t m m a rm x a a cm v m ra u c s io s • B a^S 4% .80g0 ♦ « % 0 BIT ROBEW f». ICiKPJtlCKa i I i 'fh o a la a u ta it to d to th o fto u ltq r t f tiho O raduato Sdhool o f fctee l in lv o r a lty o f SftaryXand .in p a r t ia l f u l f i l lm e n t o f t& a ro q p *iro » a n t* f o r th e d o g ra* o f fto o to r o f JPhlloaoptiy l ®3 4 ’ CHEMISTRY LIBRARY UNIVERSITY OF MARYLAND UMI Number: DP70395 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI DP70395 Published by ProQuest LLC (2015). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code uest ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor. Ml 48106- 1346 i l l « i , ! SJABUB o? cow ans® fm m S l t k w la a l P a r t . . . . . . . . . . . . . . . . . . . . . . . A ,H iaox*etioaX U iso u sa lo n ................. .. 3 .Svthod itad A pparatus ............................... IS M & # * * ■ * * ♦ » * * %* # * # * * # * * * * * * * # # # • # X# T h & DutJA *♦**********♦**»♦••***•******* V f C a lc u la tio n mid S r r a M * • * « » • • • * « * » » • * • 2 5 II iii mi 11I I utitir * ^ ^ ^ ^ ^ ^ ^ J& &######. * ■# • # # « # # # # # 9 ##### .###*# • -$ •# w l B ib lio g r a p h y .......... .................. 3 8 wmjm sTm m m mi th s im m m m m flag% % *aiIgC> ♦ 3 % 0 F o r i&asay y e a rs an ajEporlm ant haa M m s e r r ie d mxt in t li# id ra n o e d P h ys io it! C hendstry o f th is school d e a lin g w ith tho h e a t o f h y d ra tio n o f tfao dona h y d ra te o f b o rax* B a ta to o la ©king ohorohy th o m o d y iw iio e a le u la t lo n e co u ld be .saade* By knowing tho trapor p re s s u re v a r ia t io n w ith te;& psr&ture o f the doom h y d ra te , th o n ecessary d a ta oou ld M o b ta in e d * F in d in g h u t one v a in # to Hie In te r n a t io n a l C r i t ic a l T ab le s f o r th is p re s s u re , th la work waa u n d ertaken * m m m m A is p a r* The d is s o c ia tio n presaw *# o f h y d ra te s was f i r s t rooognlaod aa a definite p h y s ic a l phonocasnon to the l a t t e r p a r t o f tho 1 9 th c e n tu ry * B e fo re lf£75 th e work dona was of l i t t l e v a lu e owing to th e m g n ® Id e a s co n cern in g th e n a tu re o f tho {Aisnsciiejaon* Between 1S7B and 1SII1 s e v e ra l independent In v e s tig a to rs e s ta b lis h e d th e fund tuaeatal f e e t t h a t a t a d e f in i t e to n ip e ra ttire a f ix t u r e o f two h y d ra te s la neoeeaary to produce a d e f in i t e p res su re o f w a te r vap o r* Press* th is t in e on tho work d m lo p t d r a p id ly * In v e s tig a to rs used to # vapor p res su re idea. f o r s u b s ta n tia tin g scsas to o ra o d ^ a s io la w s , f o r b m & d liy c o n tr o l, m d f o r th e c o n s tru e tlo n of* |&m m diagram s* B orax occurs r a th e r widely d is tr ib u te d o ver to # oarth to n a tu ra l waters, old late# bods, e tc * Th» early O reeks and Homans mmw® s e l l m equatstod with s o w o f its proportion and mood It to th s beat of t h e ir knowledge* In 18S f Payen C l) d is c o v e re d and proved th o e o & p e s ltlo n o f th s p e n t# h y d ra te o r o s ta h s d rs l b s ra ju A f te r th is t in s c o n s id e ra b le work was dons on d e te rad n to g w hether o th e r h y d ra te s wore t er&ed o r n o t* A t th s p re s e n t t in s th is s u b je c t o f t li# s e d a tin g h y d ra te s o f b o rax between th s p sn ta hyclrato and. th s anhydrous s a lt l a o n ly p a r t ia l ly s o lve d * Tim mmthodm used to m a w ia g d is s o c ia tio n pros auras may bo d iv id e d in to tht^ss c la s s e s f s t a t ic , dynon&c and In d ir e c t * w i l l be d iscu ssed b r ie f l y tm dsr those head ing s* STIOT0 1 * m m 'Tim s t a t ic method w as, o f co u rse* th e f i r s t used* to e earX y sq u ip n o n t c o n s is te d o n ly o f a b aro n ® te r tub# in to s h le h fe e sample waa p is s e d * to e d ep re ss io n o f to # column waa taken as to # d is s o c ia tio n .pressure* Befcray ( 2 ) , hesooeur ( 3 ) , Wiedemann ( 4 ) end fa re a u (& ) were aiaoug tho e a r ly tov© s t ig a to r# to use to la method* i*h# c h ie f e r r o r to th ese e a r ly e x p o rto e n ts to # th a t no a t t e s t co u ld be made to o lte tn & b o adaorbod i& d ooeludod a i r fro n tho opeoitaoxu £«sang tli© ouoeooofu l afcfcosapbo to o llm ln a to I M i d i f f lo u l t y aro rooordod tho w k o f Frow ato ( 6 ) aha dovolopod th o Frow@te Tonolaiofcor* » d m o d ific a tio n * by to d ro ao C7) # a o h o ttk y (d ) n,ml MmmXmm t®)« O tho r saothoda o f o t& tle dharaeb or h a w boon d o w lo p o d by ^ohaabon C lO )f B o lt© ( X I ) , and Fraaor and h o w lr a * (It)* All of thooo m adopbod moan® o f f i r a t b o ilin g o u t th o ay® bam and than a llo w in g a c o n fin in g l iq u id to ro ach o o i& ltb rlU H t w ith t t » w a te r vap or gonoratod by tho hyd rat© syitboRt 011 0110 o ld # w ith a im a m p res su re on tho o th e r a id e * D m ijx c Th® f i r s t dyassssie method ra e a d if fu s io n method developed by Umller and iSrabaeh (13)« In th la m ethod* tho ra