tive viscosity, the diffusion coefficient would be independent of the volume fraction of added third component, if Stokes’ law were applicable. Instead, the data show a linear regression with volume fraction of addend to within 5 0.16‘/c. The slope of this line, following the form of equation 1 , i. 1.66, compared t o JYang’s value of 1.5 for I x g c unhydrated spheres. This suggests the possibility that an obstruction-effect theory may be devised to account for experiments in which the presence of small molecules slows the diffusion of other small molecules. It is further suggested that the hydrodynamic portion of the concentration dependence of diffusion, which has been treated as a question o f
[COSTRIBCTION FROM
THE
(38) A R.Grirdon, J . Chem. P/:ys., 5 , ,527 (1937). (39) C I,. S.indqiiist and P. A Lyf>ns,Tiiis JOURNAL, 76, 4G-11 (1Q.x). ( 4 0 ) A similar suggestion has been made by R. H. Stokes, Azrsliiil J . S i i e n r e , 19, 33 (lUj7).
\I.ORCESTER, ~IASSACHLXETTS
DEPARTMEST O F CHEMISTRY, SAIST LOUIS USIVERSITV]
Etherates of Lithium Borohydride. BY
solution v i s c o ~ i t ymay , ~ ~possibly ~ ~ ~ be reinterpreted as a self-obstruction of diffusion by the small diffusing m0lecules.~0 Acknowledgment.-This study was inade possible through support by U. S.Public Health Service Rcsearch Grant RC-3-149, entitled “Sediinentatiori m t l IIiiTusion of Low llolecular TVeight Substances.”
GEORGEiv. SCHAEFFER,
I. The System Lithium Borohydride-Dimethyl Ether’
TIIiZDDEUS
L.
KOLSKI’ .\ND ~ O K A L DL.
EKSTEDT
RECEIVED APRIL 27, 1957 Pressure-composition isotherms for the system litliium horohydritle-dimethyl ether a t 20.0, 0.0, -45.2, -63.5 and ,(I), LiBH4,(CH3)20 (11) and (LiBHd)$.(CH3)20(1111, -78.6” show t h a t t h e three solid dimethyl etherates, LiBH4,2(CH2)20 exist. I‘alues for t h e heats, free energies and entropies of dissociation of these compounds per mole of dimethyl ether evolved at 25’ are AHd = ( I ) 10.42, (11) 11.13 and (111) 13.23 kcal.; A F d = (I) -0.145, (11) 1.66 and (111) 2.21 kcal.; and A & = ( I ) 35.4, (11) 31.7 and (111) 33.7 e.u. The heats a?d free encrgies of formation and absolute entropies of the etherates at 25’ are AHP = ( I ) -157.1, (11) -103.4 and (1111 -149.3 kcal.!mole; AF~O = ( I ) -87.1, (11) -60.0 and (111) -91.0 kcal./mole; and So = ( I ) 77.1, (11) 49.1 and (111) 66.3 e.u.
Introduction I n recent years, lithium borohydride has come into widespread use because of its unique properties as a reducing agent for both organic3 and inorganic3v4 compounds. The reactivity of lithium borohydride places serious restrictions on the inedia which may be used to facilitate its reactions and useful solvents have been generally found among the ethers. In some reactions of lithium borohydride, the ether acts not merely as a solvent, but must play a more direct role in the chemical process. A striking example5 is the effect of diethyl ether on the rate of production of diborane in the reaction between copper (I) chloride and lithium borohydride. The reaction rate increases with the amount of diethyl ether until the mole ratio of ether to borohydride is one to one; more than this amount of diethyl ether is not reflected by a further increase in the rate of production of diborane. This fact has been interpreted t o indicate that the reacting species may be the one to one adduct oi lithium borohydride and diethyl ether rather than (1) Presented a t the 132nd meeting of the American Chemicai Society, New York, N. Y . , September, 1957. (2) Taken in part from a thesis presented by T . L. Kolski t o the Graduate School of Saint Louis University in partial fulfillment of the requirements for t h e denree of Doctor of Philosophy, June, 1957. (3) N. G . Gaylord. “Reduction with Complex Metal Hydrides,” Y.,1956. Interscience Publishers, Inc., h-ew York, hT. (4) (a) G. W. Schaeffer, J. S. Roscoe and A C. Stewart, THIS JOURNAL, 78, 729 (1956); (b) A. C. Stewart and G. W .Schaeffer, J . I ? , org. S U CChem., . 3, 19-1 (1956); ( c ) E. Wiberg, AnRew. Chern., 65, l i i (1953).
