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T H E R E F R A C T M T Y I N TE R C E P T A N D T H E S PE C IF ICR E F R A C T IO N E Q U AT I O N O F N E W T O N I

D E V E L O P M E N T O F T H E R E FR A CT IV IT Y

IN T E R C E P T A N D C O M PA R I S O N W I T HS P E C I F I C R E F R A C T I O N E Q U AT I O N S

BY

S . S . K U R T Z , J R ., A N D A . L . W A R D . t

ABSTRACT.

T h e s i gn i f ic a n c e o f r e f r a c t i v e i n d e x d a t a a n d t h e r e l a t i o n s h i p b e t w e e n t h er e f r a c t i v e in d e x a n d t h e d e n s i t y o f h y d r o c a r b o n s a r e d i s cu s se d . T h e r e a r e p r e-

s e n t e d a n e w c o n c e p t o f r e f ra c t i o n a n d a s i m p l e n e w c o n s t a n t ,n - d / 2 d e s i g n a t e dr e f r a c t i v i t y i n t e r c e p t , w h i c h i s c h a r a c t e r i s t ic o f e a c h h y d r o c a r b o n s e ri es . T h er e f r a c t i v i t y i n t e r c e p t i s s h o w n t o r e p r e s e n t a m o r e c o n s t a n t r e l a t io n s h i p b e t w e e nt h e d e n s i t i e s a n d r e f r a c t i v e i n d i c e s o f t h e m e m b e r s o f a n h o m o l o g o u s s e r i e s o fh y d r o c a r b o n s t h a n t h e u s u al e q u a t i o n s f o r re f r a c t iv i t y.

I t i s a l so s h o w n t h a t N e w t o n s s p e ci fi c r e f r a c t i o n e q u a t i o n r e p r e s e n t s t h er e l a t i o n s h i p b e t w e e n d e n s i t y a n d r e f r a c t i v e i n d e x f o r s e t s o f h y d r o c a r b o n i s o m e r sb e t t e r t h a n t h e L o r e n t z a n d L o r e n z , E y k m a n , o r G l a d s t o n e a n d D a l e e q u a t io n s .

F i n a l l y, i t i s s h o w n t h a t t h e f u n d a m e n t a l d i f fi c u lt y i n p a s t w o r k o n r e fr a c -t i v i t y w a s t h e a t t e m p t t o m a k e o n e e q u a t io n r e p r e se n t t h e e f f ec t o f b o t h t e m p e r a -

t u r e a n d c o n s t i t u t i o n o n t h e r e l a t io n s h i p b e t w e e n d e n s i t y a n d r e f r a c t i v e in d e x .F o r h y d r o c a r b o n s , i t i s d e m o n s t r a t e d t h a t i t is i m p o s s i b le f o r o n e e q u a t i o n t or e p r e s e n t b o t h t h e t e m p e r a t u r e a n d c o n s t i t u t i o n e f f e c t s .

L INTRODUCTION.

This paper is primarily a plea for a change in point of viewin regard to the significance of refractive index data and therelationship between the refractive index and the density ofhydrocarbons.

Th at there is a relationship between the two constants hasbeen evident since the properties were first studied. FromNewton to the present time investigators have attempted todevelop and use equations which would harmonize the effect oftempera ture and constitution on the relationship of density torefractive index.

Although various equations which have been developedhave been extremely useful in the study of hydrocarbons it

* D e v e l o p m e n t E n g i n e e r , T h e S u n O i l C o .t M a n a g e r , T h e C h e m i c a l L a b o r a t o r ie s , T h e U n i t e d G a s I m p r o v e m e n t C o .

563

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564 S . S . K U RT Z J R . A N D A . L . W A R D . [J . F. I.

h a s b e e n e v i d e n t t h a t n o n e o f t h e m f ul fi ll ed a ll o f t h e p u r p o s e s

f or w h i c h a t t e m p t s w e r e m a d e to u se t h e m . T h e r a p id l yg r o w i n g i m p o r t a n c e o f p h y s i c a l c o n s t a n t s in t h e s t u d y o fh y d r o c a r b o n s h a s e m p h a s i z e d t h e w e a k n e s s e s i n t h e c l a s s i c a lm e t h o d s o f t r e a t i n g d e n s i t y a n d r e f ra c t i v e i n d e x d a t a a n dj u s t if i e d a r e s u r v e y o f t h e e n t i r e s u b j e c t . A t t h e s a m e t i m et h e i n c r e a s i n g v o l u m e o f e x p e r i m e n t a l d a t a b e c o m i n g av a i la b l ef or p u re h y d r o c a r b o n s p e r m i t s c h e c k i n g a n y e q u a t i o n a g a in s te x p e r i m e n t a l d a t a t o a n e x t e n t t h a t w a s i m p o s s i b l e u n t i l

r e c e n t l y.T h e p r e s e n t p a p e r is a r e s u l t o f a n e x t e n s i v e s u r v e y o f t h e

c l a s s i c a l m e t h o d s o f r e l a t i n g d e n s i t y a n d r e f r a c t i v i t y i n d e xa n d o f a n i n te n s iv e s t u d y o f e x p e r i m e n t a l d a t a in a n a t t e m p t

I ) t o d e r i v e a r e f r a c t i v i t y e q u a t i o n t h a t w o u l d b e m o r es u i t a b l e a n d m o r e c o n v e n i e n t t h a n a n y o f t h e c l a s s i c a le q u a t i o n s f o r c h a r a c t e r i z in g h o m o l o g o u s s e ri es o f h y d r o c a r b o n sb y m e a n s o f d e n s i t y a n d r e f ra c t i v e i n d e x d a t a d e t e r m i n e d a t a

f ix e d re f e r e n c e t e m p e r a t u r e s u c h a s 2 o ° C . , 2 ) t o i n t e r p r e th o m o l o g o u s s e r i e s r e l a t i o n s i n t e r m s o f t h e n u m b e r a n df r e q u e n c y o f d i s p e rs i o n e l e c tr o n s , a n d 3 ) t o d e ri v e a n e q u a t i o nt h a t w o u l d h a v e t h e o r e t i c a l s i g n i f i c a n c e a n d t h a t w o u l de x p r e s s t h e e f f e c t o f t e m p e r a t u r e o n r e f r a c t i v e i n d e x a s a c c u -r a t e l y a s t h e em p i r i c al e q u a t i o n of E y k m a n . I n p a r t I o ft h i s p a p e r i t e m I ) o n l y w i l l b e d i s cu s s e d .

D e f i n i ti o n o f T e r m s

R e f r a c t i v e i n d e x n ) is d e f i n e d a s t h e r a t i o o f t h e s p e e d o fl i g h t i n s p a c e v a c u u m ) t o i ts s p e e d in a g i v e n s u b s t a n c e .F o r a p p r o x i m a t e p u r p o s e s t h e s p e e d o f l i g h t i n a i r m a y b et a k e n a s e q u i v a l e n t to t h a t i n s p a ce . R e f r a c t i v e i n d e x f ora n y g i v e n s u b s t a n c e v a r i e s w i t h t h e w a v e - l e n g t h o f l ig h t a n dt h e te m p e r a t u r e . T h e sy m b o l s n ~ ° = t h e r e f r a c ti v e in d e x

f o r t h e D l in e o f t h e F r a u n h o f e r se ri es s o d iu m ) d e t e r m i n e d a t2 o ° C . D e n s i t y d ) is d e f i n e d a s m a s s p e r u n i t v o l u m e ,s p e c i f i c a ll y a s g r a m s p e r m i l l il i te r. S p e c i fi c r e f r a c t i v i t y r) iss o m e fu n c t i o n o f r e f ra c t i v e i n d e x d i v i d e d b y d e n s i t y. M o l e c u -l a r r e f r a c t i v i t y mr) i s s p e c i f i c r e f r a c t i v i t y m u l t i p l i e d b ym o l e c u l a r w e i g h t m ).

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N o v., I9 36 .] R E F R A C T I V I T Y IN T E R C E P T O F N E W T O N . 6

II. HISTORICAL.

T h e e a r l i e s t e q u a t i o n r e l a t i n g r e f r a c t i v e i n d e x ( n ) a n dd e n s i t y (d ) is t h a t o f N e w t o n , 1n 2 - I ) / d = c o n s t a n t . I nd e d u c i n g t h is e q u a t i o n N e w t o n u s e d a v e c t o r ia l r ig h t t r ia n g l ein w h i c h t h e h y p o t h e n u s e h a d t h e d i r e c t i o n of t h e r e f r a c te dr a y i n t h e r e f r a c t in g s u b s t a n c e , a n d a l e n g t h p r o p o r t i o n a l tot h e r e f r a c t i v e i n d e x (i.e ., t o t h e r e c i p r o c a l o f t h e s p e e d o f t h er e f r a c t e d r a y ) .* O n e s id e o f t h e v e c t o r ia l t r i a n g l e h a d t h ed i r e ct io n o f t h e b e a m i n c i d e n t u p o n t h e r e f ra c t in g s u r fa c e a t

g r a z i n g i n c i d e n c e , a n d a l e n g t h e q u a l to u n i t y (i.e ., t o t h es p e e d o f l i g h t in a i r) . T h e t h i r d s i d e o f t h e t r i a n g l e a t r i g h ta n g l e s t o t h e r e f r a c t i n g s u r f a c e is, t h e r e f o r e , e q u a l t o ~ - I .N e w t o n re f er s t o t h e l in e ~ - I a s t h e m o t i o n g e n e r a t e d b yt h e r e f r a c t i n g f o rc e , a n d f r o m t h e g e n e r a l la w s o f f o rc e d e d u c e st h a t n 2 - I = F o r c e X C o n s t a n t a n d h e n c e t h a t n 2 - I= D e n s i t y X C o n s t a n t . F o r t h e c as e o f g r a z i n g i n c id e n c e

o n e m a y s a y t h a t ~/n-~ - I = t h e c o m p o n e n t o f t h e r e c i p r o c a lo f t h e s p e e d o f l i g h t t h a t i s a t r i g h t a n g l e s t o t h e d i r e c t i o n o fp r o p a g a t i o n .

N e w t o n s o r ig i n a l d a t a a r e p r e s e n t e d in Ta b l e I , w h i c h is ar e p r o d u c t i o n o f t h e o r ig in a l. C o l u m n I g i ve s t h e n a m e o f t h es u b s t a n c e ; c o l u m n 2 g i v e s t h e r e f r a c t i v e i n d e x ( n ) e x p r e s s e da s t h e r a t i o o f t h e s i n e s o f t h e a n g l e o f i n c i d e n c e a n d t h e a n g l eo f r e fr a c t io n ; c o l u m n 3 g iv e s n 2 - I ; c o l u m n 4 g iv e s th es p e ci fi c g r a v i t y r e l a t i v e t o w a t e r a s I ; a n d c o l u m n 5 g i v e s t h e

n u m e r i c a l v a l u e o f n 2 - I ) / d .N e w t o n w a s g r a t if ie d t o f i n d t h a t f o r s u c h a w i d e v a r i e t y o f

s u b s t a n c e s , i n c l u d i n g a ir , o r g a n i c l iq u i d s a n d m i n e r a l s , t h es p ec if ic r e f ra c t i o n v a r i e d o n l y f r o m a p p r o x i m a t e l y 0 .4 t o I . 4 .

L a p l a c e 2 d e r i v e d t h e s a m e e q u a t i o n f r o m t h e e m i s s i o nt h e o r y o f l i gh t , a n d a d d e d t h e c o n c e p t th a t f or a n y o n ec o m p o u n d th e c o n s t a n t s h o u l d b e i n d e p e n d e n t of e x te r na li n fl ue n c e s u c h a s t e m p e r a t u r e a n d p r e ss u re . L a p l a c e s

i n t e r p r e ta t i o n o f t h e N e w t o n e q u a t i o n h a d a p r o f o u n di n fl ue n c e o n t h e d e v e l o p m e n t o f re f r a c ti o n t h e o r y s in c e i t

x S i r I s a a c N e w t o n , O p t i c k s , B o o k I I , P a r t I I I , p a g e s 2 4 5 - 2 5 I , E d i t i o n o fI 7 1 7 .