t® a t mhloh w a te r eeo&ped from two Ic te n b lo a l f la s k s * on# o f w hich eenfc&taecl th e h y d ra to * « h ll© th e o th e r contained, pur# w a te r* b o th b itin g p la c e d is a d o o a te a to r* was ta k e n a# in d ic a tin g tho r e la t io n betw een th e two m p o r proa a w e s * 7mmmm C M } in 1097 in tro d u c e d th o a i r f lo w m ethod* T ill a e o n e la te o f p&aalzig a known volume o f d ry a i r th rough th o m ix tu re o f th o h y d ra te a and w eigh ing tho wmMmr absorbed by tho s i r * Then V apor p res su re » dp*** o f ggo absorbed 1 HT 10 x v e l* o f a i r T h is method ha# boon twougjht to a iitg h degree o f re fin e m e n t by B a x te r and L an sing (16), H ig h b erg e r (16)* and o th e rs * 'This method lias not; boon used on suits w hich a re kiom to approaeh e q u ilib r iu m slo ifX y* * I i i8 in a v e ry slow method* Johnafcon (1 ? ) in 1908 d ev ised th e ta o te n iiio o p o roothod* f i l l a e ® iIs b a o f tra p p in g a l iq u id in a b u lb * a llo w in g i t to b o i l f o r a tim e to remove g am s and v o la t i le Im p u r it ie s * and ®ntn p e rm ittin g th e tem p era tu re to f a l l u n t i l tb s px*e»sure to sash iM ® o f th e tra p p in g l iq u id i s th e mmm* the p res su re road is ia e d t& te ly give® th e vapor pressure at th e observed tex?sp#ratOT#* *fht® method e a s ily e lim in a te s gases end is ra p id * S m ith mmd ^ m s la a (1 0 )» a ii! Berbye mui T ijgve (1 9 ) have used th is method on p are liq u id s w ith HUOh TOO0OSS* XK111IIS01? 2M?K0»S Any in d lr e e t method do#® not measure t ® vapor p res su re d ir e c t ly * b u t b rin g s th e h y d ra te ay stem in to e q u ilib r iu m with & m h stiin o e of known vap o r p re s s u re * 'Ttm ■most comm* typo la to balsn ee th e system in a d e s ic c a to r ■with s u lfu r ic a o ld * By v a ry in g th e s o m e n tra ilo n o f th e s u lfu r ic m old , i t s vapor p re s s u re is v a r ie d * -h en e q u ilib r iu m is o b ta in e d , an tm oXysla of the s o ld will give th e vapor p re s s u re o f ths system * H n e ilt r met V a b a s h * and Taxsaann (1 4 ) and e th e rs have used th is method s u c c e s s fu lly * h in e b a rg e r (2 0 ) f i r s t suggested o b ta in in g e q u ilib r iu m by shaking the h y d ra te s with an o^seeas of a liquid in they a re insoluble, but in whidh water is somewhat s o lu b le * ru E* W ilso n (H I) and Hoyes and "Eeatbroofe (Hi) have used th is m e th o d *£ o n & ta d th a © o a d u o i i iw t r ! © n e th d d 0 f a s ia ly a lo * A V m S V ICAL 0130033X01! I f ©ooi© h y d ra te d s a lts ax*© msposod te th o ateoaphw© a tmm will mmmm to erasable and dotes*! orate* othor© will w m i n apparently onohangod, wMl® other© may ©von fora •atui»nt«d solutions* fh# first mid last, tr&asf ©naatiaas mm of in te r© a t la fch© pro ©out Foss&reh* Xu tho f i r s t ©as©* tho s a lt lo s s a i t s w a te r o f o r y a t a l l l - a a tlo n * In doing th is * th© lo s s dons n o t tali© p i no© a l l a t on©©* h u t g ra d u a lly * A© th o fcrtm afarm atlo ti proooo&s* © Ith a r a low o r h y d ra te o r tti© anhydrous s a l t Is form ed* cf l i la earns#© two h y d ra te s (o r on# h y d ra te and th© m h ydrous • a l t ) to b© p rsssx it* C o n s id e rin g now th© tra n s fo rm a tio n into th© s a tu ra te d M lu t to n * th© hydrate taha© on © u ff la la n t w ato r to onus© a p a rt o f I t to go in to s o lu tio n * L e f t f o r a lo n g e r tim e* th© on t i r o mass w i l l d is s o lv e . Bofm*© th l© happens* tfcor© ar© p rs a s n t a © a lt h y d ra te and a sa tu ra te d . d ilu t io n o f this h y d ra to * ^fhoae is a *a o t# r lo tle a o f h y d ra te d s a l to n r# dopondont upon th e ir vapor p rM s iu ro * D i l la r d d ib b a (2 3 ) in 1878 g&vo to M i developm ent o f th# Fima# Kule« -This baa boon escpreifaed m t iw m t lo & lly by f t P a C * 2 where F «§ n w ^ e f o f phases preaenb F «* degrees o f freedom 0 • n u iis ir o f e opponent* Xb the light o f this e q u a tio n , l o t uo ©tea!?!® the f t r a t system o f h y d ra te d s a l to Jmmt d escrib ed # *fhe %immm® p rea o n t e o n e la t o f tho to o h y d ra te o and th o v a p o r, m aking $ • Sfoo ©o*3peti#rit-s a ra th o anhydrous s a lt .a n d w a te r* m akin g . 2 * S o b o tltu tin g th oao m in ts in to tho above we o b ta in en s o lv in g fo r F F ** B 4* H *» 3- F « X 'fh le means th e re lo o n ly on# lmlmpmr\i%mn% v a r ia b le # I f tho tem p e ra tu re is v a rie d a r b i t r a r i l y , a l l o th e r v a r ia b le s * !^#sr»f etc.