( 5 ) R. H. Toeniskoetter, February, 1956.
M.S. thesis, Saint Louis C n i v e r s i t y ,
lithium borohydride itself. Such a diethyl etherate of lithium borohydride has been described by Schlesinger and his co-workers,6 who found that it is formed when diethyl ether and lithium borohydride are brought together at 0’. The present paper describes an investigation of the binary system lithium borohydride-dimethyl ether and subsequent papers will describe similar investigations of systems of lithium borohydride with diethyl ether and with tetrahydrofuran. It is hoped that the information obtained in these studies will prove helpful in extending the usefulness of lithium borohydride-ether systems and in elucidating the role of the ether in reactions of lithium borohydride. Results and Discussion Pressure-composition isotherms for the system lithium borohydride-dimethyl ether a t 20.0, 0.0, -43.2; -63.5 and -i8.6’ clearly show the existence of three solid dimethyl etherates of lithium borohydride : an hemi- (dimethyl etherate), (LiRH~)Y(CH&O; a dimethyl etherate, LiBH4. (CH&O; and a bis-(dimethyl etherate), LiBHq. 2 (CH3)?0. Experimentally determined pressures a t various mole fractions of lithium borohydride (n2)are given in Table I and plots of these data are shown in Fig. 1. In each of these phase diagrams, the uppermost plateau indicates the constant vapor pressure of a saturated solution in equilibrium with the solid (5) 11. 1. Schlesinjier. H. C. Rrown, H. R Hoekstrn and I.. R . Rapp, THISJ i ~ i : R x . ~ r . , 75, 199 (1953).
Nov. 20, 1957
5913
ETHERATES OF LITHIUMBOROHYDRIDE TABLE I
\'ARIOUS TEMPERATURES FOR THE SYSTEM LITHIUMBOROHYDRIDEDIMETHYL ETHER
ISOTHERMS AT DATAFOR PRESSURE-COMPOSITIOS -78.6' Comp., nz
0.000 -034 102 ,176 ,259 ,325 ,334 ,382
,458 ,508 ,547
-63.5'
Comp., nz
Press., mm.
Camp,
34.3" 31.8 32.0 31.8 32.1 32.0 16.0 0.1 .1 .0
0.0c)o ,034 . 103 ,178 ,262 329 ,333 ,335 ,356 ,458 ,508
98.5" 94.2 94.4 93.9 93.8 89.4 65.3 29.3 0.5 .5 .1
0.000 ,034 . 113 ,274 ,323 ,333 ,333 ,364 .469 .SO0 ,541 ,634
.o
0.00
-45.2'
Press., mm.
II 1
.o
.547
Press., mm.
Comp.,
Press., mm.
"86 4"
0.000 ,331 ,334 .351 ,407 ,493 .550 ,500 ,518 ,569 ,636 .672 . Gi9 ,809 .968
1986"~~ 423.9 354.2 193.7 193.8 193.8 165.3 97.0 8.3 7.9 7.9 5.8 2.9 2.8 2.9
271 9 272 6 272.8 204 9 129 9 5 8 4 0 4 1 3.1 0.1 .1
.678
.o
.741 ,969
.0 .0
nz
a R. M. Kennedy, M. Sagankoahn and J. G. Aston, THISJOURNAL, 63, 2267 (1941). cover the range -83.2 to -24.2
.
phase, an interpretation which was corroborated by visual observation. The next three plateaus correspond, in order, to the dissociation pressures of the bis-(dimethyl etherate), the dimethyl etherate and the hemi-(dimethyl etherate). The dissociations of these three compounds may be represented by
20.00 Comp.,
nz
0.493 ,529
,588
.G53 ,678 ,679
.686 .772 ,851 .974
Press., mm.
