A A A

+

+ S-*A -S

· S + S —> A

+

· (n -

+

(0,1)

+

+

· 2S

1)S + S - » A

+

(1,2)

· nS

(η -

l,n)

A t e q u i l i b r i u m the f o l l o w i n g relations w i l l h o l d AFV ΔΡ%.

M

= A F V + AF\

= -RT

In

2

= —RT In K . n

A

t

.(n-l)S

(I)

+ . . . + AFVi.»

S

(II)

1§ll

r

w h e r e P is the p a r t i a l pressure of X . x

T h u s , k n o w l e d g e of the e q u i l i b r i u m concentrations of the c l u s t e r e d species A

+

· nS o b t a i n e d f r o m experiments at different pressures of S

w i l l a l l o w d e t e r m i n a t i o n of K,,.-,,,, a n d ΔΡ,,.ι,,,. S u c h measurements d o n e at different temperatures w i l l l e a d to the e v a l u a t i o n of Δ Η „ _ ι . „

and

AS„_i,„. T h e a v a i l a b i l i t y of s u c h d e t a i l e d i n f o r m a t i o n w i l l , for instance, r e v e a l the s h e l l s t r u c t u r e since a d i s c o n t i n u o u s c h a n g e of the Δ Η » . ι , « and AS°„. i

) N

values w i l l o c c u r w h e n e v e r a s h e l l is c o m p l e t e d . F i n a l l y , the

t o t a l heat of s o l v a t i o n of the i o n c a n also b e o b t a i n e d f r o m E q u a t i o n I I I , with DO

ΔΗ

8 0 1 ν

. = 2 [ΔΗ . n=0 Μ

Μ

-

A H ^ S ) ]

(III)

equations of the same f o r m h o l d i n g for the free energy a n d e n t r o p y c h a n g e of s o l v a t i o n . It is e v i d e n t f r o m E q u a t i o n I I , that o n l y the r e l a t i v e concentrations of the i o n i c species are r e q u i r e d . T h u s , Δ Ρ ° „ - ι , „ a n d K

p

can be obtained

f r o m E q u a t i o n I I b y a s s u m i n g that the mass s p e c t r o m e t r i c a l l y m e a s u r e d i o n intensities are p r o p o r t i o n a l to the e q u i l i b r i u m p a r t i a l pressures of the ions i n the i o n source. T h e s o l v a t i o n of N H

4

+

by N H and H 0 3

3

+

are examples of this t y p e of s t u d y .

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

b y HoO,

26

MASS SPECTROMETRY I N INORGANIC

CHEMISTRY

Comparative Solvation of T w o Different Ions b y the Same Solvent. T h e r e are three v a r i a n t s o f this t y p e o f study. COMPARATIVE SOLVATION OF IONS A , C +

+

B Y S O L V E N T S. T h e t w o i o n s

are p r o d u c e d i n the same system w h i c h also contains v a p o r o f the solvent S. I n g e n e r a l , d e p e n d i n g o n t h e effective r a d i u s a n d structure o f the i o n , the r e l a t i v e c o n c e n t r a t i o n o f clusters A · n S w i l l b e different f r o m t h a t o f +

C

· m S . T h u s , f o r e x a m p l e , i n the average η m a y b e l a r g e r b y one o r t w o

+

units t h a n m . T h i s w i l l r e v e a l a stronger i n t e r a c t i o n o f A w i t h S. C o m ­ +

p a r i s o n o f η a n d m c a n b e d o n e at different t e m p e r a t u r e s a n d pressures of S i n o r d e r t o c o m p a r e the interactions i n the i n n e r s h e l l o r i n the outer shells. A n e x a m p l e o f this t y p e of s t u d y is t h e system H 0 \ N H 3

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Na

+

4

+

, and

i n H 0 v a p o r , w h i c h is d e s c r i b e d i n the s u b s e q u e n t text. 2

C O M P A R A T I V E SOLVATION O F IONS A

+

A N D B " B Y S O L V E N T S.

A n ex­

a m p l e o f this t y p e o f s t u d y w o u l d b e t h e system K a n d C I " w i t h H 0 . +

2

S i n c e t h e o r i e n t a t i o n o f t h e w a t e r d i p o l e s is r e v e r s e d i n t h e s o l v a t i o n o f p o s i t i v e a n d n e g a t i v e ions, s u c h a c o m p a r a t i v e s t u d y is o f great interest, p a r t i c u l a r l y f o r i s o e l e c t r o n i c p a i r s as the o n e q u o t e d a b o v e . W e h a v e n o t y e t p e r f o r m e d studies o n s u c h isoelectronic p a i r s . H o w e v e r , s u c h studies are p e r f e c t l y possible. T h e p a i r K a n d C I " c o u l d b e p r o d u c e d i n w a t e r +

vapor.

B y r e v e r s i n g t h e mass spectrometer controls, t h e p o s i t i v e a n d

n e g a t i v e ions i n t h e system c o u l d b e m e a s u r e d w i t h i n m i n u t e s o f e a c h other. COMPARATIVE SOLVATION O F Two

N E G A T I V E I O N S B Y S.

A n example

of this t y p e o f s t u d y f o r C l " , B C 1 " a n d B C 1 ~ b y H 0 is g i v e n i n t h e s u b ­ 2

2

sequent text. Competitive Solvation of Ion A

+

(or B") b y Solvent Molecules of

Solvents S and S . A c o m p a r i s o n o f t h e s o l v a t i n g p o w e r o f t w o different k

e

solvents c a n b e o b t a i n e d b y m e a s u r i n g t h e c o m p o s i t i o n o f i o n clusters w h e n t w o different solvents a r e present at k n o w n p a r t i a l pressures. A n e x a m p l e o f this t y p e o f s t u d y is the c o m p e t i t i v e s o l v a t i o n o f N H and N H

3

a n d the solvation of C H O H 3

2

+

4

+

by C H O H andH 0 . 3

2

by H 0 2

A dis­

cussion o f e x p e r i m e n t s d e a l i n g w i t h these t w o systems i s g i v e n l a t e r i n the text. Apparatus

and Method

T h e mass s p e c t r o m e t r i c s t u d y o f ion-solvent m o l e c u l e interactions r e q u i r e s mass s p e c t r o m e t r i c a p p a r a t u s w h i c h c a n s a m p l e ions o r i g i n a t i n g at r e l a t i v e l y h i g h pressures. T h r e e s o m e w h a t different arrangements are p r e s e n t l y i n u s e i n this l a b o r a t o r y . A l p h a Particle Mass Spectrometer (11). A recent v e r s i o n of this a p p a r a t u s is s h o w n i n F i g u r e 1. T h e gas, s u p p l i e d f r o m a c o n v e n t i o n a l gas h a n d l i n g s y s t e m , w h i c h c a n b e b a c k e d t o 1 7 0 ° C , is i r r a d i a t e d i n t h e i o n i z a t i o n c h a m b e r . T h e r a d i a t i o n is s u p p l i e d f r o m a n e n c l o s e d 200-mc.

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

3.