* N e w t o n u s e d t h e l e n g t h o f t h e h y p o t e n u s e t o r e p r e s e n t t h e m o t i o n of t h er e f r a c te d r a y, t h e r e f o r e h i s u n i t o f m o t i o n i s p r o p o r t i o n a l t o t h e r e f r a c t iv ei n d e x , i . e . , i t i s p r o p o r t i o n a l t o t h e r e c i p r o c a l o f t h e a c t u a l s p e e d o f l i g h t .

-~ L a p l a c e , M f i c h a n i q u e c ~ l e s t e ( 4 ), lO , 2 3 7 ( I8 o 5 ) .

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66 S . S . K U RT Z , J R . , A N D A . L . WA R D . [J. F.I

d i r e c t e d a t t e n t i o n t o t h e c h a n g e o f r e f r a c t i v e i n d e x a n d

d e n s i t y o f a n y o n e c o m p o u n d w i t h c h a n g e i n t e m p e r a t u r e s a n dp r e s s u r e .TABLE I.

Ne wto n s Specific Refraction D ata Pu blished in I71 7 .i J

The Propo/nan l~sea~uare th e den- t~e re , -o f the Sines of or r)t~, tel fi ty an d fra tT iv,

.The r ef ra&ing B %dies.

A Pfeudo-Topaziu~,being a natural ,l~e, uc id , britt e ,l~aky Stone , o f ayellow Col:our.

Air.Glafs of A nt i nony.A Seleniris.61aff vulgar.Cryltal of the Ro ck.[fland Cry'ftal.qal Gemnm:.M u m e .3orax.Nzter.Dantzick Vitri61.

Otl of Vitriol.Rain Water.Faum Arab~ck.;piri t" of Wine well

re&ified.Camphire.Oil Olive.bin feed O il .~,pirit o f T urp en tine .fimbar.A Diamond .

Inc idence and w m cn IRefraH ion of toe,retra-yel low Li[,ht. HingJorce

of the Bo- Idy is prop r t l o n a t e

23 to 1 4 1 2 5

3 z o r to 3 , o o o o o o 6 z 5~7 to 9[ 5686~ to 4J, z¢3

z5 to 16 '4455 to 3 778

x to 1I 38835 to 24 ~z67zz to 151~ I5 II3z to z q , 345

2 001I03 to z95

~o to 7 'o4t5z9 to 3 9 6 784531 to 2i ~79

xoo to 73 '87~$3 t o z z5

~ I t l I I 5 I I

4 ° to 27 I"I948z s . t o x7 : I 6 z 6~4 tO 9 : '4z -

tOOto ,4r 4 049

fpecifick, Pozverg ra~ t ty o f t heot theBo- Body h

of i t sdenfi ty.

, J t ' i

9 7 9 -

5zo~ ]4 8 6 45 ~8¢a543e~54506 5 3 66477,~ 5 7 o6 7 1 670797~5 t6~Z4784g'8 J 7 4 ,

I O I ~ I

I z 5 5 rz z6o 7r z S I 913zzz~3654

I n t h e p e r io d I 8 o 5 to I 8 6 3 i t w a s s h o w n t h a t t h e c o n s t a n to f t h e N e w t o n s p e c i f i c r e f r a c t io n e q u a t i o n w a s n o t i n d e p e n d e n to f t e m p e r a t u r e , a, 4 M a n y a t t e m p t s w e r e m a d e t o m o d i f y th e

8 Arago a nd Petit ,Ann. Chim. Phys . ,I, I (I816).Gladstone and Dale,Philosophical Trans.,r53, 3~I, 820 (I863).

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N o v., I9 36 .] R E F R A C T I V I T Y I N T E R C E P T O F N E W T O N . 67

f o rm u l a . O n e of t h e m o r e i n t e r e s t i n g o f t h e se a t t e m p t s w a s

t h a t o f S c h r a u f , 5 w h o p r o p o s e d t h a t n b e r ep l a c ed b y t h e A o fC a u c h y ' s 8 f o r m u l a n = A + ~? + -t- e t c . T h e A i n t h i s

f o r m u l a i s t h e h y p o t h e t i c a l r e f r a c t i v e i n d e x f o r a l i n e o fi n f in i te w a v e l e n g t h . N o o n e s u c c e e d e d in a m o d i f i c a t i o n o ft h e N e w t o n f o r m u l a w h i c h w a s c a p a b l e o f g i v i n g a c o n s t a n tt h a t w a s i n d e p e n d e n t o f t e m p e r a t u r e , a n d t h e f o r m u l a as su c hw a s d i s c a rd e d * s o o n a f t e r t h e G l a d s t o n e - D a l e p a p e r w a s

p u b l i s h e d in 1 86 3 . I t is u n f o r t u n a t e t h a t in t h e s e a rc h f o r a ne q u a t i o n t h a t w o u l d b e i n d e p e n d e n t o f t e m p e r a t u r e , t h e v a lu eo f t h e N e w t o n e q u a t i o n f o r o t h e r p u r p o s e s w a s l o s t s i g h t o f.

G l a d s t o n e a n d D a l e , 4 in a d d i t i o n t o c o n f i r m i n g t h e d e -p e n d e n c e o f t h e N e w t o n e q u a t io n o n t e m p e r a t u r e , p r e s e n t e d as i m p l e e m p i r i c a l e q u a t i o n ,n - I ) / d = c o n s t a n t , a n d j u s ti f ie di t o n t h e g r o u n d s t h a t f o r s o m e 9 o l iq u i d s, t h e c o n s t a n t in t h i se q u a t i o n d e c r e a s e d l e s s r a p i d l y w i t h i n c r e a s i n g t e m p e r a t u r e

t h a n d i d t h e c o n s t a n t o f t h e N e w t o n e q u a t i o n . T h eG l a d s t o n e - D a l e e q u a t i o n u l t i m a t e l y a c h i e v e d w i d e s p r e a d u s e ,s e c o n d o n l y t o t h e L o r e n t z - L o r e n z e q u a t i o n . ( Vid e i n fr a .)B e t w e e n 1 86 3 a n d 1 88 o, L a n d o l t 8 d i d a g r e a t d e a l o f w o r kw i t h t h e G l a d s t o n e a n d D a le M o l e c u l a r R e f r a c t i o n= - m [ n - I )/ d] a n d e s t a b l i s h e d t h e f a c t t h a t m o l e c u l a r re f ra c -t i o n w a s r o u g h l y t h e s u m o f t h e a t o m i c r e f r a c t i o n s o f t h ec o n s t i t u e n t s .

I n 1 88 o t h e L o r e n t z - L o r e n z s p ec if ic r e f r a c ti o n e q u a t i o n ,[ ( n 2 - - I ) / ( n 2 - t-2 ] I / d = c o n s t a n t , w a s s i m u l t a n e o u s l y d e r i v e db y L o r e n t z , 9 w h o s t a r t e d w i t h M a x w e l l ' s e l e c tr o m a g n e t i c

5 S c h r a u f , Pogg. An n.,IX9, 461 ( I863) .6 A . L . C a u c h y , M e m o i r e s s u r l e D e s p e r s i o n d e l a l u m i b r e , p . 6 2, A . G .

C a l u e , P r a g u e ( 1 8 3 6 ) .* I n 1 88 8, K e t t l e r ~ m o d i f ie d t h e f o r m u l a t o (v - / ~ ) ( n~ - I ) = c o n s t a n t . I n

t h i s e q u a t i o n v i s t h e m o l e c u l a r v o l u m e a n d ~ is t h e l i m i t i n g v o l u m e o f t h e m o l e c u lea s i n Va n d e r W a a l ' s e q u a t i o n .

M a n y o f t h e o t h e r e q u a t i o n s m a y a l so b e c o n s i d e r e d a s m o d i f i c a t i o n s o f t h eN e w t o n f o rm u l a . T h u s t h e L o r e n t z - L o r e n z a n d E y k m a n f o r m u lm (v i de i n fr a )a r e t h e N e w t o n f o r m u l a d i v i d e d b y ( n ~ + 2 ) a n d ( n + 0 . 4) r e s p e c t iv e l y.

7 K e t t l e r , Wied. Ann.,33 , 356 ( I888) , and 35 , 662 (1888) .s F. E i s en l o h r, S p e c t r o c h e m i e O r g a n i s c h e r Ve r b i n d u n g e n , F. E n k e , S t u t t -

g a r t ( I 9 1 2 ) .9 H . A . L o r e n t z ,Wied. Ann., 9,6 4 ( I 8 8 o ) .

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568 S . S . K U R T Z , J R . , A N D A . L . W A R D . [ J . F . I .

theory of light, and Lorenz, 10 who star ted with the undul ato ry

theory of light. The specific and molecular refractions givenby this equation increase slightly with increasing tempera-tures. Therefore, in the period 188o to 1895 there wasintensive investigation of these and many other specific andmolecular refraction formulae s until Eykman 11 presented hisempirical equation [ n 2 - i) / n + o.4)]I/d = constant , whichrepresents the relationship between refractive index anddensity accurately for any one liquid at various temperatures.

Notwithstanding the fact that the Eykman equation wasshown to be less dependent on temperature than either theLorentz-Lorenz or the Gladstone and Dale equations, the twolatter equations have continued to dominate thought con-cerning the densi ty and refractive index of organic compounds.The Lorentz-Lorenz equation in particular has been widelyaccepted because of its theoretical derivation and its closeconnection with the theory of dielectrics. Comparison ofdetermined molecular or specific refractions with those calcu-lated from the atomic refraction values has been the standardmethod of using refractive index data as an aid in determin ingthe constitution of organic compounds.

An immense amount of work has been expended upon thederivation of the atomic constants to be used in calculatingLorentz-Lorenz molecular refractions. The best of the oldervalues were given by Brfihl, 12 but the values of Eisenlohr 13replaced those of Brfihl, and recent ly Hulst 14 has undertakenthe task of revising these constants.

For carbon, hydrogen, and double bonds, the atomicrefractions, according to these three authorities are given inthe accompanying table.

TA B L E I I .A t o m i c R e f r a ct io n s f o r L o r e n t z -L o r e n z F o r m u l a a n d t he D L i n e o f S o d i u m .

Carbon. Hydrogen. Double Bond.

B r f i h l . . . . . . . . . . . . . . . . . 2 .5 O l 1 .o 5 1 1 .7 o 7E i s e n l o h r . . . . . . . . . . . . . . 2 .4 1 8 I .I O O 1 .7 33H u l s t . . . . . . . . . . . . . . . . . . 2 .5 9 0 I .O 2 5 - -

10 L . L o r e n z , Wi e d . A n n . I x , 7 o 1 8 8 o ) .n j . F . E y k m a n , Rec. t ray. c ldm. I4 , 185 1895 ) .12 j . W . B r i i h l ,Z e i t . P h y s . C h e m . 7 , 14o 1891) •18 F. E i s e n l o h r ,Z e i t . P h y s . C h e m . 7 56 0 0 1 9 1 o ) .1 4 j. L . Va n d e r H u l s t ,Rec . t r ay. ch im. Pay. Bas5 4 , 5 1 8 1 9 3 5 ) .

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N o v. , 1 93 6. ] R E F R A C T I V I T Y I N T E R C E P T O F N E W TO N . 69

A s s u m i n g m o l e c u l a r r e f r a c t i v i t y t o b e a n a d d i t i v e p r o p -

e r t y, i t f o l l o w s t h a t i f t h e c o n s t i t u t i o n a n d d e n s i t y o f ac o m p o u n d b e k n o w n , t h e r e f r a c t i v e i n d e x c a n b e c a l c u l a t e d .C o n v e r s e ly, i f t h e r e f r a ct iv e i n d e x a n d c o n s t i t u t i o n b e k n o w n ,t h e d e n s i t y c a n b e c a lc u l a t e d .