76.7 33.3 33.0 33.2 29.8 20.8 12.7 13.0
12.6 13.0
Extrapolated from data nhich
The dissociation pressures of the etherates a t various temperatures are given in Table 11. Table I11 gives empirical relations which best describe
+
LiBH4.2(CH3)20(s)= LiBH4,(CH3)20(s) (CH3)zO(g) (1) 2LiBHd.(CH3)20(s) = (LiBH4)2.(CH3)20(s)-I(CH3)2O(g) (2) (LiBH4h.(CHa)2O(s)= 2LiBHds) ( C H 3 ) ~ 0 ( g ) (3)
+
A
It is evident t h a t the hemi-(dimethyl etherate) is the lowest stable etherate formed in this system a t temperatures up to 20°, for the isothermal cGnstancy of the pressure of the system between n2 = 0.667 and n2 = 1.000 shows that lithium borohydride hemi-(dimethyl etherate) dissociates directly into lithium borohydride and dimethyl ether. Also, in view of the constancy of the saturated solution plateau up to n2 = 0.333, there are no higher stable dimethyl etherates of lithium borohydride than the bis-(dimethyl etherate) a t temperatures as low as - 78.6'.
0 0
20.0°
0.0' -45.2'
0
-63.5'
v
-78.6'
TABLEI1 DISSOCIATIOX PRESSURES OF THF DIMETHYL ETHERATES OF LITHIUMBOROHYDRIDE
A. LiBH4.2(CH3)20 Temp., ' C . Press., mm. (obsd.) Press., mm. (calcd.)
-63.5 0.5 0.6
-45.2 4.1 4.3
-22.9 33.6 33.6
0.0 194.6 1Oi.4
17.1 601.9 601.9
B. L i B H 4 . ( C H 3 ) 2 0 Temp.,
OC.
Press., mm. (obsd.) Press., mm. (calcd.)
C.
-45.2
0.1 0.1
-22.9 1.2 1.3
0.0 8.0 8.2
20.0 33.2 33.2
29.6 60.9 60.9
57.3 286.9 288.9
(LiBH&. ( C H & 0
T e m p . , '(2. Press., mm. (obsd.) Press., mm. (calcd.)
-22.9
0,4 0.4
0.0
2.8
20.0 12.9
38 0
56.2
48,0
120,0
43.5
129.9
0
COMPOSITION, Ne.
Fig. l.-Pressure-composit~~n isotherms for t h e system lithium borohydride-dimethyl ether.
3914
Vul. 7!) TAULE I11 THERMODYSAMICS O F UISSOCIATION AT 22'
F U R THE L)IMB'I'IiTL
ETIIGRATES Oli LIIXILJM BOROHTUKIDE Ji
l u g I',,,,,,. = A ;1
Process
LiBI-14,2(CI~13)?0 to LiBH4.(CIXJlzO(equatioii 1) 2LiBH4.(CH3)20 t o (LiBH4)?.(CH3):O(equatioii 2) (LiBH4)2.(CH3)r0 t o 2LiBIT4 (equation 3)
lIl.ti212
'3.XlX 10.59778
- ,; 1 B
YX(i 5 2x3 1 .9 Yij7(i. 1
SI. kcal.
11) ,1%
11.13 12.25 11 .oii ll.ti9
1/2LiBH4.2(CH3)20 to 1/2LiBH4 LiBH4.(CH&0 t o LiBH4
the dissociation pressure-tempcrature relationship and the derived thermodynamic quantities for the dissociation processes a t 25'. Standard heats of formation, free energies of formation and absolute entropies at 25' for the three dimethyl etherates of lithium borohydride which were calculated from the thermodynamic properties of lithium borohydride, dimethyl ether and the values of ' h b k TI are listed in Table IV.
kcal.
AS, e.u.