KEBARLE

Gas

27

Phase

p o l o n i u m a l p h a source. T h e p o l o n i u m is d e p o s i t e d o n a c i r c u l a r a r e a of a b o u t 1 / 8 i n c h d i a m e t e r o n the side f a c i n g the i o n source. T o p r e v e n t s p r e a d i n g of the p o l o n i u m , a d o u b l e c o n t a i n e r is u s e d . T h e r a d i a t i o n reaches the i o n source t h r o u g h t w o 10~ -inch stainless steel f o i l s . T o p r e v e n t e a r l y r u p t u r e of the foils, t w o stainless porous p l u g s are u s e d , a l l o w i n g p u m p - o u t of the a l p h a source. T h e i r r a d i a t e d gas bleeds t h r o u g h a l e a k i n t o the e v a c u a t e d electrode c h a m b e r . T h e r e the ions c a r r i e d b y the gas are c a p t u r e d b y the e l e c t r i c fields w h i l e the gas is p u m p e d a w a y . T h e ions are f o c u s e d , a c c e l e r a t e d , a n d t h e n s u b j e c t e d to mass analysis a n d e l e c t r o n m u l t i p l i e r d e t e c t i o n i n a 9 0 ° sector field analyzer tube. I n " s t a t i c " r u n s , gas is s u p p l i e d to the i o n source o n l y at a r a t e sufficient to compensate the o u t f l o w t h r o u g h the leak (0.5 c c . / s e c . f o r a i r , e q u a l to c o n d u c t a n c e of l e a k ) . T h e gas m i x t u r e s w e r e p r e p a r e d i n t w o 2-liter storage flasks of the gas h a n d l i n g system. F l o w r u n s c a n b e m a d e b y p a s s i n g gas t h r o u g h the i o n source. I n the n o r m a l r u n s , one irradiates the t o t a l v o l u m e over the leak. P r o v i s i o n s are also m a d e for p l a c i n g a c o l l i m a t i n g slit b e t w e e n the l e a k a n d the a l p h a source. T h e c o l l i m a t i n g slit w a s cut i n a t u r r e t of 6 - m m . d i a m e t e r , w h i c h s c r e w e d onto a l e a k - c a r r y i n g cone p r o v i d e d w i t h threads. T h e slit w a s e l e v a t e d over the p l a n e of the l e a k b y u n w i n d i n g the t u r r e t a c e r t a i n n u m b e r of r e v o l u t i o n s . T h e i o n source is n o r m a l l y at r o o m t e m p e r a t u r e . H o w e v e r , the t e m p e r a t u r e c a n b e v a r i e d u p to a m a x i m u m of 2 0 0 ° C . b y heaters m o u n t e d i n the heater w a l l s . T h e s e are u s e d either for b a k e - o u t o r r u n s at e l e v a t e d temperatures. T h e t i m e for r e a c t i o n a v a i l a b l e to the average i o n is of the o r d e r of a f e w m i l l i s e c o n d s w h e n the u n c o l l i m a t e d a l p h a b e a m is u s e d ( I I ) . T h i s t i m e c a n b e i n c r e a s e d b y u s i n g the c o l l i m a t i n g slit to screen off a p o r t i o n i m m e d i a t e l y a b o v e the leak f r o m i r r a d i a t i o n . Electron Beam Mass Spectrometer (6). I n a m o r e recent a p p a r a t u s a n e l e c t r o n b e a m is u s e d as i o n i z i n g m e d i u m . T h e i o n source is i d e n t i c a l to that of F i g u r e 1 except t h a t the f o r m e r a l p h a source p o r t contains o n l y one t h i n n i c k e l f o i l ( 10" i n c h ) w i n d o w t h r o u g h w h i c h the electrons enter the source. T h e electrons are c r e a t e d b y a n o r d i n a r y e l e c t r o n g u n h o u s e d i n a s i d e a r m o f the v a c u u m c h a m b e r opposite the n i c k e l w i n d o w . T h e e l e c t r o n filament is k e p t at ca. —25000 volts w h i l e the i o n source is n e a r g r o u n d p o t e n t i a l . A b s e n c e of r a d i o a c t i v e c o n t a m i n a t i o n , h i g h i n t e n s i t y (— 10 m i c r o a m p s ) a n d p o s s i b i l i t i e s for p u l s i n g ( f o r d e t e r m i n i n g i o n i c l i f e t i m e s ) are some of the advantages of the e l e c t r o n b e a m source. T h e greater scattering of electrons at h i g h i o n source pressures causes a d i s a d v a n t a g e w h i c h makes b e a m c o l l i m a t i o n a p r o b l e m . A q u a d r u p o l e mass a n a l y z e r is u s e d w i t h this i n s t r u m e n t .

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4

r>

Proton Beam Mass Spectrometer ( 5 ) . A 100-kev. p r o t o n b e a m o b t a i n e d f r o m a W a l t o n - C o c k r o f t accelerator is u s e d as the i o n i z i n g m e d i u m . T h e i o n source is not l i k e that of F i g u r e 1 b u t is of the c o n v e n t i o n a l design—i.e., a r e c t a n g u l a r b o x w i t h r e p e l l e r a n d n a r r o w e d - d o w n i o n exit slit. T h e p r o t o n b e a m enters a n d exits the i o n source t h r o u g h t h i n n i c k e l f o i l w i n d o w s ( 1 0 " i n c h ) . T h e i o n optics are of the c o n v e n t i o n a l N i e r t y p e , a n d m a g n e t i c analysis is used. A p r o t o n b e a m ( p r e f e r a b l y of e v e n h i g h e r e n e r g y t h a n u s e d b y us ) seems to b e the most c o n v e n i e n t i o n i z i n g 5

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

28

MASS SPECTROMETRY

I N INORGANIC

CHEMISTRY

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m e d i u m f o r h i g h i o n source pressures since i t p r o v i d e s h i g h i n t e n s i t y , p o s s i b i l i t y for p u l s i n g , a n d little scattering at h i g h pressure. T h e p r o t o n b e a m c a n also b e deflected e l e c t r o s t a t i c a l l y before e n t e r i n g the i o n source.

TO MASS ANALYSIS

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

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3.

KEBARLE

Gas

29

Phase

T h i s p e r m i t s v a r i a t i o n of the p r o t o n b e a m - e x i t slit distance i n the i o n source. T h e cost of W a l t o n - C o c k r o f t accelerators is r e l a t i v e l y l o w . A h i g h pressure mass spectrometer u s i n g m.e.v. protons f r o m a V a n d e G r a a f f accelerator has b e e n d e s c r i b e d b y W e x l e r (14). Conditions for Meaningful Measurements and Tests for Equilibrium. I n the discussion g i v e n i n subsequent sections it is a s s u m e d t h a t the m e a s u r e d r e l a t i v e i o n intensities represent at least the a p p r o x i m a t e r e l a t i v e i o n i c concentrations i n the i o n source. It is f u r t h e r a s s u m e d t h a t i o n cluster e q u i l i b r i u m was a c h i e v e d i n the i o n source. T h e v a l i d i t y of these assumptions has b e e n e x a m i n e d i n p r e v i o u s p u b l i c a t i o n s . I t w a s p o i n t e d out t h a t a n o n e q u i l i b r i u m g r o w t h of the clusters m i g h t o c c u r i f c o o l i n g occurs because of a d i a b a t i c expansion past the s a m p l i n g orifice. T o g u a r d against this, one must either h a v e m o l e c u l a r flow i n the s a m p l i n g l e a k ( s m a l l d i a m e t e r of leaks ) or k e e p the p a r t i a l pressure of the c l u s t e r i n g gas l o w so that the m e a n free p a t h for c l u s t e r i n g reactions is m u c h l a r g e r t h a n the d i a m e t e r of the s a m p l i n g leak. A d d i n g a n i n e r t gas u n d e r s u c h c o n d i t i o n s s h o u l d not c h a n g e the o b s e r v e d r e l a t i v e i o n intensities. C h e c k s for the presence of e q u i l i b r i u m c a n b e m a d e b y i n c r e a s i n g the i o n i c r e a c t i o n t i m e . I f the r e l a t i v e intensities r e m a i n constant, one m a y assume that e q u i l i b r i u m or near e q u i l i b r i u m has b e e n a c h i e v e d since the c l u s t e r i n g reactions p r o b a b l y p r o c e e d ( i n the f o r w a r d d i r e c t i o n ) r a p i d l y a n d w i t h o u t a c t i v a t i o n energy. T h e i o n i c r e a c t i o n times c a n b e i n c r e a s e d b y m o v i n g the i o n i z i n g b e a m a w a y f r o m the s a m p l i n g l e a k or slit a n d b y c l o s i n g d o w n the l e a k or slit. T h e latter slows d o w n the mass flow to the s a m p l i n g orifice a n d since the ions, at h i g h e r pressures a n d i n the absence of electric fields, are c a r r i e d b y mass flow to the orifice, increases the i o n i c r e a c t i o n times. Results and

Discussion

Heats and Entropies of Individual Steps, NH

3

=

NH

4

+

(a) N H t

+

* (n—1)NH«

· n N H . P r e v i o u s w o r k o n a m m o n i a (9, 12) 3

that the p r i m a r y ( p o s i t i v e )

+

has s h o w n

ions p r o d u c e d b y the a l p h a r a d i a t i o n are

r a p i d l y c o n v e r t e d b y i o n - m o l e c u l e reactions to the most stable i o n , w h i c h Figure

1.