* will vary de^ndemtly^ thu® tho vapor p ro e in ire o f m hjdrmtm system ia a fu a o tio n o f Mi# toxsporaturo* fh e use o f leot&kerm al d e h y d ra tio n la a v e ry e f fe c t iv e tool to e s ta b lis h in g wMeh liy d r iite s ar# in iH gulH hrliaau t^fsen a h y d ra te is d eh yd ra ted e v e r so aX i^afcly* ttfae e q u ilib r iu m lo e s ta b lis h e d beeauM a seeond s o lid plims# is a t onee fa m e d * 4b long &a thoao two phases a re p re s e n t anti tho tem p e ra tu re rem ains c o n s ta n t, tho p ressu re w i l l rem ain c o n s ta n t* I f ee p lo t t?ie m o u n t o f e a te r lo s t from a Itro m w e ig h t o f a h y d ra te as tho abaciaaa and the p ressu re as the ©rdiimte, ie*o should g e t ii a e r ie * o f hzx*l&&ntkX l in e s showing e o n e tim t p re s s u re rnpsu*ate4 by a t t f k i o f v e r t le & i l i i » i , eaofc p ressu re lin o baling l& if ? th an I t s predooeoM P# 3?he drops m a n th a t th e la s t tra c e o f to e h ig h * * h y d ra te h&9 &to«* appeared and- th a t a now system !ms been fo m e d # % ta w in g tho m o u n t and which h y d ra te is p r v m t a t to# start* it i s s im ple to e a le m la te to # e a s t in g h y d ra te s o f any s a l t * C o n sid er now tho d e r iv a t io n o f too V*rof fc H o ff ta o e h e r e q u a tio n upon w h ito asm w r y in te r a c t in g e ttleu l& ~ tloa* dopwnd (84).* It has 'been shown tout f m m m * p m C D By di f feres* t i sit lug t h la equation, w ith ra a p o o t to v e l w at co n s ta n t tem p era tu re wo o b ta in f o r any ia o tfa e ra a l proceae - f - T ( i $ r ~ ( B h < ■ » I f wo d if f e r e n t ia t e uguim w ith re a p e e t to to j^poratur© keep ing th e w lw a c o n s ta n t* we o b ta in 3s \ /V)2- " ( t r b h h ? ) " -m$9 a ln os the TOlum is c o n s ta n t - j u > t- i 5 -_ ( L ^ d T . { 4 j w hich on re a rra n g in g g l w i A ± - ^ h - i - h ~ 7 Ife omi bo shown a ls o th a t / ' JT \ (? ) C U . .•> C C ' S T - ^ whioli on difforont latlng with roapoot to T and V g i w § _ 2 ± £ . =» / v - ^ ( 8 )o T O v Vb\sJT 2ha» b y a tib a titu tln G a q u a tio n s 6 and B in ( 3 ) w© o b ta in * ( & ) , - 131 la ra a p o e t to tho prooeaa of v o p a rta a tlo n ., th « proaauro p is independent o f tho ? o l w * A la o t w# may rop lac© th© iaftoifeoaiaal th# a a p ra a a io n ~j~- w hioh rafox*© to ©a© mol o f tli# ©abab&no© In q u e s tio n * H«noo# fo r th© m p o r ia a tio n o f any aub ata& M wo &<$?© th© r e la t io n - * 4 ° , 3 -< ^ J L ( 1 0 )dt 7~~ is 31b m th© prooaaa la roY«r© lhXo / v r / “/ S - /'' (IX) .i'a b a ti fcufcliag 11 in 10 wa t-,s£ (1 3 ) b u t / I V ^ . K - - ”7 (1 3 ) Tho LioXal vaXun© of a gaa l a w r y la rg o In oom parlaon to th a s io la l 'm lm m o f I t a l iq u id * and th a ro fo r© m y h# d tarag u rd o d w ith o u t o aualng any ap p ro o lah l© arroa*« Equation (12) no® b##*t©» ■ '5 ^ r 7 ~ K V b u t p y * E T C M ) V ** 312/p ( M ) m 0 m illm m f o r p roaauros o f lo s s th an a m a t^ a ^ io r s {t3m pro&suroa to thin rooo&roti w#r# aaroun& X/ 7 th of on utm&np&mrm and loss) praotioally all g&sos stony Boyl##® haw g a its e to fi# ly # mqn&tttm C ia ) mmy too snbstltotsfcsd In e q u a tio n (1 4 ) f o r % w ith o u t d e s tro y in g th s v a l id i t y o f th # squat tl« m * s# o b ta in c iJ f' ( i r r - If now wo @«i dstevtatas Mio v a r ia t io n of tho irnpor prosssm*# w ith tsnspwrafenrs* wo h a w an e q u a tio n toy tmmm s f A ls h we oah e a le a la ts ^ f i o ver a p « ip o f t^ap o ra tu .rio# Solving e q u a tio n (1 7 ) fo r we o b ta in . r " c ia> th o team activity has been defined by Beitis and B a n d a li WA m E f t o % 4* O4 | 1 9 ) F ro n th is we eon o b ta in th # ehanip o f f r # # m m r ^ to »-ptos trm a a s ta ts afcere A has as a c t iv i t y o f a to a s ta te aher© a has an a c t iv i t y o f a 1 % th # e q u a tio n ^ P A » 5® to n 'A ( 2 0 ) C on sider any re o o llo n i l ■# M i a eC# 4* cUB C$1) In wSiieh a l l wutbs to n e s * a re la a s ta te ouoh th a t t h e ir a c t iv i t y is a# Than m m t o % Cm ) F j0 a RT I n itg ( $ $ ) - 10 a n t i g o f o r t h . T h e n & j L <24) 4 4 C o n sid er th e mmrn re s e tto m m ® u rrtn g in a s ta te m h th a t a l l su b stem es h a w an a e t lv t t y o f a *# ~*han, s i m i l a r l y ** # . «lt M % 4 <*»> i’he change in fro# enargsr f«r the reaction tracing place at two different activities will th en bo - ^ F „ * m I® I n ag og tiil wn"..,. IK M«r (1WW> «» I f J . ’ XT'*. M :!* ^ | ■ w ® - m w #nr* awn fjfc m m Ik -iL-.- Ef In iif? ml 4 4 tS T v Bow I f wo c o n s id e r the re a c tio n am c a r r ie d smt in th e f i r s t s tags ’f i t i an a c t iv i t y o f a as ttae re fe re n c e p o in t* o r* us %te say a l l substances a rc in th o ir s tan d ard s ta te * th e ir a c t iv i t ie s will bo n m ity and carnation (2 6 ) w i l l tm ® m m ^ < a 7 ) L o t ms no© lo o k a t a c o n c re te exam ple* the re a c tio n is? o lf© c! in t i i is re s e a rc h * I t la Ha8 B4(> 7 « ia % 0 (g ) • ♦ GHg0(g)- (SO) In th is e q u a tio n th e tw o h y d ra te s a re s o lid s and fir# th e re fo r® In t h e ir s ta n d a rd s ta te s * t h e ir n a t iv i t ie s b e in g u n ity * F o r th is re a c tio n * e q u a tio n (H7> w i l l reduce to & ? » • IK? to a£fg0 (2 9 ) & n m 8 iftf t f•rf I.p *rt*0 0& s si &m<6 s ©* %«4p*$ osO %**« ¥ I f* ft* <3 a g S I 8 430 © s 8 r’> f l If> © © mmm H 43€ 43 £ s e* o$4 ©?ES © In.43 m % $«*© ©© I14 «r§43 t*€ & W «i E m % 1 ©«rf43 g ©44 if # «r$ *<*«?43 I I£ m 3o *«4* * i E S S© 1 4« f0 w S g •0 5 3 5 g0 © I' ! !*H 43 % 43 S itf S5-N d©©vf43 I & U 43 fit fc© <** * ©43 S If-1 *» ****43 H # Jf43 ♦*f*n a*f4©#4* f t© I *©n © s. $40 ?© fe<1 fcw o ila po rt at tt i\ w m tt 0M 0 £>U an d AF £o x* tte g re ac ti on * Xx io vl ng th en # tw # {j o& at l& lg a £fc i© po a# £b X# fc o £ It©©* ^* -J* *s*J30 fc» 4»0©©*,#fim43 * ■'* © £ StS 3©4 mt*A SI <1 5 S,