-0.14s
3,;. -1
+1 titi ,
f 2 . 21
+
0.90 +1.94
31.7 33. 7 3.4.1 32.7
aiici subtracted from the detcrniiiictl voluiiie of the vapor space. Materials. -Lithiuiii brirohydridc of purity was obtaincd froiii Metal H>-drides, Inc. Purificatioti was accoinplishcd b y solutioii in diethyl ether and fi1tr:ition of the solutiim in aii encli~setlfiltration apparatus. Samples prepared iii this ~naniiershowed a purity of W.0--100.O(,!A ori the hasis of 1iytlrogc.ii cvolutioti, arri~~utit of :icitl cc~iisuinctltiuriiig liytlrcilysis, or horie acid titratim. LXiiietIiyl ether was fractionated slo~vlya t -78.6, - 140 aiitl - 196". The fraction licld a t - 140' was conde~isctl oii an excess of litliiuiii borohydride which had been puinpetl for several hours t o remove adsorbed gases. T h e complex T A B L E I\. forniecl had a dissociation pressure of about 8 mrn. a t 0 " . .issuiiiing t h a t 311 non-etlier gaseous impurities would bc iii HEATSASD FREEENERGIES OF I ~ R M A T IAO KD N .lusoLrrI: vapor phase above the complex, the vapor was successively ENTROPIESOF THE DIMETHYLETHERATESOF LITEIIUII liutnped off and allo\ved t o build up several times. Pure tliiiiethyl ether was theii collected by decomposing the rcBOROHYDRIDE AT 25' inaining etherate. Zlfter degassing, t h e followii~gvapor AIIfD, Aria, sa, tensioi~swere noted: 1.5 inm. at -111.8" (lit. 1.5 n i i n . ) , Curnpuund kcal./mulc kcal./mole e.u 34.1 rnm. a t - i 8 . 6 " (lit. 34.3 inni.) aiid281.2 m n . a t -45.2' (lit. 256.4 mm.). LiBH4.2(CH3)?O(s) -157.1 -87.1 I i.4 Introduction of Lithium Borohydride into the Apparatus LiBHa,(CHB)2 0 ( s ) -1m.1 -60.0 19.1 Ah 8 i n n ~ glass . tube with one closed end was prepared which - 149,:i - 91, ( I 60 . .3 (LiBH4)3.( CH3)2 0 ( s ) fit closely into ;I 10 iiiin. side arm senled to the sample tube a t an angle of aliproxiinately 20" above the horizontal. LiBH4(c)a - 4G.36 -30.74 1S.l:Y T h e side arm Tvas scaled off at t h e elid t o allow t h e system -27.3 ci:3 . 72 (CHd&!g)b - 43.3 t o be thoroughly pumped and "baked out" prior to introduction of the sample. The 8 n i ~ n inner . tube was charged a "Ther~~ody~ia Properties ~ ~ ~ i c of Boron Compounds a t with purified lithiuin borohydricle in the dry-box, stoppered 25'C.," National Bureau of Standards, \Vashington 25, and weighed. Dry, deoxygenated nitrogen was slowly atlD.C., -4pri1, 1954. F. U. Rossini, rl a l . , "Selected niitted tlirough the vacuuni apparatus into the san~pletube I-alucs of Chemical Thermodyiiarnic Properties," Circular of :ind when tlie nitrogen pressure in t h e system was somewhat the National Bureau of Stanclards 500, p. 128, U.S. Govern- above atniospheric, the end of t h e side a r m was cracked off. ment Printing Office, JVashingtoii 25, D. C., 1952. \Vith nitrogen flushing through the sample tube arid out of the side arm, the charging tube was opened in the nitrogen Because o€ the limitations iiiiposed by the es- strcam and inserted in the side a r m . The charge wis trmsfcrrcd into the sample tube by gentle tapping, after perimental system, it was not possible to extend the rvhich the charging tube was carefully witlitirawn arid rcobservations into the range of dilute solution, but stoppered. T h e side arm on the saniple tube w:is theii it was visually noted that a t the lowest concentra- scaled off, great care being taken not t o allow a n y sucking tion measured a t -45.2' (rz2 = 0.0344) the amount back of air into t h e system. It was cssential for the side t o be of sufficient length t o prevent water vapor frorn of solid phase remaining was extremely small. ;irm the torch from finding its \my into the s)-stem. ImtnediThe solubility of lithium borohydride in dimethyl ately after sealing off the side arm the apparatus was evacuether might be estimated to be approximately l.