I f m o l e c u l a r r e f r a c t i v i t y i s re a l ly a n a d d i t i v e p r o p e r t y i ts h o u l d c e r t a i n l y b e c o n s t a n t f o r a g r o u p o f i s o m e r i c h y d r o -ca rb ons . T he e xc e l l en t d a ta t h a t a re av a i l ab le la, 16, 17 fo r thei so m e r i c h e p t a n e s o f fe r a n e x c e l l e n t o p p o r t u n i t y f or d e m o n -

s t r a t i n g w h e t h e r m o l e c u l a r r e fr a c t io n i s c o n s t a n t f o r ar e l a t i v e ly s i m p l e c a s e s u c h a s a g ro u p o f s a t u r a t e d , n o n - c y c l i c ,l o w m o l e cu l a r w e i g h t is o m e r s . T h e d a t a a r e s h o w n i nTa b l e I I I

TABLE I I I .

Deviation ofI someric H eptanes rom A verage Specif ic Refract ion Cu rves

Compound.

2,~ d ime thy l pen t ane. . . .2,4 d ime thy l pen t ane. . . .2 me thyl hexane. . . . . . . .Norm a l hep t ane. . . . . . . . .3 me thyl hexane . . . . . . . .2,2,3 t r im e t h y l b u t a n e . .3,3 d i m e t h y l p e n t a n e . . .2,3 d i m e th y l p e n t a n e . . .3 e thy l pen t ane . . . . . . . .

Average . . . . . . . . . . .

d ~ .4

0.673;0.674.o.6783o.683~0.687(0.690(o.693co.6951o.698z

0.686(

20n ~ - ,

t.38221.38221.385cr.3878t.3887t.3894t.39Iit.392ct.3937

t.388e

Specific Refractions.

Lorent: Glad-and s tone

Lorenz andDale .

o.3457 o.567. ~0.3453 o.566~o.3453 0.56720.3449 0.567(0.3440 3.565~o,343I a.5642o,3429 3.56440.3426 a.S63g0.3423 3-5637

0.3440 3.865(

Deviat ion of ObservedRefract ive Index fromCurves I, II and III

in Fig. I.

LorentzNew- and

Lorenz.ton.C~ve (Curve III.)

• H .

1.3519 +0.0022 +0.00:3 +0.00031.35o3 j +0 .o oi 6 +0.o00 8 --o.ooo11.3528 +o.oo16 +o.ooli +0.0005x.3539 +o.ooli +o.oolo +o.ooo81.3515 o.oooo +o. oo oi +o.ooo 21.3484 J--o.oo12 --o.oo09 --o.ooo61.3491 --o.oo14 --o.ooo9 --o.ooo31.349o I--o .oo 18 --o.oo12 --0.00051.3493 --0.o022 --o .oo l 4 --o.ooo 4

1.35o7 o.oo15 o.oolo o.ooo4

Glad-s tone New-and ton.

Dale. (Curve

T h e m o l e c u l ar r e f r a c t iv i t y o f th e h e p t a n e s a c c o rd i n g t oE i s e n lo h r s c o n s t a n t s s h o u l d b e 3 4 . 5 2 6 ; a c c o rd i n g t o H u l s t sc o n s t a n t s , 3 4 . 5 3 ° . T h e a v e r a g e e x p e r i m e n t a l m o l e c u l a rr e fr a c ti o n = 3 4 .4 4 2 , w i t h a m a x i m u m o f 3 4 .6 I a n d m i n i m u mo f 3 4 .2 7 . T h e d i ff e re n c e ( o .3 4 ) b e t w e e n t h e m a x i m u m a n dm i n i m u m m o l e c u l a r re f r a ct i o n is a p p r o x i m a t e l y I.O p e r c e n t .

16 G. E d g a r , a n d G . C a l i n g a e r t , J . Am. Chem. Soc. , 5I ,I546 (1929) .16 C. P. S m y t h , a n d W. N . S t o o p s , J. Am. Chem. Soc.,50 , 1883 ( I928) .17 A. L . Ward , S . S . Kur tz , J r. , an d W. H . F u l w e i l e r , C h a p t e r o n D e n s i t y a n d

R e f r a c t i v e I n d e x in S c i e n c e o f P e t r o l e u m , O x f o r d U n i v e r s i t y P r e ss ,L o n d o n( i n p r e p a r a t i o n ) .

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7 ° S . S . KU RTZ JR. AND A. L. WARD. [J.F 1

a n d c o r r e s p o n d s t o 0 . 0 0 4 4 i n t e r m s o f r e f r a c t i v e i n d e x .

S i n c e t h e s e d e n s i t y a n d r e f r a c t i v e i n d e x d a t a s h o u l d b ea c c u r a t e t o I in t h e f o u r t h d e c i m a l p l a ce t h e d a t a s h o wd e f i n i te l y t h a t m o l e c u l a r r e f ra c t io n s a r e n o t s t r i c t l y a d d i t i v ef o r t h e s e s i m p l e c o m p o u n d s . . I n F i g . I t h e c u r v e s a r e g r a p h i cr e p r e s e n t a t i o n s o f t h e t h r e e s p e c i f i c r e f r a c t i v i t y e q u a t i o n s :L o r e n t z -L o r e n z G l a d s t o n e - D a l e a n d N e w t o n . I n e a c h c as et h e s p e c i f i c r e f r a c t i o n s w e r e c a l c u l a t e d f r o m t h e e x p e r i m e n t a ld a t a f o r e a c h o f t h e h e p t a n e is o m e rs . T h e a v e r a g e v a l u e s a r e

L 95

1.38 .

FIG I

_

0 . 6 7 O . 6 8 0 . 6 9

D e n s / t , v a t Z O ° E

0 Z0

Plot of refractive index versus density for the isomeric heptanes

s h o w n i n Ta b l e I I I . T h e c u r v e s w e r e d r a w n f r om t h e m e a ns p e ci fi c r e f r a c ti o n s f o r e a c h o f t h e t h r e e e q u a t i o n s . T h ep o i n t s a r e t h e e x p e r i m e n t a l d a t a 1~ w i t h d e n s i t i e s p l o t t e da g a i n s t r e f r a c t i v e i n d ic e s . I f t h e e q u a t i o n s r e p r e s e n t e d t h ec h a n g e i n d e n s i t y a n d r e f r a c t i v e i n d e x w i t h c h a n g e i n s t r u c -t u r e t h e p o i n t s w o u l d fa ll o n t h e c u r v e s . C u r v e I c o r r e s p o n d st o t h e a v e r a g e L o r e n t z - L o r e n z s p e c i f i c r e f r a c t i o n o f 0 . 3 4 4 0 .C u r v e I I c o r r e s p o n d s t o t h e a v e r a g e G l a d s t o n e - D a l e s p e c i f i cr e f r a c t io n 0 .5 6 56 . C u r v e I I I c o r r e s p o n d s t o th e a v e r a g eN e w t o n s p e c i f i c r e f r a c t i o n o f 1 . 3 5 o 7 .

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Nov. I936.] REFRACTIVITY INTERCEPT OF NEWTON. 571

I n o r d e r t o s i m p l i f y t h e f o ll o w i n g d i s c u s s io n o f t h e s l o p es

o f t h e c u r v e s i n F i g . I , t h e f o ll o w i n g s y m b o l s w i l l b e u s e d i na d d i t i o n t o c , d , m a n d n a l r e a d y d e f i n e d :

t = t e m p e r a t u r e ;c o n . = c o n s t a n t ;

c = c o n s t i t u t i o n ;va r. - - va r i ab le .

S i n c e b o t h t h e L o r e n t z a n d L o r e n z a n d G l a d s t o n e a n dD a l e s p e c i f i c r e f r a c t i o n s w e r e d e v e l o p e d t o g i v e c o n s t a n ts p ec if ic r e f r a c t io n a t v a r i o u s t e m p e r a t u r e s (t, v a r. ) f o r a n yp a r t i c u l a r c o m p o u n d ( c , c o n . ) , t h e s l o p e o f C u r v e I o r I I m a y

[ a n 0 ] ,b e r e p r e s e n t e d b y t h e s y m b o l s ~ I ts F o r t h e L o r e n t z -

= o .64 ; fo r t h eo re nz spec i f ic r e f r ac t ion , C ur ve I , ~ ,~

G l a d s t o n e a n d D a l e s p ec if ic r e f ra c t i o n , C u r v e l I ,

A n t i t ~ = o .5 7 f or t h e E y k m a n e q u a t i o n , w h i c h b e s t c o rr e-Ado t~

f a t e s t h e c h a n g e o f r e f r a c t i v e i n d e x a n d d e n s i t y w i t ht e m p e r a t u r e , b u t w h i c h w a s o m i t t e d f r o m F i g . I, th e s lo p e

= o .6 o . T h e e x p e r i m e n t a l d a t a i n F i g . I a r e f o r

v a r i o u s c o m p o u n d s c , va t . ) a t 2o ° C. (t, c on . ) . S in ceC u r v e I I I f o r t h e N e w t o n e q u a t i o n r e p r e s en t s t h e e x p e r i m e n t a ld a t a w e l l , o n e m a y w r i t e f o r t h i s c u r v e t h e s l o p e e q u a t i o n

c, = o .485 . S inc e fo r the he p tan es th e s lope ~ t,

= o . 6 o a n d t h e s l o p e A d t ] ~ = o ' 4 8 5 i t is c l e a r t h a t o n e a n d

t h e s a m e s p e ci fic r e f ra c t io n e q u a t i o n c a n n o t r e p r e s e n t b o t ht h e e f fe c t o f (I ) v a r i a t i o n i n t e m p e r a t u r e , a n d (2 ) v a r i a t i o n i nc o n s t i t u t i o n , o n t h e r e f r a c t i v e i n d e x a n d d e n s i t y o f t h eh e p t a n e s .

S i m i l a r l y, i t m a y b e s h o w n t h a t t h e s a m e g e n e r a l i z a t i o nh o l d s f o r h y d r o c a r b o n s o f h i g h e r m o l e c u l a r w e i g h t . T h u s , i tm a y b e d e d u c e d f ro m t h e sm a l l d e v i a t i o n s o f t h e N e w t o ns p e c i f i c r e f r a c t i o n f o r d i f f e r e n t g r o u p s o f i s o m e r s , a s s h o w n i nTa b l e I X , v i d e in f r a, t h a t t h e s l o p e ( o.4 85 ) o f t h is e q u a t i o nr e m a i n s p r a c t i c a l l y c o n s t a n t . I t h a s b e e n s h o w n e l s e w h e r e ~7

VOL 2 2 2 NO I33~ 4o

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5 7 2 S . S . K U RT Z J R . A N D A . L . W A R D . [J. F. I .

r A .c ]a l soh a t f o r a w i d e v a r i e t y of h y d r o c a r b o n s t h e s o p e [ ~ t,r e m a i n s p r a c t i ca l l y c o n s t a n t a t t h e s a m e v a l u e a s fo r h e p t a n e s ,i .e . , o .6o.