  • 43 ,0If 43© *443 ©$4 © f i % if I& 0 43£"f %4o © *d I I # • lU «* mi .mu h rm m m s F o r tho work at hand m d f iiir a d a r m ig® of tem p e ra tu re o f from 3 5 % to obout 80°C * Provtcm e work fey H tg h b erg er ( 1 6 ) #0 * r r lo d o a t in th is la b o ra to ry # had dem onstrated th a t th o a i r flo w mfcbod was n o t s a t is fa c to r y fo r tem p era tu res o f 5 0 ^ and a to v o * !2?horoforof a n o th e r method im d to bo o b ta in e d * 4 saetiod th a t warn ra p id # a llo w e d f o r tho e lim in a tio n o f absorbed a ir # and mm g iv in g p res su re re a d in g a good to a t least one to n th o f a E i i l l im t o r o ve r th o range waa d o a lre d * A fte r se@roh«* lag the literates# tte leotenlMGpe raethod •on#*! by &alth and M enalee C IS ) mmzmd to f i t mw purpose# Tho smtbyod mu e a rn e d o a t by th ese wmm In v o lv e d a c o n s ta n t p ressu re and a v a r ia b le te m p e ra tu re * I t was co n s id e re d b e t te r fo r th is problem to m a in ta in a eonabanfc tesapemfeure and o p e ra te fey v a ry in g th # p re a e u re * & ith th is in v ie w tho ap p ara tu s waa n t up t i mntmn d ii^puem fcl d a l ly in th® aeeonpsnylng s k e tc h - F ig # I# Tho g la ss p a r ts o f th o ap p aratu s were made of pyreau Bulbs F and 0 war# about 25 m * In dia# In to 0 was s e a le d a c a p il la r y tu be o f 1 zm* bore# B e fo re s e a lin g th is In # a l in o was otohod around it n e a r th e m iddle# B u lb H was need aa a tra p to p re v e n t fcho c o n fin in g l iq u id in 0 from b e in g drawn book in to th e aam ple* widLdh was co n ta in e d in b u lb I* Bulb F served &a a tra p to p re v e n t condensed w a te r vap o r from flo w in g batik In to tho rrG /. /SO TEN /SC O PE OPEN TO PUMP Q D . no f X o K J M r \ N Sc* -1 /C R,WHL J - /5 -3 4 oo st fln ln g llf tiM gh m gl ftg it® w in s# # Vh oo o n l# I I .*■•« S3 #SIA E 8*H g4> «*** 21 0*SI ft I I «m £ © 4» «0 0 5 .«•? 4* S 0 0 0 £ «g # & 2 3 1 % «*# >0 0 s# *g a 30M..*3 •*sHf 1%H © «HS s#4 V* <0 S $ 4* g0<00 £• © I * v»0 &(89 I Suft 30 0 Pt»i 1«s4 0* o 0 I f*j> *’0 1 # 80H *010 14 1? >»;4 <§?> «■*«e* w« 43d 30 00 5-0** ©s* I r** H 0 5 1 0 J> 43 xsm43 00r: 3u p® r t>0 aa lt l« li^ ia y to th ® 11 0 vo lt p® w at tp pl y, ** 14 *» ethos* ta a eosmoetod th rough a v a r ia b le rh e o s ta t d X re e tly to tho power l in e * t h M latter one was need its a eo atin u m u i h e a te r keep in g tli© te iip e ra tw e a few degrees below th e d e s ire d p a in t* ISi© Im i l tem p era tu re was re a d by o f a e a llb ra b e d 5 j m t l a a t^ 0TO»eoapX0 # -sad# fro m M ? @ r l la r i i s Ho* t 4 o a t te n covered w ire la b e le d Id o a l and Corset* ;2Iie p o te n t ia l woo rood ©in a le e d s and K o rth rtip etedoafc double rang© pe te n tto m fc e r• F o r h ig h e r tem p era tu res th an about &0°C the b a th was se ve re d w ith a la y e r o f xinXtect p a r a f f in to d serease tho h o o t le s s e e by e v a p o ra tio n * *fho ao th o d t3»od In m aking tho deteriid im tsions wan m fe llo w s t In to b u lb 0 was p lseed d lh u ty l r t ith a la te tan tlX the e s p ll la r y r is e ©uinei-ded w ith th o e to h sd lin o 011 th e e a p ll la r y * ib is a e th e d o f f i l l i n g In s u re d a te a s p b o rie p res su re b o th on tho c a p il la r y and on tho body o f tho l iq u id w iiioh in s u re d p re s s u re e < g u tlib rlis s when tho l iq u id wais In t e r a d ju s te d to th is s m e m ark* T> lb u ty l phbim lebe was ehosen as a sonfln laag l iq u id baeaass of its low speeift© g r a v ity (a b o u t 1*01 J and beeanse of its very low vapor pressure* 4b room toiaperotur© it® vapor proao*aro i* le s s then Shut o f mmtmxiPf* I t s r a t# of in ereaee . l a a X lttX o :3©?-e tlism th a t o f a o t w y # 'fhe e x te n s io n tu b# was then se a le d o f f * rfJ*e bmlb was than im asraed in witter* with p ro v is io n for ail w f a s e a o f th o ^ iith a la te to 'be a t a tm a p fc e rl© p re s s u re , a t S00€ * Stse feenperatore wma th an ra is e d to th o h u llin g p o in t o f w a te r* $hs xsenlaous was observed w ith a e a th e to a s te r to- find, ant if any change o eeu rred in th o r e la t io n of tho m 3,5 « laoniseus to th o etohsd l in e on th s asipilX m * j on ahanggo o f te a p o ra tu ro * "Hm c o n s tru c tIo n o f tho ap p ara tu s wins suah th a t tit© i»nissem§i alw ays o o in a td a d w ith U%m « t o # 4 l in o o ver th o tem peratu re rang® et^X oyed* S o j^ doea sad p e tite h y d ra te s o f bowwt ( I t was in t e r found * *fc tho p o a t