Ion source and electrode

system

(1 ) Stainless steel block forming ion source. (2) Alpha source, consisting of polonium deposited on a metal disc. Metal disc enclosed in container with stainless foil window and stainless porous plug allowing pressure equalization across foil. (3) Outer alpha source container with foil window and porous plug. Double container prevents spreading of polonium into pressure equalization system. (4) Porous stainless plug allowing pump-out of alpha source and pressure equalization across foils. (5) Gas supply to ion source and flow system (in the direction of the arrows). (6) Tube leading to vacuum system of alpha source contained. (7) Insulating material allowing voltages different from ground to be applied to ion source. (8) Cone-carrying metal foil at its truncated apex. Foil has one or several leaks through which the gas and ions enter the pumping and electrode chamber. (9) Heater and thermocouple wells for temperature control of ion source. (10) Auxiliary electron gun for gas purity determinations. (11-19) Electrodes focusing ion beam into magnetic mass analyzer

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

MASS SPECTROMETRY I N INORGANIC

30

N H

4

+

- n N H

10

3

torr23°C

5

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CHEMISTRY

6

n

10 torr

23°C

1

torr

23°C

1

torr 100°C

to

I

η Figure

2.

Schematic representation of ion clustered NH, · nNH +

t

intensities

for

3

Intensities are expressed as fractions of total ion current. Con­ dition of 1 torr and 100° shows cluster of largest concentration to be NHf - 2NH.1. Reduction of temperature at constant pres­ sure (23°, 1 torr) causes clusters to grow. Increase of pressure at constant temperature (23°, 10 torr) produces further cluster growth. Spectrum at top (23°, 10 torr) shows effect of using large sampling pinhole (70-μ diameter) producing dynamic flow. The resultant adiabatic cooling causes further nonequilibrium growth of clusters. Other three spectra taken with sampling leak consisting of a laser produced array of 30 holes, each of 10 μ diameter is N H

4

+

.

A t t a c h m e n t of a m m o n i a

A representation

m o l e c u l e s t h e n l e a d s to N H

4

+

* nNH . 3

of s o m e t y p i c a l r e l a t i v e i o n intensities o b s e r v e d w i t h i n

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

3.

KEBARLE

31

Gas Phase

the e x p e r i m e n t a l range u s e d i n t h e measurements is g i v e n i n F i g u r e 2. T h e most a b u n d a n t species at 1 0 0 ° C . a n d 1 torr a m m o n i a pressure is NH * 2 N H . A s the t e m p e r a t u r e is l o w e r e d to 2 3 ° C . a n d 1 torr pressure, the l a r g e r clusters η = 3 a n d η = 4 b e c o m e m o r e stable. I n c r e a s i n g t h e pressure at constant t e m p e r a t u r e also increases the cluster size as is e v i ­ d e n t f r o m t h e increase of t h e N H * 4NH /NH · 3 N H ratio o n going f r o m 1 to 10 torr. T h e i o n intensities g i v e n at the t o p o f F i g u r e 2 i l l u s ­ trate t h e effect o f t h e s a m p l i n g leak size. I n this case, a single l e a k o f 70/A d i a m e t e r w a s u s e d . T h e a p p e a r a n c e o f clusters o f h i g h e r mass m u s t b e a t t r i b u t e d to a d i a b a t i c c o o l i n g c a u s e d b y the e x p a n s i o n o f t h e gas jet. 4

+

3

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4

0

2

+

3

4

4

+

6

3

8

10

PRESSURE (torr ) Figure 3. Flot of log K where K = I /Is^nh > at con­ stant temperatures and variable ammonia pressure (pressure expressed in torr) J t 4

3 J T 9

3

U

R e w r i t i n g E q u a t i o n I I f o r t h e a m m o n i a system w i t h the a s s u m p t i o n that t h e r e l a t i v e i o n intensities I„ =

I(NH

4

+

· n N H ) represent 3

ade­

q u a t e l y t h e e q u i l i b r i u m c o n c e n t r a t i o n ratios w e o b t a i n E q u a t i o n I V . Plots o f l o g K , 4 3

RT l o g K . N

1)M

= RT log

7

h=—

/t - 1 '

r

NH

< > IV

3

w i t h pressure a t different constant temperatures a r e g i v e n i n F i g u r e 3.

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

32

MASS SPECTROMETRY I N INORGANIC

CHEMISTRY

T h e s e d a t a s h o w that E q u a t i o n I V is o b e y e d to a g o o d a p p r o x i m a t i o n for a pressure c h a n g e b y a f a c t o r of 10. A p l o t of l o g K .x a n d K . 2

3

4

vs.

1/T is s h o w n i n F i g u r e 4. T h e d a t a u s e d for K . 8 w e r e of s i m i l a r a p p e a r ­ 2

ance to those i n F i g u r e 3. S i n c e there is a s m a l l v a r i a t i o n of l o g Κ w i t h pressure, the values u s e d for the e n t h a l p y plots w e r e t a k e n at zero pres­ sure. T h i s w a s d o n e o n l y for the sake of consistency.

V a l u e s t a k e n at

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5 t o r r pressure l e a d to s i m i l a r e n t h a l p y d a t a .

Figure n-lNH ;i

4.

Plots + NH

:}

giving enthalpy changes for reaction NH, · = NH ; · nNH where n - I , n is 2,3 and 3,4 +

t

f

s

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

3.

KEBARLE

Gas

33

Phase

T h e slopes l e a d to Δ Η ο No

data

were

obtained

=

3

for

w h i c h w o u l d be observable A K

4

5

—17.8 a n d ΔΗ3.4 = the

clustering

—15.9 k c a l . / m o l e .

Reactions

0,1

and

1,2

o n l y at c o n s i d e r a b l y h i g h e r t e m p e r a t u r e s .

c o u l d s t i l l b e m e a s u r e d b u t o n l y at the l o w e s t t e m p e r a t u r e ( 2 5 ° C . ).

It is of interest to p o i n t o u t that the r a n g e c o v e r e d e v e n t h o u g h insuffi­ c i e n t for d e t e r m i n i n g a w i d e r set of reactions is still q u i t e T h u s , the m e a s u r e d r a t i o Ι / / 2

extensive.

increases i n the r a n g e (10 t o r r , 23 ° C . to

4

1 t o r r , 100 ° C . ) b y a factor of 100,000. T h e t h e r m o d y n a m i c d a t a o b t a i n e d are s u m m a r i z e d i n T a b l e I.

It c a n b e s h o w n t h a t the e n t h a l p i e s a n d

entropies of T a b l e I agree w i t h estimates b a s e d o n t h e r m o d y n a m i c cycles

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and calculation.

Table I.

Thermodynamic Data on Clustering Reactions

NH ;

· (n - l)NH (g)

f

- i , η

b c

- * NH,;

s

·

nNH (g) 3

AS° (298°K.), e.u.

ΔΗ, kcal./mole

(298°K.)"

2,3 3,4 4,5 a

+ NH (g)

s

-38 -40.5 (-33)

-17.8 -15.9 (-9)

-6.4 -3.8 -0.5

6

c

Standard state of ammonia, 1 atm. Obtained from AF° and the estimated entropy loss. Estimated.

F i g u r e 5 shows the e n t h a l p i e s for the first five c l u s t e r i n g reactions of N H

4

i n N H . T h e values for Steps 2 - 5 are those f r o m T a b l e I .

+

S

The

Steps 0,1 a n d 1,2 w e r e e s t i m a t e d f r o m the c y c l e s h o w n i n F i g u r e 6a. F r o m this c y c l e w e o b t a i n E q u a t i o n V : ΔΗ

0 > 4

=

ΔΗ

Λ 1 Ώ η

Substituting: ΔΗ

β ν β

,(ΝΗ ) 4

ΔΗ

ρ.(ΝΗ ) =

β η ι 1 1 1

3 ι 4

4

. ( Ν Η ) - AH

·

4NH )

=

3

—80 k c a l . / m o l e .

( f r o m T a b l e I ) one obtains Δ Η

m a g n i t u d e s of Δ Η . ι a n d Δ / / 0

1 2

(NH · 4NH )

amm

3

4

-30

(NH

amm

0>

ΔΗ

.(NH

β ν β ρ

— 5 k c a l . / m o l e a n d &H .

8

( 9 ) , one obtains Δ Η 4 = and

4ΔΗ

+

4

+

) =

3

kcal./mole

=

(9)

—90 k c a l . / m o l e

S u b t r a c t i n g f r o m this ( ) > 2

(V)

—46 k c a l . / m o l e .