L a p l a c e a s s u m e d t h a t t h e f u n d a m e n t a l s p ec if ic r e fr a c ti o ne q u a t i o n w o u l d r e p r e s e n t t h e r e l a t i o n s h i p b e t w e e n r e f r a c t i v e

i n d e x a n d d e n s i t y w i t h c h a n g e i n t e m p e r a t u r e , ~ t,

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

a t o m i c r e f r a c t i o n s s u p e r i m p o s e d o n t h e o l d e r c o n c e p t o fs p e c i f i c r e f r a c t i o n t h e i d e a t h a t t h e f u n d a m e n t a l s p e c i f i cr e f r a c t i o n e q u a t i o n w o u l d a l s o r e p r e s e n t t h e r e l a t i o n s h i pb e t w e e n r e f r a c t iv e i n d e x a n d d e n s i t y w i t h c h a n g i n g s t ru c t u r e ,

a t l e a st f or c o m p o u n d s o f c lo s e l y r e l a t e d s t r u c t u r e ,~ t C '

s u c h a s, f o r e x a m p l e , s a t u r a t e d n o n - c y c li c h y d r o c a r b o n s .To o m u c h h a s b e e n e x p e c t e d o f t h e i d e a l s pe cific

r e f r a c t i o n e q u a t i o n . S i n c e s p e c if ic r e f r a c t i o n r e p r e s e n t s ar e l a ti o n s h i p b e t w e e n r e f ra c t iv e i n d e x a n d d e n s i t y i t s h o u l d n o tb e a s s u m e d t h a t a n y p a r t i c u l a r r e f r a c t i o n e q u a t i o n a p p l i e df o r a n y c o n d i t i o n s e x c e p t t h o s e f o r w h i c h i t i s d e r i v e d .

III . THE R EFRACTM TY INTERCEPT.

A p l o t o f r e f r a c t i v e i n d e x a g a i n s t d e n s i t y, F i g . 2 , f o r t h ew h o l e h o m o l o g o u s s e r i e s o f p a r a f f i n h y d r o c a r b o n s r e v e a l s t h e

f a c t t h a t a n e q u a t i o n s u c h a s n = o .5 2 0 × d e n s i t y + I.O 3 19m o r e n e a r l y r e p r e s e n t s t h e r e l a t i o n s h i p b e t w e e n r e f r a c t i v ei n d e x a n d d e n s i t y a t 2 o ° C . t h a n d o e s t h e N e w t o n e q u a t i o n .

T h u s i t isn t h i s e q u a t i o n t h e s l o p e o . 5 20 e q u a l s ~ . . . .. .

n e c e s s a r y t o c o n s i d e r t h e e ff ec ts o f t w o v a r i a b l e s o n r e f r a c t iv ei n d ex a n d d e n s i t y :( I) S t r u c t u r e o r C o n s t i t u t i o nc) , a m o n g a g r o u p o f i s o m e r s .

(2) M o l e c u l a r w e i g h t ( m ) i n a n y h o m o l o g o u s s er ie s .[A n , , m ] ~'S in ce t h e s lo pe / ~ Jc, -- a p p r o x im a t e l y 0 .48 5 a n d s in ce

= a p p r o x i m a t e l y o .5 2 o i t w a s d e c i d e d toh e s lo p e ~ . . . . .

w r i t e an a p p r o x i m a t e e m p i ri ca l l in e a r e q u a t i o n y = m x-P- b

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N o v. i9 3 6. ] R E F R A C T I V I T YINTER EPT O F N E W T O N

-...z

c7o e u ' . x ' ,g p U / , 9 / ~ 4 9 1 o . . , ,~ t , 9 , ~

5 7 3

I ~

~ 6

k

t~

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5 7 4 S . S , K U R T Z , J R . , A N D A . L . W A R D . [ J .F. I.

i n w h i c h y = n ; m = 0 . 5 0 ; x = d ; a n d b = a c o n s t a n t .

S u c h a n e q u a t i o n s e r v e s b o t h f o r g r o u p s o f i s o m e r s a n d f o rh o m o l o g o u s s er ie s o f h y d r o c a r b o n s . T h e c o n s t a n t b is t h eh y p o t h e t i c a l r e f r a c t iv e i n d e x a t z e r o d e n s i t y, i .e ., o n a g r a p ho f r e f ra c t iv e i n d e x p l o t t e d a g a i n s t d e n s i t y f o r a n h o m o l o g o u ss e ri es i t is t h e i n t e r c e p t o f t h e c u r v e w i t h t h e r e f r a c ti v e i n d e xo r d i n a t e if t h e a b c is s a b e g i n s w i t h z e ro d e n s i t y. T h e c o n s t a n tb is g i v e n b y t h e e q u a t i o nb n d / 2 a n d is n a m e d t h e

R e f r a c t i v i t y I n t e r c e p t . U n l e s s o t h e r w i s e s p ec if ie d i t is

u n d e r s t o o d t h a t in t h is e q u a t i o n n = n D a n d d = d 2 o- . T h e4

r e f r a c t i v i t y i n t e r c e p t is a c o n s t a n t c h a r a c t e r i s t i c o f e a c hh o m o l o g o u s s er ie s a s s h o w n i n Ta b l e s I V, V a n d X a n d F ig . 2.

TA B L E I V.

Approximate Values for Refractivity Intercepts of Hydrocarbons at 20 ° C. for D Line(Sodium).

Series.

P a r a f f i n s .S a t u r a t e d m o n o c y c l i c . . . . . .S a t u r a t e d p o l y c y c l i c .A r o m a t i c s .

M o n o o l e f i n e s .N o n c o n j u g a t e d d i o le f in e s . . . .C o n j u g a t e d d i o l e f m e s .

C y c l i c u n s a t u r a t e sO n e d o u b l e b o n d . . . . . . . . . IT w o c o n j u g a t e d d o u b le

b o n d s . • I

Refrac-No. of t iv i tyIndi- In ter-

v idua l cep tHydro- d

carbons . = n 2

[] 63 1 .04 628 1 1 . 0 3 9 6

• I 5 1 .02 854 9 1 . 0 6 2 9

79 1 .O521I 8 1 . O 6 0 227 1 . 0 8 1 9

5 5 I - O 4 6 0

8 I .O6 I 7

Devia t ion f romAverage X lO4.

Ari th-. . . . . . . . m e t ic M a x i - M a x i-m u m m u m

M ean P lus . M inus .4-.

1 4 3 5 5 1I 8 5 2 l O 83 3 4 6 8 92 0 [ 5 3 5 7

2 0 5 3 4 64 3 i 9 3 9 86 0 9 7 14 8

I

2 1 ] I I 0 I O I

4 2 i 8 0 5 3

ProbableError X lO4.

SingleMean . Ob-serva-

tion.

1 4 I22 .O 18

2 . 4 1 7

1 . 8 I 67 . 7 3 29 . 1 4 7

2 . 9 2 1

1 3 . 6 3 6

I t s h o u l d a g a i n b e e m p h a s i z e d t h a t t h e R e f r a c t i v i t y

I n t e r c e p t is i n t e n d e d t o g i v e th e s i m p l e s t p o s s ib l e r e l a t io n s h i pb e t w e e n r e f r a c ti v e i n d e x a n d d e n s i t y f o r h o m o l o g o u s s er ie so f h y d r o c a r b o n s a n d f o r s e ts o f h y d r o c a r b o n i s o m e r s, all a t ac o n s t a n t t e m p e r a t u r e . * I t s fi el d o f u s e f u l n e s s is, t h e r e f o r e ,

* T h e l in e a r r e la t io n o b t a i n e d o n p l o t t i n g r e f r a c t iv e i n d e x a g a i n s t d e n s i t y f o r'n o r m a l p a r a f f in s h a s b e e n k n o w n f o r a l o n g t i m e ( c. f. E n g l e r - H 6 f e r ,Das E r d 6 1 ,1 9 13 , Vo l. I , p . I I 2 ) , b u t t h e p r a c t i c a l v a l u e o f t h e r e l a t i o n h a s n o t b e e n r e a l i ze d .

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N o v . , I9 36 . ] R E F R A C T I V I T Y I N T E R C E P T O F N E W T O N . 575

TA B L E V.

M ost Probable Va lues for Re fractivity In terce pts of Hydrocarbons at 20 ° C. fort h

D L i n e S o d i u m ) .

Series.

P a r a f f in s . . . . . . . . . . . . . . . . . . . .

S a t u r a t e d m o n o c y c l i c . . . . . . . .A r o m a t i c s . . . . . . . . . . . . . . . . . .

M o n o o l ef in e s . . . . . . . . . . . . . . .N o n c o n j u g a t e d d i o le f in e s . . . .C o n j u g a t e d d i ol ef in e s . . . . . . . .

C y c l i c u n s a t u r a t e sO n e d o u b l e b o n d .Tw o c o n j u g a t e d " "c lo ui Jl e

b o n d s . . . . . . . . . . . . . . . .

No . of R~frac-Ind i - uv i ty

vidual I In ter- [Hydro- cep tc a r b o n s . / = n - - ~ .

I . O 4 6 I

I . O 4 0 0I . O 6 2 7

1 . 0 5 2 11 . % 9 21.0877

1 . 0 4 6 1

1 . 0 6 4 3

Devia t io~ f romAverage X lO4.

JArit l- [Maxi M axi-m e t l m u f f m u m

M~an P lus Minus .

I 2 I 2 4 2 6I I ] 2 9 2 9I 4 / 3 O 2 9

1 6 2 9 2 92 3 4 7 4 92 7 4 3 4 5

2 0 3 3 I 2 7/

ProbableError X Io ' .

SingleMean . Ob-

serva-tion.

1 .2 IO1 2 I 01 . 8 I I

1.5 125 . 1 I 95 . 9 2 3

1 8 13

7 - 5 I 7

d i ff er en t f ro m t h a t o f t h e E y k m a n e q u a t i o n w h i c h re p r es e n tst h e r e l a t i o n s h i p b e t w e e n r e f r a c t i v e i n d e x a n d d e n s i t y w i t hc h a n g e i n te m p e r a t u r e .

T h e r e is s o m e e v i d e n c e t h a t t h e c h a r a c t e r i st i c f r e q u e n c yo f v i b r a t i o n o f t h e e l e c t r o n s i n p a r a f f i n h y d r o c a r b o n s d e -c r e a se s w i t h i n c r e a s i n g m o l e c u l a r w e i g h t a n d t h a t i t is f o rt h i s r e a s o n t h a t t h e N e w t o n e q u a t i o n d o e s n o t a p p l y f o r aw h o l e h o m o l o g o u s s er ie s. T h e r e f r a c t i v i ty i n t e r c e p t m a yt h e r e f o r e b e c o n s i d e r e d a s a n e m p i r i c a l m o d i f ic a t i o n o f t h eN e w t o n e q u a t i o n w h i c h t a k e s a c c o u n t o f t h e d e c r e a s e i nf r e q u e n c y o f v i b r a t i o n o f t h e d i s p e rs i o n e l e c t r o n s w i t hi n c r e a s i n g m o l e c u l a r w e i g h t .

I V C H A N G E I N R E F R A C T IV I T Y I N T E R C E I ~ r W I T H C H A N G E I N T E M P E R A T U R E

A s s t a t e d a b o v e i n t h e c a s e o f p a r a ff in s t h e i n c r e a s e inr e f ra c t i v e in d e x w i t h d e c r e a s e in t e m p e r a t u r e is a p p r o x i m a t e l yo .6 o t i m e s t h e in c r e a s e i n d e n s i t y. F o r a f u r t h e r d i s c u ss i o ns ee W a r d K u r t z a n d F u l w e i l e r 17 b y w h o m i t w a s s h o w n t h a tt h i s r e l a t i o n s h i p h o l d s f o r t h e o t h e r h y d r o c a r b o n s e r i e s a sw e l l a s fo r pa ra ff ins .