i h is n o t noe&od) were ipround t r o t t e r and pXaoed in 'bulb 1 d o li was th an soalsd in p irn s * vvith th o b a th tem p era tu re a d ju s te d and th o b u lb s in th a ra a l e q u ilib r iu m w ith tb s b a th , tho e n t ir e a c u te s was s v w u a te d u n t i l * w ith th o pu^p tu rn e d o f f * n ®m%<mmm stream o f bubble© flo w e d o a t o f tho e a p il la r y in 0 * t o is a llo w e d m il o f tho s i r to be washed o a t o f b u lb s X and H* A f te r some. tim e m p®.rImps an h o a r oi*4, * o f b o ilin g o u t* a i r was a * ia it te d to te th® t h r o a t B #C*t u w ith 0 o lo ss d * If too rntoh a i r was a d m itte d * 0 was op#n#d and a l i t t l e drawn o u t, J* hatring boon r^ o v io u s ly o o s p lo te ly t w i M t i d * In th is ta&wwx* tho p res su re to K was a d ju s te d .so th a t th s la o l^ jit o f th e l iq u id to th o c a p i l la r y o f Cl a|§ato c o in c id e d w ith te e e tch ed Xto®* A f te r b o in .i su re th a t 1 m s a t tto rm aX and p ressu re s q u ill* * b r im - te te rm to e d by te e th e r th e re m s any . « f « l o f tho m eniscus is th e eapiXXm ry on sfcandi?*$ &mm t to e - th o p ressu re in X* which was tho f t p w p ressu re o f tho h y d ra te mymtmi# was e q u a l to tho ssansm trlQ p re s s u re * By re a d in g b o th tho met«»-* m otor and te a barom eter a t the same tim e on te e same s c a le , all c o rre c tio n s 'sjceept tessporaturo wore e lim in a te d ms n e g lig ib le , and tho d iffe re n c e h o t w o n the two g a te th o f i l m o f te o vapor p re s s u re * - 16 - * l I J . ) I I 4 ’> The b o rax uo«kI was th e f in e s t sodium te tra b o ra te doetdsgrdrate o b ta in a b le fro n a & iX fc a k ro itt C Jim iieal cionpmxf * th in was fu r th e r p u r if ie d by ra e ry a tm lld s a tlo n fro m w ta ? a t 00 € * The p e n t* h y d ra to m p rep ared by ra cs ^ a fc s lX i n a tio n o f ths souse s to o l m a te r ia l a t th o tem p era tu re o f b o ilin g ; o f i t s s a tu ra te d s o lu tio n # B oth wmrm aaaiywa-si by fu s io n in m p la tin u m o r u e ib l* arid found to bo th o j i r t h y d ra te s * *%&&¥ were s to re d in w e ll s toppered b o t t le s fr& a w LIeh tb e y wop# token and g m m d as needed* The d ib u ty l p h th o lo to us#4 as a o a a fiiito g l iq u id was o b ta in e d fro m th o ^mMttmm Kodak Cotipiaay and used as reeeiTO d# I t had a b o ilin g p a in t ran§© o f from 2 0 0 ° to 30§% a t 20 mtm p re s s u re * Tho & e re u ry .used in th o immm mtnr «*»ui Imremm%m* wan washed 0 tim es btirouiiti a s o lu tio n o f *r 2$ ♦ 11^10^* T h is washed m a te r ia l was th en distillo d in- a c u rre n t of air aeoor& lng t® IS o lo tt and In e h ln (2 $ )« Ths d is t i l l e d $n*odttct m s f i l t e r e d through. a p in h o le d ir e c t ly Into the desired t a b s * - 17 - t h i; data In o t& ot that th o to rap o ra tw o o f th o izmWi eo o ld bs aoeuratoly rsad# ths had t# bo ©alibratod. '2h# most s m is ltlv © aaat-i-sod o f o a lte r a t io n is m # in stfaleh a vo ry la rg o ohango in a prpporfcy o eo w o f o r m w r y m a l l ehaago o f to itporaburs • Tho v a r ia t io n o f tho w ith ts n p o ra tu rs smafc- bo known -to a h ig h d#gr©© o f p ro o la lo n * It m s doeldod th a t tli# m p o r proosuro of pot© witlii* wag tho roost oonsl& ltro propsrtey a v a ila b le f o r our uso* Tho of thl® property of wator with baraporatUF© imm boom very s & ro fu lly workod out* It gave th o dogroo of a o n s tttv lb y d s a lro d f o r tho c a lib r a t io n of th o f^ isrtstoocmpl© * T h is was cImm lay p la c in g tw lo o d i s t i l l sd w ato r in tho b u lb of -th© la o to n lM o p e * Tim th & tm m rn m l® - tho ju n c tio n s te in g Icwsorsod in d lb m ty i phfeolatso ** was p loqod c t lro o ily bsaldo th o b u lb b o ln g \sa©ci* Tho vapor p ro ssuro was ro ad as dooorlhod p ro v lo fu s ly * and th o poison fcionotox* was r®ad» A i l ro sd ln g o fg .f i ohookod on oaoh tmXh# Tho paroaouro r e a d in g co u ld bo' abookod to i 0*011 m # , m d th o p otontlo raobor re a d in g s co u ld tm ohoekoU to « Q«.OG& iswv* o&aa&lar d a ta was H » n o b ta in e d on tho otthor b u lb * I t was obsarvod t im t th o oUmrtmimtmT in &/& bath had a variation of «• 9#CS €* *ia.o o f th is v a r ia t io n was p ro b o M y duo to d r a f ts cm tins lo n g stciia o f tho tfcs& aoristor* s in o o th e sasipl# was onoasod in and n o t ® t lr r o d t and aim©# on a ta a d ln g undsr o o n tlm s a l • is • oheervatlim at ti-m rmntmmm to the ®ppm*mbtm d id n e t enow it w&m eonaider'ed that thd toerwoRaefcer v a r ia t io n d id not ahow the v a r ia t io n to th e sam ple* and th a t th e siKKsle d id n o t v a ry to tm p a r a tw e m a r ly mm s«aet% b u t was a t th e m a n to iaporaturo o f th e b ath # * M a nam ifeion. ahould bo tru e f o r to # y # w loem ipi# too# f in d « tm t variation there was in «ne mermeouple* tho standard ooll was eheoked upon and a re a d in g o f th e toerciieeougAe m e mclo e ire ry th re e m in u te * ovof a p e rio d of art hour# ^hin wa# done a t all point# to tho o & X tb r& tim . iiiooh of Wm read to & a h m Xn it tho p o e a lb U lty of e r r o r in th e acsiml to rflporatitre o f tho tm th end a ls o e r r o r to nnttlug th e In e tm a a n t* A t^ p lo o l i i m p l t o f too## re a d in g s is ^ v e n to fa ta le 2 * ? *t> le 2 V a r ia t io n l a bn to teaajK^mturo a t #6#3% S iiX X ro X te D e v ia tio n from H#V. D e v ia tio n from ia .8 ? 