ΔΗ

w e r e selected as —25 a n d —21 k c a l . / m o l e

w h i c h n u m b e r s g i v e a c o n t i n u o u s increase of Δ Η i n the d i r e c t i o n Δ Η to Δ Η 0 . 1 ·

2 3

The

W h i l e the p r o c e d u r e i n o b t a i n i n g F i g u r e 5 is s o m e w h a t

t r a r y , w e b e l i e v e t h a t it does g i v e a g o o d q u a l i t a t i v e p i c t u r e of

3 > 4

arbi­ the

e n t h a l p y changes i n the i n d i v i d u a l s o l v a t i o n steps. (b)

H 0 3

+

( n - l ) H 0 + 2

H 0 = 2

H 0 3

+

· n H . O . A system of greater

i m p o r t a n c e t h a n the a m m o n i u m i o n d e s c r i b e d a b o v e is the w a t e r - c l u s t e r e d

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

34

MASS SPECTROMETRY I N INORGANIC

hydronium ion, H 0

+

3

*nH 0. 2

has b e e n p u b l i s h e d (12). single (constant)

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gave Δ #

=

3 > 4

CHEMISTRY

A n e a r l y , p r e l i m i n a r y s t u d y of this system

I n that s t u d y K „ - i , „ was d e t e r m i n e d o n l y at a

pressure of w a t e r , a n d A r r h e n i u s plots of these

—20 ± 5 , AH

4J}

— —24 ± 5 , ΔΗ ,. > = Γ

1.2

2.3

—13 ± 5

(

3.4

K's

kcal./mole.

4.5

Solvation Reaction Figure 5. Enthalpy changes for reactions: NH · (n—l)NH + NH = NH · nNH (n—l,n). Some of the data are based on estimates as described in the text +

f)

/t

3

S

3

O n l y r o u g h estimates of the expected enthalpies c a n b e m a d e o n the basis of a v a i l a b l e t h e r m o d y n a m i c data. T h e c y c l e s h o w n i n F i g u r e 6 b is of the same t y p e as that u s e d for a m m o n i a (k here is the as of yet u n s p e c i f i e d n u m b e r of i n n e r s h e l l w a t e r m o l e c u l e s ) .

F r o m F i g u r e 6b

we obtain Equation V I . ΔΗ„,* = Δ Η ^ , ( Η 0 ) 3

T o evaluate AH , ()k

and H 0 3

· kR 0.

+

2

+

- *ΔΗ,

ν η ρ

.(Η 0) 2

AH

h y d r

. (H 0* · *H 0) 8

(VI)

2

w e n e e d values for the heats of h y d r a t i o n of H 0 3

ΔΗ

h y d r

. (H 0 ) 3

+

c a n be e v a l u a t e d f r o m the c y c l e

+

of

F i g u r e 6c. T h e r e q u i r e d p r o t o n affinity of w a t e r , P A ( H 0 ) , is p r o b a b l y 2

170 k c a l . / m o l e

(3,

Δ#

- 2 8 3 kcal./mole

1 ι ν ( 1 1

AJT

,(Η ) =

I i y d P

+

.(H 0 ) 8

+

=

13).

T a k i n g the heat of h y d r a t i o n of the :î

a n d ΔΗ .

—123.5 k c a l . / m o l e .

4

νΛΙ>

. (H 0 ) = 2

A n estimate of Δ Η

ZcHoO) c a n b e o b t a i n e d f r o m the B o r n equations

(4).

proton

10.5, w e o b t a i n l i y d P

. (H O a

(Examples

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

+

· of

3.

KEBARLE

Gas Phase

35

calculations w i t h t h e B o r n equations are g i v e n b y B a s o l o a n d P e a r s o n (2).

T a k i n g 1.5 A . f o r t h e r a d i u s of H 0 3

+

a n d 2.76 A . f o r the d i a m e t e r

of t h e w a t e r m o l e c u l e s ( 2 ) i n the first s h e l l , one has a t o t a l r a d i u s o f t h e first s h e l l cluster e q u a l to 3.76 A . S u b s t i t u t i n g this v a l u e i n t o t h e B o r n equations, one obtains the estimate A H mole.

h V ( l r

. (H 0 ·

fcH 0)

3

=

2

—39 k c a l . /

S u b s t i t u t i n g into E q u a t i o n V I , w e t h e n o b t a i n : ΔΗ ^ « —123.5 — {)

10.5& + 39 =

—84.5 — 10.5fc. T h i s y i e l d s f o r the average s o l v a t i o n step

i n t h e first s h e l l ΔΗ„. ι „ =

— — (84.5/fc) —10.5 k c a l . / m o l e . F o r

AH

ok

~~k~ different values o f k w e thus o b t a i n i n k c a l . / m o l e Δ Η . ι . « = —31.6 (k = 4 ) , - 2 7 . 4 (k — 5 ) , - 2 4 . 6 (k = 6 ) , - 2 2 . 5 (k = 7 ) , a n d - 2 1 (k = 8 ) . T h i s c r u d e estimate shows t h a t t h e d a t a o b t a i n e d i n o u r earlier s t u d y are i n t h e r i g h t range.

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Μ

NH;

(fl)

+

4ΝΗ

3 ( β )

^ V N H ; . 4 N H

AHamm. (NH*)\

3

(

e

)

Δ H amm.(NH '4NH ) 4

3

-4ΔΗβναρ.(ΝΗ ) 3

NHj (ammoniated) ΔΗ W

k

H

A

.

)

3

H

Δ H hydr.iKjO*) \ -Ι(ΔΗβναμ(Ηρ)

/

0

+

k

H

2 ° (

9

)

AHhydr^Hp+kHjO)

H3O (hydrated) or H(hydrated) +

H

(9)

+

™2°A9)

^

AHhydr.(H ) \ - Δ H evap(H20)

/

+

H

3

°

(9)

AHhydr.(H30+)

H30 (hydrated) or Hi hydrated) +

Figure

6.

Thermodynamic

cycles

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

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36

MASS SPECTROMETRY I N INORGANIC

CHEMISTRY

1h I

I

0.1

I

I

I

I

I

I

I

1.2

2.3

3.4

4.5

5.6

6.7

7.8

I

I

(n-i n) #

Figure

7.

Plot of AF\_ > ltIl

at 298° K. (Standard

state of water 1 atm.)

Results obtained with two different leaks, one slit leak with slit width 7μ and a laser produced array of 30 leaks of 10-μ diameter

Since the e a r l y s t u d y w a s o n l y p r e l i m i n a r y , a second, m o r e extensive research o n t h e h y d r o n i u m - w a t e r system w a s started i n this l a b o r a t o r y a year ago. T h e a l p h a p a r t i c l e - a n d p r o t o n b e a m mass spectrometer are b e i n g used. T h e s e t w o instruments p r o v i d e v e r y different i o n i c r e a c t i o n times, a n d t h e i r c o m b i n a t i o n a l l o w s a g o o d test f o r t h e presence equilibrium.

U n f o r t u n a t e l y this s t u d y is not yet c o m p l e t e d .

has a p p e a r e d c l e a r l y f r o m t h e d a t a o b t a i n e d . ( J O ) t h a t i n aqueous solution the i o n H 0 3

of

O n e result

It is g e n e r a l l y a s s u m e d

* 3 H 0 has h i g h s t a b i l i t y .

+

2

Regardless w h e t h e r this a s s u m p t i o n is correct or not, i n the gas phase this s p e c i a l s t a b i l i t y n e e d n o t a p p l y since t h e c o n s t r a i n i n g influence of the s u r r o u n d i n g l i q u i d lattice is absent.

T h u s , the positions a b o v e a n d

b e l o w the p r e s u m a b l y p l a n a r t r i h y d r a t e are free, a n d since the i n t e r a c t i o n is l a r g e l y a p u r e l y electrostatic one, the h i g h e r hydrates—i.e., H O · 4 E U O ; i

etc. m a y have stabilities w h i c h are not too different.

+

T h i s v i e w is s u p ­

p o r t e d b y the p l o t i n F i g u r e 7. T h e s t a n d a r d free energies for t h e cluster­ i n g Reactions ( n — l , n ) s h o w a continuous change i n the range η = to η =

8. Some f u r t h e r i n f o r m a t i o n o n the H O a

+

2

· n H 0 system is g i v e n 2

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

3.

KEBARLE

Gas

37

Phase

i n the next section w h i c h deals w i t h the c o m p a r a t i v e h y d r a t i o n of H 0 , +

3

N H , and Na\ 4

+

Comparative (a)

Solvation of

Different

Ions by the

COMPARATIVE HYDRATION OFNa , H 0 , AND N H +

ion

3

+

+

4

.

Same

Solvent.

F i g u r e 8 shows

i n t e n s i t y ratios for w a t e r c l u s t e r i n g a r o u n d N a , H 0 , a n d +

T h e ions H 0

and N H

+

3

4

+

NH

+

3

4

+

.

were produced simultaneously b y irradiating

w a t e r v a p o r ( a t pressures 1-5 t o r r ) c o n t a i n i n g several parts p e r m i l l i o n NH .