A s w a s e m p h a s i z e d i n t h e p r e v i o u s d i sc u s s io n t h e d i ff er -

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5 7 6 S . S . K U R T Z J R . AN D A . L . WA R D . [J. F. I .

a n d L ~ J o f t h e c u r v e sn c e in t h e s lo p e s ~ J t

p r e c l u d e s t h e p o s s ib i l it y o f a n y o n e e q u a t i o n r e p r e s e n t i n gb o t h c u r v e s. T h e d if fe re n c e b e t w e e n 0 .6 0, t h e t e m p e r a t u r es l o p e , a n d 0 . 5 0 , t h e r e f r a c t i v i t y i n t e r c e p t s l o p e , m e a n s t h a tt h e i n t e r c e p t w i ll d e c r e a s e s l i g h t ly w i t h a n i n c re a s e in t e m p e r -a t u r e . T h i s d e c r e a s e is g i v e n b y t h e e q u a t i o n : A i n t e r c e p t= o . IA d e n s i t y. T h e o r d e r of m a g n i t u d e o f t h e c h a n g e isa b o u t 0 . o 0 o 6 t o o . o o o 8 p e r I o d e g r e e s C e n t i g r a d e c h a n g e i n

t e m p e r a t u r e . H o w e v e r , s in c e t h e t e m p e r a t u r e c o ef fic ie n tsf o r b o t h d e n s i t y a n d r e f r a c ti v e i n d e x h a v e b e e n e s t a b l i s h e d 17t h e r e is li tt le i n c o n v e n i e n c e in u s i n g t h e r e f r a c t i v i t y i n t e r c e p tw i t h d a t a p u b l i s h e d f or t e m p e r a t u r e s o t h e r t h a n 2 o ° C .

V R E F R A C T IV I T Y I N T E R C E P T O F P U R E I-IYDROCARBONS.

T h e f ir s t t e s t t o w h i c h a n y p ro p o s e d c o n s t a n t , w h e t h e ri t b e e m p i r i c a l o r t h e o r e t i c a l , m u s t s u b m i t i s t h e a c c u r a c y

w i t h w h i c h i t c o n f o r m s t o t h e e x p e r i m e n t a l d a t a . F o r ag r o u p o f p a ra f fi n s o f k n o w n h i g h p u r i t y, t h e r e f r a c t i v i t yi n t e r c e p t r e p r e s e n t s t h e d a t a w i t h s a t i s f a c t o r y a c c u r a c y.F o r e x a m p l e , t h e d a t a f o r a ll o f t h e h e p t a n e s g iv e a n a v e r a g ei n t e r c e p t c o n s t a n t o f 1 .0 45 0 4 - o . o o I o , m e a n d e v i a t i o n , 0 . 00 0 5.T h i s is, o f c o u rs e , n o p r o o f o f t h e c o n f o r m i t y to t h e d a t a o fo t h e r p a ra ff in s , t o s ay n o t h i n g o f th e c o n s t a n c y o f th e e q u a t i o nf o r h y d r o c a r b o n s o f o t h e r se rie s. S i n ce t h e e q u a t i o n i sa d m i t t e d l y a n a p p r o x i m a t i o n e v e n f or t h e p a r af fi n h y d r o -c a rb o n s , a c o m p r e h e n s i v e s u r v e y o f t h e a c c u r a c y a n d s c op eo f t h e e q u a t i o n b e c a m e i m p e r a t i v e . T h e r e f r a c t i v i t y i n te r -c e p t s o f a l a rg e n u m b e r o f h y d r o c a r b o n s w e re , t h e r ef o r e ,c a l c u l a t e d . S u c h a t e s t of a p r o p o s e d c o n s t a n t f o r h y d r o -c a r b o n s c a n n o w b e c a rr ie d o u t w i t h a t h o r o u g h n e s s w h i c hw a s e n t i r e l y o u t o f t h e q u e s t i o n w i t h t h e l i m i t e d a m o u n t o fd a t a a v a i l a b l e f o r h y d r o c a r b o n s w h e n t h e c l as si ca l r e f r a c t i v i t ye q u a t i o n s w e r e f o r m u l a t e d .

T h e d a t a f or h y d r o c a r b o n s w i t h w h i c h t h e r e f r a c ti v i tyi n t e r c e p t w a s c h e c k e d h a d b e e n s e l e c t e d f r o m t h e l i t e r a t u r ea s b e i n g t h e m o s t a c c u r a t e p u b l i s h e d v a l u e s f o r a ll o f t h ek n o w n m e m b e r s o f t h e c o m m o n h y d r o c a r b o n se rie s in c on -n e c t i o n w i t h a t a b u l a t i o n m a d e f o r a n o t h e r p u r p o s e . 17

I n c a l c u l a t i n g a c o n s t a n t f o r s u c h a la r g e n u m b e r o f

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Nov. I936.] REFRACTIVITY INTERCEPT OF NEWTON. 577

hydrocarbon s, the results become a test not merel y of the

validity of the constant but also of the accuracy of the data.Obviously with such a large mass of data, some of it is muchmore reliable tha n the rest. In the case of the commonhydrocarbons in which several different investigators havereported closely agreeing data, it is an easy matter to selectsound values. However, in the case of hyd rocar bon s forwhich one or more investigators have reported values thatdo not agree closely, the task of the compiler is much more

difficult. For hyd rocar bon s for which only one set of valueshas been published, there is, of course, no possibility ofselection. The values for 387 individual hydr oca rbons of 9series are shown in Table IV. Althou gh the deviations fromthe averages may appear excessive, actually the percentage ofthe total number of hydrocarbons showing wide deviationswas small. Considering the difficulties in the mere accura tedetermination of density and refractive index and the very

much greater difficulties in the synthesis and purification ofhydrocarbons, the agreement may be regarded as excellent.Nevertheless, it seemed desirable to study the results todeterm ine to what extent the deviations were due to unsounddata rather than to inherent deviations in the refractivityintercept. As a result of this study, the values for a nu mb erof hydrocarbons were eliminated and more probable averagevalues for the different series were established. Th e mos tprobable values are summarized in Table V and are showngraphi cally in Fig. 2. A discussion of the statistical and otherconsiderations which lead to the elimination of the rejecteddata follows.

P a r a f f i n s

Sixty-three different saturated non-cyclic hydrocarbonsgave an average refractivity intercept of I.O462, with a meandeviation of 4- o. oo i 4 . The probable error of the average

r o = o . 6 7 4 5 ~ l E ~ 2 / n n -I was o.oooI 4 and of an individualdetermi nation was o.ooi2. The m axi mum deviation waso.oo5I. On a statist ical basis, therefore, none of the valuesmay be discarded.

A study of the values showed one deviation greater than4 o, four great er th an 3o and fourte en grea ter than 2o. All of

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578 S . S . K U RT Z JR . A N D A . L . W A R D . [J. F. I .

t h e f o u r w i t h d e v i a t io n s g r e a t e r t h a n 3 ° w e r e d a t a p u b l i s h e d

b y o n e i n v e s t i g a t o r f o r h y d r o c a r b o n s f o r w h i c h n o o t h e rv a l u e s w e r e f o u n d i n t h e l i te r a t u r e . I t s e e m s r e a s o n a b l e t od i s c a r d t h e s e d a t a t h e r e f o r e . I f t h i s is d o n e t h e a v e r a g ev a l u e f o r 5 9 p a r a f f i n s i s I . O 4 6 I w i t h a m e a n d e v i a t i o n o f4 - o . o o i 2 . T h e p r o b a b l e e r r o r o f t h e a v e r a g e is o . oo o i2 a n do f a s in g le o b s e r v a t i o n is o .o oo 97 . T h e m a x i m u m d e v i a t i o nis 0 .0026 .

S a t u r a t e d M o n o c y c l ic s N a p h t h e n e s ) . .

T h e a v e r a g e r e f r a c t i v i ty i n t e r c e p t o f 8 I s a t u r a t e d m o n o -c y c li c s w a s I .O 3 96 w i t h a m e a n d e v i a t i o n o f 4 - o . o o i 8 . T h ep r o b a b l e e r r o rs o f t h e m e a n a n d o f a n i n d i v id u a l v a l u e w e re0 .0 00 20 a n d o . o o i 8 r e s p e c ti v e l y. T h e d e v i a t i o n s o f t h r e eh y d r o c a r b o n s w e r e g r e a t e r t h a n t h e s t a t i s t i c a l e x p e c t a t i o n .A l l t h r e e w e r e c y c l o p e n t a n e d e r i v a t i v e s f o r w h i c h o n l y o n ei n v e s t i g a t o r h a d r e p o r t e d v a l u e s . S i n ce d e n s i t y v a l u e s p u b -l i s h e d b y r e p u t a b l e i n v e s t i g a t o r s f o r c y c l o p e n t a n e i t s e l f v a r yin t h e se c o n d d e c i m a l p la ce i t m u s t b e c o n c l u d e d t h a t t h ed a t a f o r f iv e m e m b e r e d s e ri es a re i n a n u n s a t i s f a c t o r y s t a t e .

I f u n c o n f i r m e d v a l u e s f or th r e e o t h e r h y d r o c a r b o n s a r ee l i m i n a t e d a s b e i n g q u e s t i o n a b l e a l t h o u g h w i t h i n s t a t i s t i c a le x p e c t a t io n s t h e a v e r a g e f o r 7 4 s a t u r a t e d m o n o c y c l i c s isI .o 4 o o w i t h a m e a n d e v i a t i o n o f 4 - o . o o I I . T h e p r o b a b l ee r r o rs o f t h e m e a n a n d o f a n i n d i v i d u a l v a l u e a r e o .o o o i2 a n do . o o I o r e s p e c t i v e l y.

Satura ted Di - and Polycyc l ics .

T h e d a t a fo r t h es e h y d r o c a r b o n s ar e t o o m e a g e r to p e r m i tt h e e s t a b l i s h m e n t o f a s o u n d v a l u e . F o r t h r e e d i cy c li cs t h ea v e r a g e i s I.O 2 9 8 w i t h a m e a n d e v i a t i o n o f -4- o . o o i 4 . T h ev a l u e f o r t r i c y c li c s is p r o b a b l y a b o u t I .o 2 o o .

Oleflns.

B e c a u s e o f t h e g r e a t e r d i f f ic u l ty i n p r e p a r i n g p u r e u n -s a t u r a t e d h y d r o c a r b o n s t h a n s a t u r a t e d o n e s i t w a s t o b ee x p e c t e d t h a t t h e d e v i a t i o n s f r o m t h e a v e r a g e w o u l d b el a rg e r in t h e c a se o f t h e u n s a t u r a t e d h y d r o c a r b o n s . T h i sp r o v e d t o b e t h e c a s e a l t h o u g h t h e d e v i a t i o n s w e r e le ss t h a nm i g h t b e e x p e c t e d u n d e r t h e c i r c u m s t a n c e s .

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Nov. I936.] REFRACTIVITY INTERCEPT OF NEWT ON. 579

The average of 79 olefins was 1.o521 with a mean devia-

tion of 4- 0.0020. Th e probable errors of the aver age and ofan individual value were o.oools and o.oo16 respectively.The ma xi mu m deviation was 53. This is within statisticalexpectations.

Of the 79 hydroc arbons uns upp ort ed values for 4 showeddeviations of grea ter th an 4 ° and for I2 showed great er tha n30. Elim ina ting these the following values are arrived at:

N o . o fO l e f i n s .

7567

Av e r a g eR e f r a c -t i v i t y

n t e r c e p t .

1.o52o1.o521

M e a nD e v i a t i o n

ion

1816

M a x i m u m D e v i a t io nX Io 4

~ - . - .

37 3829 29

P r o b a b l e E r r o rX xo4.

I n d i v i d u a lM e a n . Va l u e .

1.6 141 . 5 I 2

U n s a t u r a t e d C y c l ic s w i t h O n e D o u b l e o n d i n t h eR i n g .

For 55 hydroc arbons the average was I.O46O with a meandeviation of 4-o.oo21 and probable errors of o.ooo29 ando.oo21 respectively for the mean and for a single value.Of the 55 6 showed devia tions gre ate r th an o.oo5o. Ofthese 6 5 were cyclop enten e derivatives. Elim inati ng thevalues for these six hydroc arbo ns leaves 49 with a re fra ctiv ityint erc ept of I.O461 a m ean d evia tion of o.ooi 5 and probab leerrors of o.ooo18 for the mean and o.oo13 for an individualvalue.