9 ••0 0 6 3 1 8 .8 8 6 + .0017 x s .s a # •«oooa 1 3 .3 0 6 4.. 0017 2 2 .8 8 4 •*0 0 0 3 1 2 .9 8 6 > .00 17 2 2 .0 3 0 ♦*002? 1 3 .0 8 4 -.0 0 0 3 22*834 • * ’0003 1 3 .0 8 6 > .0007 12.S S 4 •*0 0 0 3 I S . 304 -.0 0 0 ® X 2 .a ee ♦*003? 1 3 .8 8 4 - .0 0 0 6 12 .88B ♦*000? 1 3 .0 9 2 - .0 0 2 8 ia *8 0 & 1 2 . BBS ' mmi * «W« #*tvi. »j#ai<.**1 t ■Iitfa ;feaw* *. -ir 1. xxrp a t 0 ° 0 } and th e fo u r m i l l i v o l t re a d in g s * th e tem p e ra ta re was o b ta in e d by e q u a tio n ( 3 4 ) . The d a ta f o r th is h y d ra te system in g iv e n in T a b le 3« T a b le 3 fV f V a r ia t io n o f th e H yd ra te Syataia Tem perature in 0 ° Pro a sure In ;n * o f Hg at 0 ®CV 8 3 .8 7 © ° 2 0 .9 0 a n . 4 6 .0 9 0 01.7© 5 2 .1 0 7 0 0 .0 2 5 9 .5 2 3 133.0© For the benefit of future oaleuiatlone if :1a data was put into an equation %fetoh book the form of p • - 4 3 .0 0 3 ♦ 4.23445% - O.lSOOOOt2 + 0.00109174% ^ (3 5 ) where t Is C and p Is on. of Hy a£ 0°G. C ;is da&a is plotted in Fig# 2# The m>rk by X># P* Higjiborgor (X o o .o lt . ) by tl*e a i r flo w method mid tho e a r ly work in m is th e s is 2 4 0 220 VAPOR PRESSURE CURVES 200 * A - S A T . S O L //. O F 5 H Y D R A T E B ~ tO + S H Y D R A T E S Y S T E M G - S A T S O L N . O F 10 H Y D R A T E 1 6 0 1 4 0 120 t o o 8 0 4 0 20 T E M P E R A T U R E /A t C T O4 03 42 8 by o ioofcenlsoop© ssethod w horoto b o th o&aoo w©r# uaod fo r ft®m m iring fco'.^joraiu**# a » to 0£P*©#3a©»b w ith in o x p o rto o n to l © rro r* f k ia M a t d a te * u sin g a tl» m o o o n p to f g«av« a t i f f f i a u d ib ly high«® hist paraXXoX to th a p ro viou o w ork* la ordor tso bo ©or# that tho doom hytirato of borax « d th© penfca hydrat# war© la o q u lX U x rlw with #aoh abhor* tli# apparsbao was is o d lfto d s l ig h t ly aind ©a loo&horsaal d e h y d ra tio n o f m o © a w !# *! o u t* 2n pin©# of ©a# of tho sasapX# buXbo m © pXaoed a ground glass joint* oa© »rto©nbal d i f f io u i t ie o «&iieh develop ed * A t v e ry low prooauroa t l 10 d ib a ty X phthaXat© In v a ria b X y bubbled o o p in to tho a m p lo b o tt lo oin&ai&g tli# lo s s o f th o m m * Booauao o f th o la c k o f tto © „ th is study m © not carried imioh beyond tho first brock in th© c a m . fh© t to # re q u ire d f o r fch© saipX© to e®3§ to 4 mp 5 p $ €t g ctI 0 H gu 0 jSl *SP©«©! 0 *1 Ih if |8 * % mmo p m. f t *•3 & S’ I* 0s &£SMrr * $# I $»s*& f tM* < I H* tS 5**f m trH0 I* H Vh*0ft- ?& Mi S3 I *■*« rr M>@1 &0 **♦4 I m «* i*& P B a € IXHI* f** Pct s e ¥>m i \s im 4 mm 9 S p* •«& FIG. 3 ISOTHERMAL DEHYDRATION OF BORAX 10 Hf 0 5 0 D-- (P---- ' 0 ■ i — 1 8 4 o Va ' 1 ...•*< i • « i 10 5 HYDRA 1rE GRAMS WATER L O S T 0 H i 'D R A T E \ Ryun. 7 i / > r fo . 2 .4 . & .3 1 ,0 / . I 1 ,4 1 ,6 tu d m tc p e mul ap p ara tu s as vaa used fo r fe@ o tirw o f th e h y d ra te system# do tia ra o f th e aolufeicm b e in g s a tu ra te d * a s a tu ra te d a o lu t l on tmu ae d * up in a beaker n t a tenperafcure t i i^ ta r th an th a t a t v h ib h t£h© m was to be made and a llo w e d to c r y s t a l l is e in the b a th a t t$sc h ig h e s t to tp e ra iu re d e s ire d in tit# ruxw T h is p o in t m s d eterm in ed f i r a t# Bach su ccessive lo w e r tiw p s r& tu r# was taken in order# fhis insured the liquid being at all t im e iu e q u ilib r iu m w ith the s o lid h y d ra te m & i t f t f i tim e in waiting for s a tu ra tio n to Is# reached# T h is d a ta ia g iv e n in T a b le 3 and i s p lo tte d on F ig # S* iliermodynamiea requires Min at the saturated solution cu rve o f th e doom Ily d ra te s h a ll in te r s e c t th e s a tu ra te d s o lu tio n cu rve o f th e pent® a t th e saisa point; a t widloh tJsis l a t t e r m s m in te r s e c ts th e d is s o c ia t io n o a w o f th e p e n t* liy d ra t# «*> deem h y d ra te system# ^o oh@elc up mi th is p o in ty th e vap or p ressu re cu rve o f th e s a tu ra te d s o lu tio n o f th e d e e * h y d ra te o f b o n a m s d € b e r a i» 4 In t lie &mm iosnner a# b e fo re# T h is d a ta is g iv e n in fa b le 0 and is p lo t te d on fa b le S H e la tlo n o f S a tu ra te d a o lu t l on o f F e a ts Si ira te o f B orax F in issm* Of *bHv&mt#********-** * '"•'■■'*■•' ■ v»»..VS*##*.'ilMU'UfciUMl&JaiN 60#875 e3#7^9 TO#779 X 4 f.S 4 « • X@3*40 887*81 - 24 ** 0 * Tufel# 6 f - f B a ta o f n o iu tla n o f IQ I f f d ra t# o f B orax 0°0 87.849® 38.93 aa 3 3 .4 8 8 3 7 .3 8 41.783 89.34 48.791 34.53 85.117 113.98 39.158 137.78 mm***m ww>*j»wiiiwr)#i.jmw)»9immmwmi: ww whh* :>aiMwp»rtrwr w*r«wri