U n d e r these c o n d i t i o n s , the a m m o n i u m i o n m u s t b e p r o d u c e d

3

p r o t o n transfer f r o m h y d r a t e d h y d r o n i u m ions (see concentration H 0 Downloaded by RUTGERS UNIV on May 17, 2017 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch003

3

of

ammonia

leads

to

the

Reaction 1).

complete

by

Higher

disappearance

of

· nH 0.

+

2

H,0

· W H 0 + N H -» NH

+

2

3

4

+

· n * H , 0 + (w + 1 - η * ) H 0

(1)

2

I n R e a c t i o n 1 w e h a v e i n d i c a t e d that after a d d i n g a m m o n i a to the h y d r o ­ n i u m cluster ( a n d p r o t o n t r a n s f e r ) , some w a t e r molecules w i l l b e " b o i l e d " off.

T h i s effect is to b e expected since the p r o t o n affinity of a m m o n i a is

some 35 k c a l . h i g h e r t h a n that of NH

4

4

The

ammonium

hydrate

2

with NH

water.

· n * H 0 c r e a t e d b y R e a c t i o n 1 m u s t engage i n f u r t h e r collisions

+

water

molecules

before

reaching

its

equilibrium

composition

· nH 0.

+

2

T h e s o d i u m ions w e r e not i n t r o d u c e d i n t e n t i o n a l l y . T h e i r presence was i n f e r r e d f r o m i o n intensities at mass 59, 77, 95, etc. w h i c h are of the same mass as N a ute

this i o n

series

+

· 2H 0, Na 2

to

+

· 3H 0, Na 2

some sodium

+

· 4 H 0 , etc. W e a t t r i b ­ 2

containing

impurity which

in

some m a n n e r leads to the f o r m a t i o n of s o d i u m ions. A s p o i n t e d out i n p r e v i o u s w o r k , ions of l o w i o n i z a t i o n p o t e n t i a l o r i g i n a t i n g f r o m

trace

i m p u r i t i e s often represent a n a p p r e c i a b l e f r a c t i o n of the t o t a l i n t e n s i t y . T h e d i s t r i b u t i o n of the h y d r a t e s g i v e n i n F i g u r e 8 is for a w a t e r p r e s ­ sure of 1 torr. D a t a w e r e o b t a i n e d at pressures f r o m 1-6 torr. T h e e q u i ­ l i b r i u m constants for the three ions c a l c u l a t e d f r o m E q u a t i o n I I r e m a i n e d constant i n this pressure range. s o d i u m clusters ( F i g u r e 8 ) five w a t e r molecules. w a t e r molecules.

T h e d i s t r i b u t i o n s of h y d r o n i u m a n d

are s i m i l a r , the average cluster c o n t a i n i n g

T h e average a m m o n i a cluster contains o n l y f o u r

E x p e r i m e n t s w e r e also p e r f o r m e d at h i g h e r t e m p e r a ­

tures w h e r e the average a m m o n i u m cluster is N H

4

+

· 3 H 0 . T h e water 2

and

s o d i u m clusters w e r e a g a i n h i g h e r b y one u n i t — i . e . , H 0

and

Na

3

+

3

+

* 4H 0 2

2

h y d r a t e are almost c e r t a i n l y " i n n e r s h e i r molecules. H 0

+

· 4 H 0 . A l l w a t e r molecules i n the a m m o n i u m t r i - a n d t e t r a S i n c e the N a

+

and

u n d e r the same c o n d i t i o n s h o l d one m o r e w a t e r m o l e c u l e , w e m a y

c o n c l u d e that the f o u r t h a n d fifth molecules i n the s o d i u m a n d h y d r o ­ n i u m hydrates are h e l d v e r y strongly a n d are thus p r o b a b l y i n n e r s h e l l molecules.

C o n c e r n i n g the H 0 , this c o n c l u s i o n is i n agreement 3

+

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

with

38

MASS SPECTROMETRY I N INORGANIC

NH^nHp

CHEMISTRY

1 torr H20 23° C

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\

ι\

. 1

5

1

6

7 Η3θ ·ηΗ2θ +

1

1,

1

3

Γ 6

>

i

i

Γ 7

Να + ·ηΗ 2 0

Figure 8.

Comparative

f solvation of NH, , H0

Η Ο , and Na

+

t

ν

+

+

by

2

The sodium and hydronium ion behave similarly while the am­ monium ion holds in the average one less water molecule

the d i r e c t H 0 3

tion.

+

* wH 0 2

m e a s u r e m e n t s m e n t i o n e d i n t h e p r e c e d i n g sec­

F r o m the d a t a of F i g u r e 8 a n d those at h i g h e r t e m p e r a t u r e s , i t

f o l l o w s that for the h y d r a t i o n s -

AF° . (Na )

«

-

AF\ ,(H 0 )

> -

-

AF\ (Na )

«

-

AF\ (H 0 )

>

4

5

+

;

3

+

AF\ (NH 5

+

4

)

and 4

+

4

3

+

-

AF° . (NH 3

4

4

+

)

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

3.

KEBARLE

39

Gas Phase

A s s u m i n g t h a t these differences expect:

-ΔΗ . (Να ) 4

-Atf , (Na ) 3

+

4

«

«

+

Β

-ΔΗ

3

4

reflect ΔΗ,,.ι.,,

-Δ#

(Η 0)

4

(Η 0 )

5

>

3

differences

>

+

3

4

-Δ// . (ΝΗ 3

we would

-ΔΗ . (ΝΗ

4

4

).

+

5

+

4

)

and

These data can be

c o m p a r e d w i t h t h e t o t a l heats of h y d r a t i o n o b t a i n e d f r o m t h e r m o d y n a m i c cycles ing

-Aff

I i y d l

section)

,(Na ) +

«

and —ΔΗ

100°, - A H ,

1 ι ν ( 1 1

.(NH ) 4

b e t w e e n the t o t a l h y d r a t i o n of N H d a t a b u t t h e difference b e t w e e n

i y d r

«

+

4

+

H 0 3

.(H 0 )

«

+

8

130 (see

70 k c a l . / m o l e .

preced-

T h e difference

a n d H 0 , N a is reflected i n o u r +

3

+

a n d N a is n o t . F u r t h e r

+

+

mass

s p e c t r o m e t r i c w o r k o n this system is r e q u i r e d b e f o r e m o r e m e a n i n g f u l comparisons c a n be made. C O M P A R A T I V E S O L V A T I O N O F C l " , BC1", A N D B C 1 " B Y H 0 .

Downloaded by RUTGERS UNIV on May 17, 2017 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch003

2

Figure 9

2

shows t h e h y d r a t e d n e g a t i v e ions C l " , B C 1 " , a n d B C 1 " .

T h e original

2

i n t e n t i o n h a d b e e n to s t u d y o n l y t h e h y d r a t i o n o f C I " . F o r this p u r p o s e a mixture of a chlorine-containing c o m p o u n d

( C C 1 a n d C l ) , water, a n d 4

2

excess of N w e r e a d m i t t e d to t h e i o n source. I n a d d i t i o n to C I " * n H 0 , 2

2

t w o other groups of ions w e r e o b s e r v e d .

T h e s e ions w e r e i d e n t i f i e d as

B C 1 - · n H 0 a n d B C 1 " · n H 0 o n the basis of t h e t y p i c a l 2

3 3

C1,

3 7

2

1 0

2

B,

n

B and

C 1 isotope ratios. T h e t w o b o r o n ions o b v i o u s l y arise f r o m s o m e

i m p u r i t y present i n t h e i o n source ( p o s s i b l y solder flux ) . T h e i r presence p e r s i s t e d over m a n y m o n t h s . A t t h e l o w w a t e r pressure CI" · H

2

( F i g u r e 9 ) t h e d o m i n a n t species are

0 ( w i t h some C I " · 2 H 0 ) , B C 1 " · 2 H 0 a n d B C 1 " · 4 H 0 . T h i s 2

2

2

2

difference i n w a t e r content c a n b e u n d e r s t o o d i f i t is a s s u m e d t h a t a l l three ions h o l d a b o u t one w a t e r m o l e c u l e as a h y d r a t i n g species

(i.e.,

w i t h h y d r o g e n s t o w a r d the n e g a t i v e i o n ) a n d B C 1 " a n d B C 1 " h o l d r e s p e c ­ 2

t i v e l y one a n d three w a t e r m o l e c u l e s i n a d a t i v e b o n d o x y g e n lone p a i r .

involving the

T h e c o r r e s p o n d i n g e l e c t r o n i c structures of t h e b o r o n

ions a r e g i v e n i n F i g u r e 10. W h e n t h e w a t e r pressure is i n c r e a s e d ( F i g u r e 9)

CI" · H

2

0 g r o w s to C I " · 4 H 0 a n d C I " · 5 H 0 b u t t h e B C 1 " a n d 2

2

B C 1 " h y d r a t e s g r o w o n l y b y t w o a n d one w a t e r m o l e c u l e s w h i c h c o u l d 2

b e e x p e c t e d c o n s i d e r i n g that these ions are m u c h b u l k i e r . Competitive Solvation of a Given Ion by T w o Different Solvents, a.