U n c o n j u g a t e d D i o l e f i n s .

Because of the known difficulties in preparing pure di-olefins it was expect ed tha t this series would show relat ivelywide deviations . This proved to be the case. It is parti cu-larly unfortun ate therefore th at the num ber of hydrocarbo nsavailable is so limited that the values for any constant of thischaracter cannot be established with the accuracy of thosediscussed above. Ninet een hydr oca rbon s were listed. Be-cause of the uncer taint ies of the positions of the double bondsin several of them these ma y include several duplications.Of the I9 one was elimina ted on statistical grounds. Thisleft 18 with an average intercept of I.O6O2 a mean deviationof o.oo43 and probable errors of o.ooo77 and 0.oo32 for the

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58 0 S . S . KURTZ JR. AND A. L . WARD. [J . F. I.

mean and an individual value respectively. Elimi natin g the

oth er four having t he widest deviations left 14 with an averageof I.O592 , a mean of 4- o.oo23 and probable e rrors of o.ooo51and o.oo19.

Conjuga ted Dioleflns.

The deviations are naturally worse in the case of thecon jug ated diolefins. Here, the individual deviations areve ry large. Th e average interce pt of 27 hydr ocarb ons wasI.O819, with a mean deviation of o.o060 and probable errorsof o.ooo91 and o.0o47. In at te mp ti ng to arrive at the mostprobable value based on the best data available, two coursesare open. Th e first is to eliminate the values showing thelargest plus and minus deviations. This gives for 15 hydro-carbons an average of 1.o856, a mean deviation of 4- o.oo33and probable errors of o.ooo68 and o.oo26.

In the case of this class of hydrocarbons, however, thecommo n procedure does not app ear to be justified. The

possibilities of contamination with either a monolefin or anunconju gated diolefin or both are very much greater than thepossibilities of contamination with anything which wouldgive a higher inter cept. Accordingly, it seems bet ter toelimi nate the lower values. This gives for 12 hyd roc arb onsan average intercept of I.O877, a mean deviation of 4- o.oo27and probable errors of o.o0o59 and o.oo23.

U n s a t u r a t e d C y c li c s Tw o C o n j u g a te d D o u b l e B o n d s .

Seven hydro carb ons with six carbon rings have an averageintercept of 1.o617, a mean deviation of 4-o.oo42 andprobable erro rs of o.oo138 and o.oo36. Two of the hydro-carbon s had low values. One was a me th yl hexadiene withdouble bonds in uncert ain positions. Although specific dis-persion was low for two conjugated double bonds, it was toohigh for a non-conjug ated hydro carbon. The oth er was

hexadiene I,3). Its inter cept is low enough to cast dou bt onthe pur ity of any sample for which dat a have been published.Eliminating cyclopentadiene and these two hyd rocarbonsleaves five hydrocarbons with an average intercept of I.O643,a mean deviation of 4- o.oo2o and probable errors of o.ooo75and o.oo17.

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Nov. 1936.] REFRACTIVITY INTERCEPT OF NEW TON . 581

A r o m a t i c s

F o r th i s s er ie s, 4 9 h y d r o c a r b o n s w e r e av a i la b l e . T h ea v e r a g e v a l u e w a s I.O 6 29 w i t h a m e a n d e v i a t i o n o f 4 - o .o o 2 o .A l t h o u g h t h e m e a n d e v i a t i o n w a s n o t e x c es siv e , th e r e w e r e an u m b e r o f u n s u p p o r t e d v a l u e s w h i c h s h o w e d r a t h e r w i d ed e v i a t i o n s . E l i m i n a t i n g t h e s e l ef t 3 9 h y d r o c a r b o n s w i t h a na v e r a g e i n t e r c e p t o f 1 .o 62 7, a m e a n d e v i a t i o n o f 4 - o . o o l 4a n d p r o b a b l e e r r o r s o f o . oo o i 8 a n d o . o o l I .

G e n e r a l C o m m e n t s

I t w il l h a v e b e e n n o t e d t h a t t h e d a t a e l i m i n a t e d , w i t h t h ee x c e p t i o n o f t h e d i o le f in s a n d c e r t a i n o f th e c y c l o p e n t a n ed e r i v a t i v e s , h a d n o a p p r e c i a b l e e f fe c t o n t h e a v e r a g e s .T h u s , t h e m a x i m u m c h a n g e , d u e t o e l im i n a t io n of d a t a , int h e a v e r a g e s f o r t h e p a r a f f i n s , o l e f i n s , c y c l i c u n s a t u r a t e s a n da r o m a t i c s w a s o . o o o 2 .

VL SUMMARY OF EFFECT OF UNSATURATION ON REFRACTIVITY INTERCEPT.

T h e e ff ec t o f i n t r o d u c i n g o n e d o u b l e b o n d i n to t h e m o l e c u leo f e i t h e r a n a c y c l i c o r a c y c l ic h y d r o c a r b o n is t o i n c r e a s e t h er e f r a c t i v i t y i n t e r c e p t b y a p p r o x i m a t e l y o .o o 6 . I n t h e c a se o ft h e a c y c l lc c o m p o u n d s a t l e a st , t h e i n t r o d u c t i o n o f a s e c o n d

n o n - c o n j u g a t e d ) d o u b l e b o n d h a s a v e r y s im i l ar e ff ec t. T h ee ff ec t o f c o n j u g a t i o n a p p e a r s t o b e m u c h m o r e p r o n o u n c e d int h e c as e o f a c y cl ic t h a n o f c y cl ic c o m p o u n d s . A l t h o u g h th eu n s a t i s f a c t o r y d a t a m a k e i t u n s a f e t o a c c e p t t h i s c o n c l u s i o nw i t h o u t f u r t h e r p r o o f , i t i s o f i n t e r e s t t h a t s p e c i f i c r e f r a c t i v ed i sp e r s i o n s h o w s a n a n a lo g o u s e ff ec t. T h e d a t a a r e s u m m a r -i ze d i n Ta b l e V I . T h e e f fe c t o f u n s a t u r a t i o n i n m i x e d t y p ec o m p o u n d s , s u c h a s s o m e o f t h e t e r p e n e s, i s m o r e c o m p l e xa n d w i l l n o t b e d i s c u s s e d h e r e .

Vii. R S F ~ C ~ V I T Y ~ N T E R C E P T S O F m G H M O L E C U L A R W S m H T C O M P O U N D S

T h e d a t a a v a i la b l e fo r p u r e c o m p o u n d s a re , fo r t h e m o s tp a r t , r e s tr i c t e d t o c o m p o u n d s of lo w m o l e c u l a r w e i g h t ;t h e r e fo r e , t h e a v e r a g e v a l u e s g i v e n in Ta b l e s I V a n d V a r eh e a v i l y w e i g h t e d in f a v o r o f lo w m o l e c u la r w e i g h t c o m p o u n d s .

T h e d a t a i n Ta b l e X s h o w t h a t f o r p a r a ff in s a n d o l ef in st h e r e i s l i t t l e s h i f t i n t h e v a l u e o f t h e r e f r a c t i v i t y i n t e r c e p tw i t h c h a n g e in m o l e c u l a r w e i g h t . To o b t a i n f u r t h e r in fo r-

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5 8 2 S . S . K U RT Z , J R . AND A. L . WAR D. [ J. F. I .

TABLE VI

E ff e c t o f U n s a t u r a t i o n o n R e f r a c t i v i t y I n t e r c e p t a n d o n S p e c i f i c R e f r a c t iv e D i s p e r s i o n

Type.

Saturated . . . . . .One double bond.Two double

bonds...Two eonjugate~l

bonds...

Saturated . . . . . .One double bondTwo double

bonds..Two conjugated

bonds.

Acyclic Hydrocarbons. Cyclic Hydrocarbons.

[ Refractivi tyIntercept.

I.o4611,o52I

1.0592

I.O877SpecificRefractiveDispersionng -- nC

dIo

I53187

216

354

Change X IO 4.

ForFor For [ TwoOne Two ' Conju-

Double Double gatedBond. Bonds. Doub le

' Bonds.

6o

I29

416

34

63

2oi

RefractivityIntercept.

I.O4OOI.o461

I.o643SpecificRefractiveDispersionng -- nC

dX 104

I54186

295

Change X lO 4.

ForFor For TwoOne Two Conju-

Double Double gatedBond. Bonds. Doubl(

Bonds.

61

243

32

I4I

* Insu ff i ci en t da t a to ju s t i fy an ave rage va lue .

mar ion r e l a t i ve t o t he r e f r ac t iv i t y i n t e r cep t s o f ve ry h ighmolecu lar we igh t compound s Tab le V I I was p repa red Th i s

TABLE VII.

Refract iv i ty Interce pts for H ydrocarbons Hav ing Very Large Molecules .

Compound.

H y d r o - r u b b e rH y d r o c y c l o r u b b e rC y cl o r u b b e r .

R u b b e r.

Pur i f i ed rubbe rSmoked shee t rubbe rS y n t h e t i c m e t h y l r u b b e r

Lit-era- ] Temp.

ture.

ts 16Is I61 9 16

i s 1 6

2 2

2 2

2 2

Density.

0.85850.9860.992

0.920

0.9237o.92170.9292

Refrac-tive

Indexn D •

1.47681.52641.5387

1 52221 52191 52081 525

RefractivityIntercept.

I6° C. 20 ° C.

1.O476 1.04741.O334 I.O332I.O427 I.O425

I

1.0622 I.O620

11.O6Ol1.06001.06O 4

lS H . S taud inge r, D ie Hoch M oleku la r enJul ius Spr inger, Ber l in , 1932.

ISH. L. Fisher, Chem. Rev. 7, 119 (193o).20 In t e rna t ion a l Cr i t i ca l Tab le s , McGra w-Hi l l

(1927).

Organ i schen Verb indungen ,

Co., Ne w York , Vol. II , 259

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N o v., 1936.] R E F R A C T I V I T Y I N T E R C E P T O F N E W T O N . 5 8 3

table shows that the refractivity intercepts of rubber and

related hydrocarbons having extremely long chain moleculesare reasonably well in line with the refractivity intercepts forcompounds in the gasoline boiling range. Hydrogenatedrubber corresponds to a paraffin hydrocyclo rubber corre-sponds to a saturated polycyclic compound cyclo rubbercorresponds to a cyclic unsatura ted compound and rubberitself to an unconjugated polyolefine. All of these hydro-carbons have molecules of such length as to attain colloidal

dimensions and colloidal properties is The agreement be-tween the refractivity intercepts of such extremely highmolecular weight and low molecular weight compounds isvery encouraging and demonstrates that for any liquid singletype hydrocarbon the average refractivity intercept may beused without serious error.

The recent publication of Mikeska 21 provides data on avariety of mixed type compounds containing aromatic or

naphthenic rings and long paraffin side chains. Par t of thesedata are summarized in Table VII I. The distinction betweenthe naphthene and aromatic ring compounds is quite cleareven though each ring has one or more long paraffinic sidechains which cause the properties of the compound to besimilar to the properties of a mixture of paraffinic and y l ihydrocarbons.

TA B L E V I I I .

Average Refractivity Intercepts for M ixe d Typ e Pur e Hydrocarbons of Hig h MolecularWeight According to Mikeska. 2t

Type of Compound.

O n e b e n z e n e ri n g w i t h s a t u r a t e d s id e c ha i n . . . . . . .N a p h t h a l e n e , d i p h e n y l o r 2 b e n z e n e r i ng s w i t h

s a t u ra t e d c h a i n s . . . . . . . . . . . . . . . . . . . . . . . . . . .S a t u r a t e d c y cl ic s I r i n g a n d s id e c h a in . . . . . . . . . .D e k a h y d r o - n a p h t h a l e n e o r d o d e k a h y d r o d i p h en -

y l w i t h s id e c h a in s . . . . . . . . . . . . . . . . . . . . . . . . .