mp- B j plotting Vmnm ctunroa mx oapooi&lly largo p&por all war# found to Intorooot at 80#$# & 9*0%* Hits is tli# tra n s it io n , point o f tlx# dooa fcgrdrat* into Mx# p en t# B y d ra t# • - 88 - AM) In. th e th e o ry o f t i l l# psipor mm d e riv e d an e q u a tio n (1 3 ) by a t a $ o f w htoh A ll ©maid ho e& lauX ated# P By d if f e r e n t ia t in g e q u a tio n ($ 5 ) w ith re s p e c t to t « • o b ta in , o d ft/A t * 4 .2 0 4 4 5 - 0 .2 4 1 7 '33fc ♦ O.0O5O7S23ts (3 0 ) A ls o , b y e q u a tio n (3 0 ) w® eari © alcu lab ® th e va jK jr jb?»8»uj[*® f o r tiny d e s ire d te jfjperatfu re# 'W ith th e s e v a lu e s i t 1© im #aey m a tte r to o a lo u la te z^H fo r th e re a o tio n a/6 H ftg j^ O y .lC ^ O ta ) « a/s HagB4 07 .S I% O (a ) + %o(a) (37) T h is was done# th e d a te feeing: g i f t s in T a b le V ©nd b e in g p lo t te d in T ig * 4« A g lan o # a t th is t u r f t o lm t i t to bo w r y W t t i i * A d e ta ile d d is s u a s io n o f a l l e x p e rifc e n ta l e r ro rs t h e ir p ro p a g a tio n will fo llo w * The m m e r r o r le s s f so to r was n fte e a e a rtly o o n s ld ere d to be th e vapor p re s s u re ta b le s o f p ir e e a te r in th e X n ';>em atio n al C r lt le a X fa b lo n w:ii-eit were ueed fo r o a llb r & ila n * These imtI to be ooinsidered as a b s o lu te * Xn the e& litR p & tlo n of tin© n *cm pX ef tli# e r r o r o f & 0 *0 8 sea* in re e d in g th e mud the error of £ 0 * 0 0 2 w * in reading the p o te n tio m e te r g iv e an a e e u m la t lv e e r r o r in th e te m p e ra tu re * T lila tfccwraulated e r r o r ean be e & le u la te d b y th e eq u atio n . F in a l e r r o r i s t w ® (e r ro r In v ) s •* ( e r r o r to ro e 2 2 9 0 0 A H F O R T H E R E A C T IO N & f U e j , o 7- m o p ) = ' / s t L & o y s - t p ® + % o $2 8 0 0 2 7 0 0 2 6 0 0 2 5 0 0 T E M P E R A T U R E IN A 3 3 03 2 03 / 03 0 0 ** -20 2 (» 0 0 2 )S * { .0 S )S {39J I'h is g iv e s as if® ? ag # e r ro r la . % o f £ 0 *0 X 3 ° over %im used* H o st* th e re Is en « ^ w in the p re s s u re do* to th e %n t mud ml mo dum to th e e r r o r In re a d in g th e smnesgeter* M i sa$ey£iulmt#d ®r?®r l a p res su re ©an be e s lo u le te d b y an e q u a tio n o f th e smut fo m as was used above ( 5 8 ) . te e s # m lu e # m*#t at 3 0 % tbs error in p a | 0 * 8 4 5 m* a t 4 0 % th e e r r o r in p *• «* 0.O 51 at 8 0% the error In p » ^ 0 * 0 0 0 '.Che e r r o r la d p /d t was e s lo u ls to d s im ila r ly f o r th e mmm m m ® of fcessmrsfcures* . 3?hese errors range frm * 8 *0 0 1 to * 0*0O T* C «m sldering a l l o f th ese e r ro rs * mud c o n s id e rin g th e e o n s ta n t B to bo © rro r le s a ( th e e r r o r In th e a b s o lu te tem p era tu re *£ was found to b# n e g lig ib le ) th e f r o s t la n s ! e r r o r in /M I man be e&lonl&feed b j the e q u a tio n where is th e e r r o r in e«en fu n s tio n ju s t saentloned above* C s le u le tln g th ese f ; 4 m o tio n a l » p w « mad t r a ils * fo n a ln g them in to A b so lu t# e r ro rs * w© fin d , th e e r r o r In /MI f o r resetion (W) as written to be In ©simulating these errors ev#ry opportunity was used ;rro r in£>H s t 30 % ^ 8 . s a le r r o r in ^ H a t 4 5 % «« $ 5# s a ls >ror in A If at 80 0 m Z 2* oals bo tn e re a e e ra th **r than dft«sr«ai§it th e e r r o r * t lp « •aramtoatfon of theae # m p i ®& of the curve f t is p la in th a t even i f th e e r r o r m « t!i a l l o f th e p o is ts # Ae i t ! * p e l l o r t t» p e to te l i e on a eaooth en rv e w ith th e a d o p t io n o f e e o r too ah ltfh a re aro o u stad f o r by -she s& tou labed e rro r# in o a le u la tia n e o f n o t to e , ■*#».% p re c is ia n d> II 1 m o r d in a r ily eox&elderecl to b# ooxs&iant w a r a m a l l rann # 'csiapom tw e# F o r a o r# p re c is # c a lc u la t io n a , i t s varia tion for many substances and reaction is found to be g ra d u a l* The equa<m f o r oK preeaing th is nor lo t io n la o b ta in e d by In te g r a t in g th e equablce* i4«t th e v a r ia t io n o f th e s p e c if ic h e a t w ith tem p e ra tu re o f each c o n s titu e n t o f re a c tio n (4 $ ) h# rep re& en ted by aw # wm*me u r t * buppoae w# o o n e ld er th e re a c tio n 4 e » m 0 ♦ » (48) «t 1^ *■ J&jT 4* ♦ mm-mmtm, (4 b ) CPB m % ♦ * *»**’*'**•** (44) ©BO * % ^ ♦ Uig3?® 4- og!?