COMPETITIVE SOLVATION O F C H O H 3

2

+

BY WATER

AND METHANOL.

A

s t u d y of t h e ions i n m e t h a n o l v a p o r i n t h e pressure r a n g e 1-10 t o r r s h o w e d that most o f the ions b e l o n g e d to t h e series C H O H 3

2

+

* nCH OH. 3

T h i s suggested t h e p o s s i b i l i t y of o b s e r v i n g t h e c o m p e t i t i v e s o l v a t i o n of CH OH 3

2

+

b y w a t e r a n d m e t h a n o l m o l e c u l e s . F i g u r e 11 shows t h e r e l a t i v e

intensities o f t h e m i x e d clusters o b t a i n e d w h e n i r r a d i a t i n g m i x t u r e s of 5 % m e t h a n o l , 9 5 % w a t e r a n d 2 0 % m e t h a n o l , 8 0 % w a t e r b o t h at 5 torr t o t a l pressure a n d 50 ° C . i o n source t e m p e r a t u r e . I n t h e m i x e d m e t h a n o l w a t e r clusters, t h e q u e s t i o n of the s t r u c t u r a l assignment arises.

Thus,

the i o n of mass 119 c o u l d b e assigned as H

2

+

· 2CH OH 3

* 3 H 0 or

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

MASS SPECTROMETRY I N INORGANIC

40

-10"

5 0 0 x l O " torr

torr H 0

3

H 0

3

2

CHEMISTRY

2

Downloaded by RUTGERS UNIV on May 17, 2017 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch003

Cfn H.0

BCI7n H 0 2

L

Figure 9. Comparative solvation of Cl~, BCl~, and B Cl~ at two different water vapor pressures and room temperature 2

Water pressure not accurately known. At lower water pressures BCl~ and BClr contain one and three water molecules more than Cl~. This excess is probably caused by dative bonds as shown in Figure 10

CH OH 3

2

+

· C H O H · 3 H 0 or H 0 3

2

the n o t a t i o n C H O H ; J

2

+

3

· CH OH 8

+

· 2 C H O H · 2 H 0 . W e h a v e selected 3

2

· 3 H 0 (or C H O H 2

3

2

+

the g e n e r a l cluster w h e r e M a n d W s t a n d for C H O H 8

· mM · wW,

for

and H 0 and m 2

a n d w for the n u m b e r of m e t h a n o l a n d w a t e r m o l e c u l e s ) . T h e p r o t o n

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

3.

KEBARLE

Gas

41

Phase

was assigned to the m e t h a n o l o x y g e n i o n since the p r o t o n affinity of m e t h a n o l is some 1 0 - 2 0 k c a l . / m o l e (13)

h i g h e r t h a n that of w a t e r .

JO >DIBIBIQl)~ ,01 H

u

(H>OIBIGI)

(

Figure 10. Electronic formulas of BCl~ - H 0 and B Cl~ - 3H 0 suggested by water content of clusters shown in Figure 9

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2

2

2

T h e clusters o b t a i n e d w i t h 5 % m e t h a n o l ( F i g u r e 11) c o n t a i n , o n the average, c o n s i d e r a b l y m o r e m e t h a n o l t h a n w a t e r e v e n t h o u g h the p a r t i a l pressure r a t i o of w a t e r to m e t h a n o l is 19:1. T h u s , m e t h a n o l is the stronger solvent i n the o b s e r v e d clusters—i.e., clusters c o n t a i n i n g u p to six solvent molecules.

W e s h a l l b e a b l e to u n d e r s t a n d the m e a n i n g of this r e s u l t

better after a m o r e d e t a i l e d treatment of the d a t a . It c a n b e s h o w n t h a t the d i s t r i b u t i o n of w a t e r a n d m e t h a n o l i n the o b s e r v e d clusters f o l l o w s q u i t e closely a p r o b a b i l i t y d i s t r i b u t i o n . C a l l i n g the p r o b a b i l i t i e s

for

i n c l u s i o n of w a t e r a n d m e t h a n o l ω a n d μ, for a cluster w i t h a t o t a l of I solvent molecules the p r o b a b i l i t y d i s t r i b u t i o n w i l l b e g i v e n b y the b i ­ n o m i a l expansion of the t e r m ( ω -f- μ.) .

F o r example, if a probability

1

d i s t r i b u t i o n is f o l l o w e d , the cluster c o n t a i n i n g three s o l v a t i n g m o l e c u l e s CH OH 3

2

+

* mM · wW,

where I =

r e l a t i v e intensities: C H O H 3

W2M

: CH OH 3

2

+

•3M =

2

+

m + w =

· 3W

3, s h o u l d s h o w the f o l l o w i n g

: CH OH 8

or : 3ω-> : 3ωμ! : / Λ 2

2

+

• 2WM : CH OH 3

2

+

·

W e h a v e o b t a i n e d values

for o) a n d μ b y fitting b i n o m i a l expansions to the e x p e r i m e n t a l l y o b s e r v e d d i s t r i b u t i o n . T h e c a l c u l a t e d intensities s h o w n i n F i g u r e 11 demonstrate that a r e l a t i v e l y g o o d fit of the e x p e r i m e n t a l data c a n b e o b t a i n e d .

In

o r d e r to express the p r e f e r e n c e for i n c l u s i o n of m e t h a n o l a n d w a t e r p e r IP u n i t m e t h a n o l a n d w a t e r pressure w e define ν = as the factor for p r e f e r e n t i a l take u p of m e t h a n o l , P a n d P b e i n g the p a r t i a l pressures Μ

/τ>

M

w

of m e t h a n o l a n d w a t e r present i n the i o n source.

T h e y s calculated i n

this m a n n e r are g i v e n i n F i g u r e 11. T h e results at 5 % a n d 2 0 % m e t h a n o l s h o w t h a t the y s for a cluster of a fixed size (i.e., I =

c o n t . ) are a p p r o x i ­

m a t e l y i n d e p e n d e n t of the m e t h a n o l - w a t e r pressure r a t i o .

This inde­

p e n d e n c e was c o n f i r m e d i n a n u m b e r of other runs w i t h 2, 4, 5, 8, 20, 5 0 % m e t h a n o l at 2 a n d 5 torr t o t a l pressure. T h e y s are f o u n d to decrease as I increases. T h u s , m e t h a n o l is t a k e n u p p r e f e r e n t i a l l y b y a factor of 55,

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

42

MASS SPECTROMETRY I N INORGANIC

CHEMISTRY

21, a n d 8 for clusters c o n t a i n i n g three, f o u r , a n d five solvent m o l e c u l e s . F i g u r e 12 shows a l o g γ p l o t vs. the n u m b e r of s o l v a t i n g molecules. p l o t is almost l i n e a r a n d a l l o w s a n e x t r a p o l a t i o n to l o g y =

The

0 or y =

T h i s occurs w h e n the cluster contains seven s o l v a t i n g molecules. I >

1. For

7, y becomes less t h a n u n i t y — i . e . , w a t e r begins to take p r e c e d e n c e .

F i g u r e 13 also shows results o b t a i n e d w i t h the p r o t o n b e a m mass spec­ trometer.

T h e t o t a l pressure i n these runs was m u c h l o w e r (0.6

torr),

a n d the r e a c t i o n t i m e was m u c h shorter ( s e v e r a l microseconds vs. a f e w m i l l i s e c o n d s i n the a l p h a p a r t i c l e i o n s o u r c e ) .

O n e m i g h t suspect t h a t

u n d e r these c o n d i t i o n s c l u s t e r i n g e q u i l i b r i u m m i g h t not b e

achieved.

H o w e v e r , the results are q u i t e s i m i l a r to those o b t a i n e d w i t h the a l p h a Downloaded by RUTGERS UNIV on May 17, 2017 | http://pubs.acs.org Publication Date: June 1, 1968 | doi: 10.1021/ba-1968-0072.ch003

i o n source.