No. ofCom

pounds.

5

12

4

Approx. IAverage

Formula.

C 4 4 H 8 2

C 29 H 4 3C 2 8 H 5 6

C 3 1 H 6 I

Intercept at25 ° C.

1.o533

1.o6851.o442

1.o442

VIII. COMPARISON OF DIFFER ENT REI~RACTMTY EQUATIONS APPLIED TO PUREHYDROCARBON DATA.

It has been shown that the refractivity intercept isreasonably constant in each homologous series for compounds

2 1 L . A . M i k e s k a ,Ind. Eng. Chem.a8 , p . 971 1936 ) .

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584 S . S . K U RT Z , J R . , A N D A . L . W A R D . [ J. F. I .

ha v in g a w ide r ange o f m o le c u l a r we ig h t s . I t is, t h e r e fo re ,

p e r t i n e n t t o d e t e r m i n e w h e t h e r a n y o f t h e s p e cif ic r e f ra c t io ne q u a t i o n s y i e l d c o n s t a n t s w h i c h a r e e q u a l l y a s s u i t a b l e a s ,o r m o r e s u it a b l e t h a n , t h e r e f r a c t i v i t y i n t e r c e p t f o r c h a r a c te r -i z i ng ho m ologo us s e ri es .

I n o r d e r t o c o m p a r e t h e d i f f er e n t e q u a t i o n s , Ta b l e s I Xand X w ere p r epa red . I n Ta b l e IX a ve ra g e s pec if ic r e fr ac-t i ons c a l c u l a t ed fo r @0 by t h e e qu a t i on s o f Lo r en t z -Lo re n z ,E y k m a n , G l a d s to n e a n d D a le , a n d N e w t o n , a n d b y th e

r e f r a c t i v it y i n t e r c e p t f o r m u l a h a v e b e e n t a b u l a t e d f o r 6 3p a ra ff in s a n d 5 o n a p h t h e n e s . I n Ta b l e X t h e r e is s h o w n t h ee f f e c t o f i n c r e a s i n g m o l e c u l a r w e i g h t o n t h e r e f r a c t i v i t yin t e r cep t an d t he fou r spec if ic r e f rac t ion s .

I f a t t e n t i o n b e c o nf in e d t o t h e p a ra ff in s i n Ta b l e s I X a n dX , i t w i ll b e s een t h a t f o r a g iven s e t o f i somer s, t he r e f r ac t i v i t yi n t e r c e p t a n d N e w t o n e q u a t i o n s s h ow t h e s m a l l e st d e vi a ti o n s.Fo r a l a rge d i f fe r ence i n m o le cu l a r we i gh t s , t h e r e f r a c t i v i t yi n t e r c e p t e q u a t i o n i s m u c h m o r e c o n s t a n t t h a n a n y o f t h eo lde r equ a t i ons . Th i s is bec au se t he sl o pe wa s ch os en a s a

[ A n t ] ='== a n d [ A nt ' m ] c*com prom ise be tw een t he s l op es fo r ~ c,. ~ , I_ ad , . . . .

F o r o le fin s, t h e s a m e t w o e q u a t i o n s s h o w t h e l e a st d e v i a -t i ons fo r l a rge chang es i n m o l ec u l a r w e ig h t a s sh own i nTa b l e X . T h e a d v a n t a g e o f t h e N e w t o n e q u a t io n o v e r t h er e f r a c t i v i t y i n t e r c e p t w o u l d b e e x p e c t e d t o b e c o m e l e s s i f

d a t a f o r m u c h h i g h e r m o l e c u l a r w e i g h t o le fi ns w e r e a v a il a b le .T h e d a t a o f L e b e d e w a n d K o b l i a n s k y 22 a r e o f i n t e r e s t i n t h i sc o n n e c t i o n , s i n c e t h e y p r o v i d e d a t a f o r p o l y m e r s o f i s o -b u t y l e n e c o n t a i n i n g f r o m 8 t o 28 c a rb o n a t o m s w h i c h s h o wn o t r e n d i n t h e r e f ra c t i v i t y i n t e rc e p t . T h e s e d a t a a r e g i v e ni n Ta b l e X I .

F o r th e s a t u r a t e d c y cl ic s a n d a r o m a t i c s ( Ta b l e X ) , t h ed i ff e re n c e i n t h e d e v i a t i o n s o f t h e d i f fe r e n t e q u a t i o n s is m u c hless than fo r pa ra ff ins and o le f ines , because the range o fm o lecu l a r w e igh t f o r t he cyc li cs is so sma l l . T h e G lads ton e -D a l e e q u a t i o n s h o w s t h e s m a l l e s t d e v i a t i o n f o r b o t h a r o m a t i c sa n d n a p h t h e n e s .

T h e d a t a p r e s e n t e d f or t h e cy c li c h o m o l o g o u s s e r i e sa r e l i m i t e d to c o m p o u n d s w i t h o n e r in g , h e n c e t h e i n c re a s e i n

22 S . W. L ebedew an d C. G . K obl ian sky,Ber. 63, Io3 an d I432 I93o) .

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Nov., ]936 .] REFRACTIVITY INTERCEPT OF NEWTON. 58 5

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Nov. I936.] R E F R A C T I V IT Y IN T E R C E P T O F N E W T O N .

TABLE XI .

Refractivity Intercepts for Polym ers o f Isobutylene.

587

Formula. 2 0 n~O Refractivityd 4 Intercept.

C 4 H s ) ~ . . . . . . . . . . .C 4 H s ) 3 . . . . . . . . . . .C 4 H 8 ) 4 . . . . . . . . . . .C , H 0 . . . . . . . . . . . .C , H s )C ,H~)~) . . . . . . . . . . .C ~ Hs ) ~ . . . . . . . . . . .

o.7195o .76ooo.7944o.8176o.81460.834o0.8455

1.41121.43o61.44821.46oi1.45771.46841.4739

1.O5151.o5o6I . o 5 I oI.O513I.O5O41.o514I .o512

molecular weight and density in these compounds is mainlyarrived at by adding side chains, which are essentially paraf-finic in nature. It is, therefore, not unreasonable that therefractivity intercepts of the naphthene and aromatics withlarge side chains should tend to shift toward the value forparaffins. This is also shown by the data of Mikeska? 1

In any comparison at constant temperature except fortwo pentanes) that has been made on hydrocarbon data, theLorentz-Lorenz equation has shown the widest deviation ofany of the five equations.

i x s p ~ c ~ i c F r£ T D S O F U S E F ~ N S S S O F C LA SSIC AL S Q U AT I O N S

Before continuing with the discussion of the refractivityintercept, it may be well to review the specific advantages ofthe Lorentz-Lorenz, Eykman, Gladstone and Dale, andNewton equations. It has been shown that the Newton equa-

[An, m] c,tion is the best of these equations for expressing e i t h e r [ ~

L t m C 1

or ~ jc,, ,~, and that the Lorentz-Lorenz equation is the least

valuable for either purpose. .Of the three commonly usedequations, however, there are other purposes for which theequations are used. Their relative values for two of these aresummarized as follows:

I) The Eykman equation is the most useful of theclassical equations for expressing the relationship betweenrefractive index and density with changing temperature

VOL. 222, N0. I 3 3 1 4 i

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5 8 8 S . S . K U R T Z J R . A N D A . L . W A R D . [ J . F . I .

2 ) T h e L o r e n t z - L o r e n z e q u a t i o n is t h e m o r e us e fu l o f t h e

c l a s s i c a l e q u a t i o n s f o r b r i n g i n g o u t t h e r e l a t i o n s h i p b e t w e e no p t i c a l a n d e l e c tr i c a l p r o p e r t i e s .3 ) T h e G l a d s t o n e a n d D a l e s p ec if ic r e f r a c ti o n a n d t h e

N e w t o n s p ec if ic r e f r a c t io n m a y b o t h b e u s e d t o c la s s if yn a p h t h a s r o u g h l y a c c o r d in g t o h y d r o c a r b o n t y p e . T h eG l a d s t o n e a n d D a l e s pe c if ic r e f r a c t io n i s m u c h b e t t e r f o r t h i sp u r p o s e t h a n t h e L o r e n t z - L o r e n z o r E y k m a n s pe cif ic r ef ra c -t i o n , b u t is n o t s o g o o d a s t h e r e f r a c t i v i t y i n t e r c e p t . 17

T h e r e a s o n s f o r I ) a n d 3 ) h a v e b e e n g i v e n a b o v e . Ad i s c u ss i o n o f t h e b a s i s f o r 2 ) w o u l d b e b e y o n d t h e s c o p e o f t h i sp a p e r.

X. PRACTICAL USE OF THE REFRACTIVITY INTERCEPT IN THE STUDY OF HYDRO -CARBONS AND HYDROCARBON MIXTURES.

T h e r e f r a c t i v i t y i n t e r c e p t h a s a w i d e r a n g e o f u s e f u l n e s sb e c a u s e i t p r o v i d e s a c o n s t a n t c h a r a c t e r i s t i c o f e a c h h o m o l o -g o u s s e r i e s o f h y d r o c a r b o n s , a c o n s t a n t w h i c h i s p r a c t i c a l l yi n d e p e n d e n t o f b o i l in g p o i n t o r m o l e c u l a r w e i g h t . T h i s p a p e ris p r i m a r i l y c o n c e r n e d w i t h t h e r e l at i o n o f t h e r e f r a c t iv i t yi n t e r c e p t t o s p ec if ic r e f r a c t io n a n d d i s p e rs i o n t h e o r y, t h e r e -f or e, t h e p r a c t i c a l u s e s o f t h i s c o n s t a n t w i ll b e t r e a t e d v e r ybr ie f ly.

a S e l e c t i o n of D a t a

I n c o m p i l in g t a b l e s o f d a t a o n t h e p r o p e r t i es o f p u r eh y d r o c a r b o n s i t i s n e c e s s a r y t o h a v e c r i t e r i a b y w h i c h t od i s t in g u i s h b e t w e e n r e li ab l e a n d u n r e l ia b l e d a t a . T h e d a t af o r t h e i s o m e r i c h e p t a n e s m a k e i t c l e ar t h a t o n e c a n n o td e p e n d e n t i re l y u p o n t h e c a l c u l a t e d m o l e c u l a r r e fr a c ti o n f o rt h i s p u r p o s e . C a l c u l a t i o n o f t h e r e f r a c t i v i t y i n t e r c e p t d o e sn o t b y i t s e l f p r o v e t h a t d a t a a r e a c c u r a t e , e v e n t h o u g h t h ei n t e r c e p t m a y c o i n ci d e w i t h t h e a v e r a g e v a l u e f o r t h e h o m o l o -g o u s s e ri es i n q u e s t i o n . H o w e v e r, w i d e d e v i a t i o n s in t h ei n t e r c e p t f r o m t h e a v e r a g e f o r t h e p a r t i c u l a r t y p e o f h y d r o -c a r b o n , n o r m a l l y i n d i c a t e e r r o r s o f s o m e k in d . I n p r a c t i ce ,t h e r e f r a c t i v i t y i n t e r c e p t h a s p r o v e n v e r y v a l u a b l e i n ca l li n ga t t e n t i o n t o : I ) e r r o r s i n t h e t r a n s c r i p t i o n o f d a t a , 2 ) i m -p r o p e r c o r r e c ti o n f or t e m p e r a t u r e , 3 ) u n c e r t a i n t y o n th e p a r to f t h e o r i g in a l a u t h o r c o n c e r n i n g t h e p u r i t y o f t h e c o m p o u n d ,4 ) u n s o u n d d a t a .