^ ♦ ********** (4 b ) CPU a I4 + a# * a^ .’8 + 0 4 a' 3 ♦ ——— (48) m • Thm total ehange in heat eapMlty t o the reaetton (40) la than ^Cp * Cpc ♦ Cp0 - Opa - Cpb im) Putting equation* (43) to (46) taeluaiwe to their prop#** plaee* imd embinlng all 1 ito tom* m obtain m^l ♦ ^afl? *^«SP® (48) By arubatituting ©quatioon (48) to equation (€1) t o ACy and in te g ra tin g * F le e in g the te m ^ H ^ to p lm m of toe oonetont o f in teg ra tio n (meaning toot to ie l e toe yalw* o f i f toe veM tlo a oould to earrled out a t # 1 ) we obtain A S . £11. ♦ * » (4®> f fh l* e q u a tio n should f i t to e e x p e rto e n tm l o u o to * th e re meat be te w jdiesiooMeiOvi’ oausing thl* variation in toe to o t e e p e o it ie e o f to e a o lld a t o i t o to to m eaueea to e variation to I t m e th ou g h t to o t th e re m ig h t to a ehaitge. « f e r y a ta i a to n e to re a t ab o u t 55°G # where to e to e a k to to e e w e eeew ra* to an endeavor to o o u f im to to p to re s wee e iy s t a l l le e d m m l s l i d e * e t 43°C end 20*0# Fhotonioro@ r*ephe w ere mad*. o f eeoht end eaoh m e exam ined u nd er e p o to r le in ^ mle re e e e p e * f t o a * e m & rim tle n e * a tn e * to e r a te o f e ry e ta X X is a tlo n had to to e« m # ld er*d e f fe e t to g t t o outw ard appearane# o f to e © ry a ta l* d id n o t t o w any d if f o ran ee to tw een th e tw o o ry a b a la * I t wae toon d ec id ed th a t toe d i f f e r one# e ig h t n o t to o f e i t f f ie ie n t m agnitude to to a to m b y th ese m ethod** eo mmm X«*ray * 39 «• p l& tu r * * * b y th e powder :a»thod ** u e re ta k e n * fh e sam plea, an b e fo re , w ere e i^ ta X X Ie e d a t 45°0 m A 30 °C , ground up and vdLxwtiL w ith 3>$se.e e m m t* A f te r m teeh n l$u e hud been a c q u ire d , to o ira ff ie£@ ft%ly good p le tu re a w#:r# o b ta in ed # A f te r th e e a X e u l& tlo n e had been c a r r ie d o u t, aU . th e l im a «m eaoh f ib a ©hooked each e th e r t i M a th e X fo its & t e r ro r o f th e e & p e riM n t# fh ln ahow«€ th e two eryebeXe %m bn o f th e mmm m f a r ms th e m%mm r e f lo a te d th e X**rmyau Tim o n ly o th e r in flu e n e in g fo o t o r n o t y e t ean & ld ered m i th a v a r ia t io n in th e e p e e lfte ha a t o r 'tlx© e o n a tltn e n te * ffeia variation for water is w r y w X l knewn* However, f o r the l i d h y d ra te * , n o th in r e l ia b le e o u ld b# fo un d* I t aooiaa £iu>at p ro b a b le tfmfe ^ho f io i^ i im t im o f iho Uoab © a p a o ltle s o f th e a e lid ecm atituanfca o f th in re a o tio n would aooount f o r th e v a r ie tie s * in th in fim o tlo n * ^ b is pbas# o f th e «oi*k la b e in g .o& rrled an In th is la b o ra to ry in o rd e r to t r y to f in d the reaeon fo r th e dhupe o f th ia eurve* It iiti-mid be pointed out, however* that the work w ith trie :alereaeope and th e X<*ray m u n o w o r le a a o ru de* i t %b p o a a lb lo th a t e x p e rt te e im ie ia n a *d .th thene two to o l* isitght bo a b le w ith im m r e f in e d ajpparabuo to ahow sane u l f f o r ©nee betw een e r y e ta le m d e a t thee© two tem p eratu res# In a l l prcnrieua w o rk , o u th a re o f p a p e r* have used the rtetihod o f p lo t t in g lo g p a g a in s t X/ 2 to o b ta in zhH* By zm & feiplylug th e i M p o f th e m o w eurvs by 2#3026 p / t e a -m km o f A H is o bta ined # f h ia method le n o t T M arly as nearnra't© os te e one us#cl in th ia pepe*** In th e f i r s t pXaoe* i f a l i r g # rang© is re q u ire d i t la im p o s s ib le to o b ta in la rg e enough gm ph p ap er eo th a t Mi# p lo t m y be M.d@ w it li th e mrnm d eg ree o f p re c is io n aa th e data# 3eao£idX7f tsh# mfche&s o f o b ta in in g ta n g e n t a to n e a r ly a tm lg h b l im e mrm v e ry In a e e u ra te # I f on# e«m o b ta in a p re c is io n o f » 300 e a lo r ie e by tho above method on# is Xnefcy# #fhe above d a ta was p lo tte d to. th is way a«*& «aa e s s e n t ia lly ' s t r a ig h t l in e was o b ta im d # She m in e o f A ll by th is raotfood was about tli«t m a n o f th e o a le u la to d v a iu e « ** W 3 c o ls # C a lo u l& tlo m i in e a r l ie r w r k by tb ie tanciawt method showed e ts s lla r v a r ia t io n * vdiioh w ere a t t r ib u te d to a r r e r s In th e je t t e d * A f te r e a re fu X ly €an sld© F ifig a l l p o e a lb le e r r o r s , ten omrv# appears to be a u th e n tte m id to in d ie s to a phm om non n ot y e t In o p e ra tin g is the system# By e q u a tio n ( d l ) t t e m lu o off F f o r th e m u o tio n m s eaX oulated# Bile Is g iv e n In *« h le 7 and la plotted In F ig * 5# By m a n s o f e q u a tio n (5 S ) | A S was e o le u la te d # ^ ' Is d a ta is g iv e n In fa b le 7 and la p lo t te d In F ig * 6 * l id s cu rve la q u it# p e c u lia r aXso# th e b reak b e in g a t about tli# c a m tem p era tu re as te a b reak in te e A H curve# Ofhe &mm • $& ** a n im a t io n w i l l mm doubt m&tfkf to b o th eurvo## I l f wmmnm o f o tfu o tlo a {$© ) was emiomX&todU Xhto data %& tabulated In ttiblm ? and pilot tod to Fig* 7* ao to ho oo$oot«d» thio oufoo roooofoloo tho ^11 ow w o* tty ro o d in g tit# oXopoo o f th o and. o w fo o w ith a to n g o n t u io to r vo lu o o o f A 0 F and wot*© ©hfeoitaod* f£h#0*t va lu o o a r# te lm X atod in T ah lo 0 and p lo tto d in F ig * t« 311 'X.blo 7 Y a lu ea f o r tho Ro«u»ttr ti| xia».i ifn ~inrrnW T n r -in i ■> rni rrmnni -r i *.110111 ■**’ i/iSr9. CAi’Cf&m# *»£#&* 704 (X9&X) 20* :Arr#ts I. aoatbroole: ~ IWi 4 3 . 72© CX92X) m . Ojlbbft - Am»is. Com. Ae«d* aoi# (1574-1078) 24* H* 8* X&jrlOT ** X'ro&fc* Fhva. Chem* 89 &oe* M * 23* Kulatt A Flmaalilri - Phyo« Aev. u8B {1905)