T h i s m i g h t b e t a k e n to m e a n that c l u s t e r i n g e q u i l i b r i u m

establishes r a p i d l y a n d that the p r o t o n b e a m results a p p r o a c h e q u i l i b r i u m . I n i n t e r p r e t i n g the present results c o n s i d e r a b l e h e l p c a n b e o b t a i n e d f r o m the "electrostatic t h e o r y " for m e t a l - i o n c o o r d i n a t i o n complexes

(2).

T h i s theory, u s i n g s i m p l e electrostatic concepts, a l l o w s one to c a l c u l a t e the b i n d i n g energies of m e t a l complexes i n the gas phase. T h e results of s u c h c a l c u l a t i o n s h a v e b e e n i n m a n y cases successful.

I n g e n e r a l , the

p o t e n t i a l e n e r g y of a c o m p l e x i o n is b u i l t u p of f o u r terms. T h e s e are a t t r i b u t e d to the a t t r a c t i o n b e t w e e n

the i o n a n d the p e r m a n e n t

and

i n d u c e d d i p o l e of the l i g a n d s , the m u t u a l r e p u l s i o n of the d i p o l e s , the e n e r g y r e q u i r e d to f o r m the i n d u c e d d i p o l e s a n d the v a n d e r W a a l s repulsions b e t w e e n the l i g a n d s a n d the c e n t r a l i o n . C o m p a r i n g the p o t e n ­ t i a l energies of a n i o n h a v i n g w a t e r or m e t h a n o l molecules as l i g a n d s , i t is f o u n d that the first t e r m is the d e c i s i v e one. It contains the s u m of the p e r m a n e n t d i p o l e a n d the p o l a r i z a b i l i t y . T h e d i p o l e m o m e n t s of w a t e r a n d m e t h a n o l are 1.85 a n d 1.69 D w h i l e the p o l a r i z a b i l i t i e s are 1.48 a n d 3.23 Α Λ

T h e p o t e n t i a l e n e r g y of a n i o n d i p o l e i n t e r a c t i o n varies i n v e r s e l y

w i t h the square of the distance w h i l e the p o l a r i z a b i l i t y i n t e r a c t i o n d e ­ p e n d s o n the f o u r t h p o w e r .

T h e r e f o r e , the m e t h a n o l m o l e c u l e s ,

with

their slightly lower dipole but considerably higher polarizability, w i l l be m o r e s t r o n g l y s o l v a t i n g t h a n w a t e r at close r a n g e to the i o n . T h e e x p e r i ­ m e n t a l l y o b s e r v e d preference for m e t h a n o l is thus to b e u n d e r s t o o d

as

r e s u l t i n g f r o m the h i g h e r m e t h a n o l p o l a r i z a b i l i t y . It c a n b e s h o w n that the p o s s i b i l i t y of

fitting

the o b s e r v e d clusters

w i t h a g i v e n I b y a p r o b a b i l i t y d i s t r i b u t i o n suggests that for I <

6 all

solvent m o l e c u l e s b e l o n g to a n i n n e r s o l v a t i o n shell. Suppose that for I = 5 some of the molecules w e n t into a n i n n e r s h e l l ( f u l l y o c c u p i e d ) a n d the rest i n t o a n outer shell. T h e preference for m e t h a n o l over w a t e r i n the i n n e r s h e l l w i l l b e different f r o m that i n the outer s h e l l .

It m i g h t

e v e n b e e x p e c t e d that w a t e r w i l l be p r e f e r e n t i a l l y t a k e n u p i n the outer shell.

It f o l l o w s that the w a t e r - m e t h a n o l d i s t r i b u t i o n i n a cluster c o n ­

t a i n i n g i n n e r a n d outer s h e l l molecules c o u l d not b e fitted b y a single

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

3.

KEBARLE

Gas

43

Phase

18 f-

Experimental

Calculated

14 10 6 -

ι • • 111

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2 -

Φ 26 _

22

S

18

σ

14 10 6 2 ι

Γ

m = W =

3 2

V

Τ

Figure 11. mCH OH 3

3 4

ι

t

12

V

3 4 5

0

1 0

4 3 2 1 0

5 4 3 2 1 0

I =4

I = 5

I =3

12

0

13

Mixed water and methanol content in CH OH - wH 0 clusters. Ion source temperature 50°C. 3

+

2

2

p r o b a b i l i t y d i s t r i b u t i o n of the t y p e ( ω + μ)

1

b u t that the i n n e r a n d outer

s h e l l w o u l d h a v e to b e fitted separately. S u c h a case is i n fact o b s e r v e d i n the c o m p e t i t i v e s o l v a t i o n of N H

4

+

b y H 0 a n d N H w h i c h is d i s c u s s e d 2

3

i n the next section. S i n c e the w a t e r - m e t h a n o l clusters of I =

3, 4, 5 c a n

e a c h b e fitted w i t h a p r o b a b i l i t y d i s t r i b u t i o n , w e c a n c o n c l u d e that these clusters d o n o t c o n t a i n molecules w h i c h o c c u p y a d i s t i n c t outer s h e l l — i.e., that the i n n e r s h e l l contains at least five solvent m o l e c u l e s .

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

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44

MASS SPECTROMETRY I N INORGANIC

Figure

12.

Plot of hg y vs. number of solvating

CHEMISTRY

molecules

y is factor for preferential take up of methanol over water into ion CH. OH> · mCH: OH - wH_,0, where m + w = 1. For low 1 methanol is taken up preferentially. As size of cluster increases preference for methanol decreases, y = 1 at 1 = 7 where water and methanol are taken up with equal preference t

+

f

T h e a b i l i t y to fit a cluster of constant I w i t h a p r o b a b i l i t y d i s t r i b u ­ t i o n is, to a c e r t a i n extent, s u r p r i s i n g even i f a l l m o l e c u l e s b e l o n g to t h e same s o l v a t i o n s h e l l . A p r o b a b i l i t y d i s t r i b u t i o n means, f o r e x a m p l e , that i n t h e five cluster t h e p r e f e r e n c e f o r m e t h a n o l o v e r w a t e r is t h e same w h e t h e r a l l t h e r e m a i n i n g f o u r l i g a n d s are w a t e r or m e t h a n o l or a m i x t u r e of t h e m .

O b v i o u s l y this c a n n o t b e s t r i c t l y true.

T h e m e a n i n g of t h e

e x p e r i m e n t a l result m u s t b e that t h e n a t u r e of t h e other occupants i s , i n t h e first a p p r o x i m a t i o n , n o t i m p o r t a n t . W h i l e y r e m a i n s a p p r o x i m a t e l y constant for a cluster d i s t r i b u t i o n with I =

const., i t w a s o b s e r v e d that y « const, decreases f r o m I = t

3 to

Ζ — 5. T h i s c a n b e u n d e r s t o o d i f one assumes that w h e n e v e r I is i n c r e a s e d b y one u n i t , t h e effective r a d i u s of t h e ( i n n e r )

s h e l l increases.

This

causes t h e p o l a r i z a b i l i t y to b e c o m e less i m p o r t a n t a n d leads to a decrease of the p r e f e r e n c e for m e t h a n o l . A n increase of t h e effective r a d i u s m i g h t

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

3.

KEBARLE

Gas

45

Phase

b e e x p e c t e d b e c a u s e of the m u t u a l r e p u l s i o n a t t r i b u t e d to d i p o l e a n d v a n d e r W a a l ' s forces b e t w e e n the l i g a n d s . b.

COMPETITIVE

WATER

INNER

ANDAMMONIA

AND OUTER

MOLECULES.

d e s c r i b e d i n a p r e v i o u s section.

SHELL

The

SOLVATION

s o l v a t i o n of

N H

4

+

OF N H by

4

N H

+

3

BY was

W h e n w a t e r v a p o r w a s a d d e d to a m ­

m o n i a , n e w i o n peaks c o u l d b e o b s e r v e d w h i c h c o r r e s p o n d e d to the m i x e d clusters Ν Η η Ν Η ΐ ί / Ή 0 . 4

+

3

2

D a t a of three representative runs are s h o w n

i n T a b l e I I . T h e first e x p e r i m e n t is d o n e at v e r y l o w a m m o n i a pressure w h e r e the l o w e r solvates (I =

2, 3, 4 ) are of h i g h e s t a b u n d a n c e .