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N ov ., 1 93 6. ] R E F R A C T I V I T Y I N T E R C E P T O F N E W T O N . 589

b E v a l u a t i o n o f P h y s i c a l D a t a f o r C o m p o u n d s N o t I s o l a t e d o r S y n t h e s i z e d P r e v i o u s l y

I n c o n f ir m i n g t h e s t r u c t u r e o f a n e w h y d r o c a r b o n a n de s t a b l i s h i n g t h e p r o b a b i l i t y o f i ts p u r i t y t h e re f r a c t i v i t yi n t e r c e p t is v a l u a b l e p a r t i c u l a r l y i f t h e p r o p e r t ie s o f c o m -p o u n d s i s o m e r ic w i t h t h e n e w c o m p o u n d a r e a v a il a b le .

F o r s u c h p u r p o s e s i t m a y s o m e t i m e s b e ad v i s a b l e to u s e t h ea v e r a g e i n t e r c e p t f or t h e h y d r o c a r b o n i so m e r i c w i t h t h e o n e i nq u e s t io n r a t h e r t h a n t h e a v e r a g e f or t h e w h o l e s er ie s. T h i ss h o u l d b e d o n e o n l y i f t h e i n t e r c e p t s o f f iv e o r m o r e i s o m e r s

a r e a c c u r a t e l y k n o w n .c, Qua l i ta t ive Ana lys i s o fOrganic L iquids.

T h e r e f r a c t i v i t y i n t e r c e p t s o f t h e l o w e r a lc o h o ls m e r -c a p t a n s e t h e r s s u lf id e s k e t o n e s o rg a n i c h a l i d e s e t c . a r e i ng e n e r a l le ss t h a n I .o o o w h e r e a s h y d r o c a r b o n s w i t h t h ep o ss ib le e x c e p t io n o f s o m e h i g h m o l e c u l a r w e i g h t p o l y n u c l e a rn a p h t h e n e s a r e a b o v e I.O IO . T h e r e f o r e t h e r e f r a c t i v i t y

i n t e r c e p t p r o v i d e s a r e a d y m e a n s f o r d i s t i n g u i s h i n g b e t w e e nh y d r o c a r b o n s a n d c o m p o u n d s c o n t a i n i n g ap p r e c ia b l e p ro -p o r t i o n s o f o x y g e n s u l fu r o r h a l o g e n .

I n t h e c a se o f h y d r o c a r b o n m i x tu r e s t h e r e f ra c t i v i t yi n t e r c e p t m a y b e u s e d to d i s t i n g u i s h b e t w e e n s a t u r a t e d c y c li ca n d a r o m a t i c c o m p o u n d s b o t h o f w h i c h h a v e re l a t i v e ly h ig hd e n s i t y a n d re f ra c t iv e i nd e x. A s s h o w n b y W a r d K u r t z a n dF u l w e i l e r 17 a l a r g e n u m b e r o f n a t u r a l l y o c c u r r i n g n a p h t h a s o f

h i g h d e n s i t y h a v e low r e f r a c t i v i ty i n t e rc e p t s . O n e m a yt h er ef o re c o n c lu d e t h a t m o s t n a t u r a l n a p h t h a s w h i c h h a v e ah ig h d e n s i t y c o n t a in m u c h m o r e s a t u r a t e d c y cl ic t h a na r o m a t i c m a t e r i a l .

Tw o e x a m p l e s o f q u a l i t a t i v e a n a l y s i s f o l l o w :E x a m p l e N o I . A C a l i f o r n i a g a s o l i n e 23 y i e l d e d a n a r r o w

c u t h a v i n g t h e f o ll o w in g p r o p e r t ie s :

Bo i l ing po in t = 79 .2 ° C .D e n s i t y d l ° = o .7 3 78R e f r a c t i v e i n d e x n ~ = 1 .4 o 9 rR e f r a c t i v i t y i n t e r c e p t = I .o 4 o 2.

~3 j . B . Hi l l , L . M. H end erson , and S . W. F e r r i s ,Ind. Eng. Chem. i9, 1281927).

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59 0 S . S . KURTZ JR. AND A. L. WARD. [J. F. I.

This cut clearly owes its high density to saturated cyclic

compounds. All the cuts of this naphtha were either naph-thenic or paraffinic in quali ty.E x a m p l e N o 2 An aviation fuel yielded cuts of which

the following is typical in quali ty:

Boiling point = I85 ° C.,Density, d 240 . = o.8718 ,Refractive index, n ~ = 1.5o2o,

Refractivity intercept = I.o66I.This naphtha is distinctly aromatic in type.

d. Quantitative Analysis of Hydrocarbons

In the analysis of hydrocarbon mixtures physical prop-erties such as density, refractive index, specific refraction,aniline point, etc. have frequently been used to estimate theproportion of two constituent types, such as paraffins andnaphthenes, in the binary mixture remaining after the removalof aromatics and olefines. It is possible by means of therefractivity intercept to de termine graphically the proportionof three constituent types such as paraffins, naphthenes andaromatics in naturally occurring naphthas, or aromatics,noncyclic olefins and cyclic olefines in cracked naphthas. Themethod depends upon plotting refractivity intercept againstdensity for pure compounds, thus obtaining a physical

property triangle suitable for graphical analysis of theunknown three component mixture. Master graphs of thistype are prepared for each of 7 cuts of fixed boiling range. Adirect plot of refractive index against density gives a physicalproperty triangle which is too elongated for practical use.Dispersion plotted against density for such constituents alsoyields a physical property triangle of approximately theproper form, bu t the refractivity intercept-density triangle is

more convenient and more accurate.A complete description of a method for analyzing naphthawhich uses I) fractional distillation, 2) chemical trea tmentand 3) physical property triangles will be given by Kurtzand Headington3 ~

~4 S. S. Kurtz Jr. and C. E. Headington Paper to appear soon in Ind. Eng.Chem. or Ind. Eng. Chem. Anal. Ed.

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N ov ., I936 .] R E F R A C T I V I T Y I N T E R C E P T O F N E W T O N . 5 9 1

X I T H E E L E C T R O N I C I N T I ~ R P R E T A T I O N O F T H E R E F R A C T I V I T Y I N T E R C E P T

A n a p p r o x i m a t e e q u a t i o n n 2 - I =B / v o 2 - v2) w h i ch hasb e e n d i s c u s se d b y R i c h t m e y e r 25 a n d u s e d b y D r u d e a n d E r f le 26m a y b e us e d to e s t i m a t e t h e n u m b e r a n d f r e q u e n c y o f t h ev i b r a t i n g e l e c t r o n s i n r e f r a c t i n g s u b s t a n c e s . O n t h e b a s is o f ap r e l i m i n a r y i n v e s t i g a t i o n , i t a p p e a r s t h a t t h e d i ff e re n c e i n t h er e f r a c t i v i t y i n t e r c e p t s o f p a r a f f i n s a n d n a p h t h e n e s i s o w i n g t ot h e f a c t t h a t t h e r e a r e a p p r o x i m a t e l y I 3 .8 X I o 22 d i s p e rs i o ne l e c t r o n s p e r g r a m i n n a p h t h e n e s , a n d I4 .O t o I 4 .3 X I o 22

d i s p e r s io n e l e c t r o n s i n p a ra ff in s . T h e n u m b e r o f e l e c t r o n s p e rb o n d a p p e a r s t o b e a p p r o x i m a t e l y I .o 6 6 fo r s a t u r a t e d h y d r o -c a r b o n s , a n d t h e f r e q u e n c y o f v i b r a t i o n a p p e a r s t o b e e s-s e n t i al l y t h e s a m e f or a p a ra ff in a n d n a p h t h e n e o f t h e s a m ed e n s i t y. A c c o r d i n g t o t h i s p o i n t o f v i e w, t h e r e f r a c t i v i t yi n t e r c e p t s o f p ar af fi n s a n d n a p h t h e n e s a r e c l o s e ly r e l a t e d t ot h e i r c a r b o n a n d h y d r o g e n r a t i o s s i n c e t h e n u m b e r o f b o n d sp e r g r a m d e c r e a s e s a s t h e p r o p o r t i o n o f h y d r o g e n d e c r e a s e s .

I n t h e c a s e of o le fi ns a n d a r o m a t i c h y d r o c a r b o n s , b o t h t h en u m b e r a n d f r e q u e n c y o f t h e d i s p er si o n e le c t ro n s a re m u c hle ss t h a n i n s a t u r a t e d h y d r o c a r b o n s , b u t t h e d e n o m i n a t o r i nt h e a p p r o x i m a t e e q u a t i o n d e c r e a s e s m o r e r a p i d l y t h a n d o e st h e n u m e r a t o r a n d t h e r e f o r e t h e n e t e f f e c t i s a r e l a t i v e l y h i g hr e f r a c t i v e i n d e x f o r a g i v e n d e n s i t y i n t h e c a s e o f o l e f i n s a n da r o m a t i c s .

A s p o in te d ou t b y H o u s t o u n y t he N e w t o n eq u a t i o n m a yb e d e r i v e d a s a s p e c i a l c a s e o f t h e a b o v e a p p r o x i m a t e d i s -p e rs io n e q u a t i o n . C o n s i d e r a ti o n o f t h e N e w t o n e q u a t i o nf r o m a d i s p e r s i o n p o i n t o f v i e w m a k e s i t s e e m r e a s o n a b l e t oa c c o u n t f o r o b s e r v e d d e v i a t i o n s f ro m N e w t o n s s pe cificr e f r a c t i o n e q u a t i o n a s b e i n g c a u s e d b y s m a l l c h a n g e s i n t h ea p p a r e n t f r e q u e n c y o f t h e d i sp e rs io n e l e ct ro n s , p a r t i c u l a r l yw i t h c h a n g e s in t e m p e r a t u r e a n d m o l e c u l a r w e i g h t s.

T h e s e c o n d p a r t o f t h is p a p e r p r e s e n t i n g a m o r e d e t a i le ds t u d y o f t h is i n t e r p r e t a t i o n o f t h e r e f r a c t i v i t y in t e r c e p t a n d t h eN e w t o n e q u a t i o n w i l l b e p u b l i s h e d i n a n e a r l y i s s u e o f t h i sj o u r n a l .

2 5F. K . R i c h t m y e r , I n t r o d u c t i o n t o M o d e r n P h y si c s, M c G r a w - H i l l ,N e w Yo r k , I 9 28 , p p . x I I - I 2 I .

28 H . Er fle ,Zeits . f . phys ik. Chemie6 I , 3 9 9 - 4 2 I 0 9 o 8 ) .27 R . A . H o u s t o u n , Tr e a t i s e o n L i g h t , L o n g m a n s G r e e n & C o ., N e w Yo r k ,

I93 o , p . 429 •

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592 S .S. KURTZ, JR., AND A. L. WARD. [J. F. I.

SUMMARY

I. It is shown by a thorough statistical study of data forparaffin hydrocarbons that Newton's specific refraction equa-tion expresses the relationship between refractive index anddensi ty for sets of hydrocarbon isomers, whereas the equationsof Gladstone and Dale, Lorentz and Lorenz, and Eykman donot.

2. The fundamental reason for the failure of the Lorentz-Lorenz, Eykman, and Gladstone-Dale equations to express

the change of refractive index with density for hydrocarbonisomers is shown to be the difference in the slopes of therefractive index density curves which express the effect of(a) temperature and (b) constitution.

3. It is shown that the Ref rac tiv ity Intercept , definedas Refractivity intercept = n - d / 2 is a useful constant forclassifying hydrocarbons according to homologous series, andfor analyzing hydrocarbon mixtures.

4. A preliminary electronic interpretation of the re-fractivity intercept and the Newton specific refraction equationis presented.

A c k n o w l e d g m e n t . The authors wish to acknowledge theencouragement of Dr. T. G. Delbridge, of the AtlanticRefining Company, in connection with the publication of thiswork, and the assistance of Mr. P. F. Dougher ty in makingmany of the calculations summarized in Tables VIII and IX.