It c a n

b e seen that these ions c o n t a i n m a i n l y a m m o n i a m o l e c u l e s even t h o u g h

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t h e w a t e r - t o - a m m o n i a pressure r a t i o is e q u a l to three. I t is also e v i d e n t t h a t the m i x e d o c c u p a n c y f o l l o w s q u i t e n e a r l y a p r o b a b i l i t y d i s t r i b u t i o n . C a l l i n g the p r o b a b i l i t y for a m m o n i a i n c l u s i o n α a n d that for w a t e r ω, t h e c a l c u l a t e d p r o b a b i l i t i e s for a n I solvate w i l l b e e q u a l to the b i n o m i a l e x p a n s i o n terms of ( a +

ω) . 1

T h u s , for the I =

2 g r o u p the intensities

of the ions s h o u l d b e i n the ratios or : 2αω : or. T h e r a t i o α / ω s h o u l d b e g i v e n b y the i o n i n t e n s i t y ratios 2 7 / I > , I53/2I54 a n d (I^/h*) ' 52

r

Taking

1 2

3

the values f r o m the t a b l e w e c a l c u l a t e for α / ω the values 10.6, 7, a n d 8.6.

log./

outer

inner shell

shell

+2

+1

0

θ

-2

2Î

3

I s number Figure 13.

4

5

6

7

8

of solvating molecules

Plot of log y for different solvation shells of ion

NH

+

Jt

y is a factor giving the observed probability for preferential take up of ammonia over water into ion: NHf · slNHS · wH^O, where a + w = 1. Ammonia is taken up with preference into inner shell (\ < 4), water is taken up with preference into outer shell

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

46

MASS SPECTROMERTY I N INORGANIC CHEMISTRY

Table II. Mass Spectra of Ammonia-Water Mixtures Showing the Competitive Solvation of the Ammonium Ion by Ammonia and Water Molecules p(NH )(torr) p(H 0)/p(NH )

0.05 3

3

2

s

Ion - Mass

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NH NH NH NH etc.

NH etc.

4

4 4 4

4

b

· 2NH NH · H 0 · 2H 0 · 3NH

+

3

+

3

+

2

2

+

3

· 4NH

+

NH · 4NH 1 N H etc. 4

Intensity

+

3

3

·

3

NH · 4NH · 2 N H etc. 4

+

3

3

52 53 54 69 70 71 72 86 87 88 89 90 103 104 105 106 107 120 121 122

11.1 2.1 .15 104.0 40.0 6.3 d 5.1 8.3 3.2 0.6

34 0.003

1.8 1.5

e

Inten­ sity • 15 »

c

7 32 21 25 23 19

c

y

15

11.5 4.4

7 12 11

Intensity

°

b

y

100 d

d

0.027

335 360

d

d

9 3.2

d

0.036 0.047

800 1300 380

Contains also 20 torr. xenon to make the signals detectable. * Arbitrary units. Factor of preferential take up of ammonia to water ( see text ). Low intensity, not measured accurately. a

c

d

I n o r d e r to express the preference

for a m m o n i a p e r u n i t pressure

we

define, i n a n a l o g y w i t h the treatment of the m e t h a n o l w a t e r clusters, a γ w h i c h is g i v e n b y the e q u a t i o n y —

—-.

T h e y s c a l c u l a t e d i n this

ω/ Γ Η 0 2

w a y are g i v e n i n T a b l e I I . A s I increases f r o m 2 - 4 one observes a decrease of γ f r o m a b o u t 25 to 10. T h i s change is s i m i l a r to that o b s e r v e d i n the w a t e r m e t h a n o l system. I n clusters w i t h I =

5, 6, etc. a n e w p h e n o m e n o n

is o b s e r v e d n o t p a r a l l e l e d b y the w a t e r m e t h a n o l system. T h e a m m o n i a clusters w i t h I >

4 c a n not b e fitted w i t h a s i m p l e p r o b a b i l i t y d i s t r i b u ­

t i o n . T h i s is seen c l e a r l y f r o m the results at 1.8 a n d 34 torr of a m m o n i a ( T a b l e I I ) . A t 1.8 torr of a m m o n i a the c a l c u l a t e d γ for the I =

4 group

is close to t h a t o b t a i n e d at the l o w pressure s h o w i n g a n a m m o n i a p r e f e r ­ ence γ =

15. B u t the N H

4

+

· 5NH

3

i o n of mass 103 is essentially m i s s i n g .

T h e first i o n of significant i n t e n s i t y is N H

4

+

4NH

3

H 0 (mass 1 0 4 ) . 2

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.

This

3.

KEBARLE

47

Gas Phase

result c a n b e u n d e r s t o o d i f i t is a s s u m e d that a n i n n e r s h e l l of

four

molecules has b e e n b u i l t u p a n d t h a t w a t e r is t a k e n u p p r e f e r e n t i a l l y i n the outer shell. T h e preference for w a t e r i n the outer s h e l l c a n b e m e a ­ s u r e d f r o m the result at 34 torr. T h e m u c h h i g h e r

ammonia-to-water

r a t i o u s e d i n this r u n leads to a f u l l y a m m o n i a t e d i n n e r s h e l l so t h a t the ions of h i g h e r mass are c a u s e d b y w a t e r presence i n the outer s h e l l o n l y . T h e c a l c u l a t e d y s for outer s h e l l o c c u p a n c y are s m a l l e r b y a factor of n e a r l y 1000.

T h e results f r o m a n u m b e r of runs at different pressures

a n d w a t e r - t o - a m m o n i a pressure ratios are s u m m a r i z e d i n F i g u r e 4, w h i c h gives a p l o t of l o g y for different I. T h e values for I < 4 represent i n n e r

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s h e l l ys.

T h e values for I >

4 w e r e t a k e n at h i g h e r a m m o n i a - t o - w a t e r

pressure ratios w h e r e the i n n e r s h e l l was essentially c o m p l e t e l y m a d e u p of a m m o n i a . T h i s a l l o w e d the c a l c u l a t i o n of y s for outer s h e l l s o l v a t i o n . T h e drastic c h a n g e f r o m I =

4 to I =

5 is e v i d e n t also f r o m these results.

T h e c o n s i d e r a b l e scatter of the points is b e l i e v e d to b e m a i n l y a t t r i b u t e d to the difficulty i n m e a s u r i n g a c c u r a t e l y the a m m o n i a a n d w a t e r pressures i n the i o n source. T h e p r e f e r e n t i a l take u p of a m m o n i a i n the i n n e r s h e l l a n d of w a t e r i n the outer s h e l l c a n be u n d e r s t o o d o n the basis of the p o l a r i z a b i l i t i e s a n d d i p o l e m o m e n t s of w a t e r a n d a m m o n i a .

Ammonia

has the h i g h e r p o l a r i z a b i l i t y b u t l o w e r d i p o l e ; therefore, i f it c a n w i n o v e r w a t e r , i t m u s t d o so i n the i n n e r s h e l l . T h e result of a n i n n e r f o u r s h e l l is i n agreement w i t h the ΔΗ . η

i „ measurements w i t h p u r e a m m o n i a f

d e s c r i b e d i n the s e c t i o n : " H e a t s a n d E n t r o p i e s of I n d i v i d u a l Steps."

Literature

Cited

(1) Altshuller, A. P., J. Am. Chem. Soc. 77, 3480 (1955). (2) Basolo, F., Pearson, R. G., "Mechanisms of Inorganic Reactions," p. 64, John Wiley & Sons, New York, 1958. (3) Bell, R. P., "The Proton in Chemistry," Cornell University Press, Ithaca, New York, 1959. (4) Born, M., Z. Physik 1, 45 ( 1920). (5) Collins, G. J., Kebarle, P. (to be published), (β) Durden, D. Α., Kebarle, P. (to be published). (7) Hamer, W. J., ed., "The Structure of Electrolytic Solutions," Chapter 5, John Wiley & Sons, New York, 1959. (8) Hogg, A. M., Kebarle, P., J. Chem. Phys. 43, 449 (1965). (9) Hogg, A. M., Haynes, R. M., Kebarle, P., J. Am. Chem. Soc. 80, 28 (1965). (10) Kebarle, P., Godbole, E. W., J. Chem. Phys. 39, 1131 (1963). (11) Kebarle, P., Haynes, R. M., Searles, S. K., ADVAN. C H E M . SER. 58, 210 (1966). ( 12) Kebarle, P., Hogg, A. M., J. Chem. Phys: 42, 798 (1965). (13) Munson, M. S. B., J. Am. Chem. Soc. 87, 2332 (1965). (14) Wexler, S., ADVAN. C H E M . SER. 58, 193 (1966). RECEIVED October 11, 1966.

Margrave; Mass Spectrometry in Inorganic Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1968.