(i ated and pumping was co~itil~ued for several hours t o r e m ( ~ v e ally adsorbed gtses from the solid. T h e weight of thc lithg./100 g. a t -45.2" ium borohydride introduced into tlie system \ m s taken as the difference in weight of the ch~irgingtuhc before and Experimental Lifter the addition. Determination of Isotherms.-Composition of thc sample T h e reactivity of litl~iumborohydride with air and mois\v:is varied by both additions mid withdrawals of tliiiiethyl ture and the nature of the measurements involved ncc ether, liquid nitrogen being used to condense the diniethyl tated t h e use of high vacuuni techniques. These arc :ideether portion in either tlie sample tube or the vapor-mc:isurquately describcd in Sanderson's m o ~ i o g r a p l i . ~ Apparatus.-The essential conipnnents of the apparatus ing system. Tlic amount of each increment or decrerner~t include a sample tube with its connected manometer and a r w s ineasured in the system of calibrated v d U n l e s by applisystem of calibrated volunies for measuring atiiourits of cli- c:itioii of tlie ideal gas relationship. After each :idtiition or witlitlra\val, the sainple tube rvas ~naintairieci:it thc methyl ether added to or withdra~vnfrom the sample atteiiiperaturc uiitil the ol~ser\-etl pressure of t h e tached t o the usual high v:icuuiri apparatus. hl(ile fracrcaclietl :I c~instant\-:due. This usunlly requiretl tions were corrected for the aniount of gascous dinietliyl 111 iiirist casts the equilihriuiri pressure \vas tleterIiours. ether contained in this volume. In regions of coinpositiori where an appreciable amount of liquid phase was present mined bj- approaching from both a higher and ;I lower teniI)crature to aswre that the measured pressure \vas Lissociatctl in the sample tube, t h e liquid volume was computed from nitli true equilibrium. the density of dimethyl ether a t the temperature concerned Constant Temperature Baths.-The ordin:iry low teniperature slush bat115 or a srnall constant temperature bath, (7) R. T. Sanderion, "Vacuum RIanipulation of Volatile Com$11 that it could be elevated about the sarnple tube :irrangctl pnuntis," J o h n Wiley and Sons, I n r , h-ew York, S . Y . , 1048. r-
%'/A
EFFECTOF WATERON ,ICID--BASE EQUILIBRIA IN ACETICACID
Nov. 20, 1957
and which would maintain t h e temperature constant t o within 0.1" were found adequate. I n the event t h a t equilibrium was not reached before t h e bath was nearly spent, a
[CONTKIDUTION FROM
5'315
fresh bath could be substituted for the depleted one rapidly enough S O t h a t the sample tube did not warm.
ST.LOUIS,RIISSOURI
THE SCHOOL O F CHEMISTRY,
UNIVEKSITY
OF MINNESOTA]
Acid-Base Equilibria in Glacial Acetic Acid. V. The Effect of Water on Potentiometric and Indicator End-Points in Acid-Base Titrations in Acetic Acid BY S. BRUCKENSTEIN AND I. M. KOLTHOFF RECEIVED JUNE 14, 1957 T h e effect of watcr 011 acid-base equilibria in acetic acid can be calculated quantitatively for titratious carried out potelltiornetrically or with indicators. The equations governing the shape of potentiometric titration lincs of bases in acetic acid as a function of water concentratiou have been derived and experimentally verified. These relatiomhips have been used t o calculate the change in e.m.f. in the vicinity of, a t and after the equivalence point for bases of differeut concentration and strength. They predict t h a t titration t o an equivalence potential, which is independent of concentration of base, will be a n accurate procedure. T h e relationships determining the ratio of acid t o basic color of a n indicator base over t h e titration range in water Containing acetic acid also have been established and tested aud used t o predict t h e color change of p-naphtholbenzein (PXB) in a sodium perchlorate solution.
Water is an undesirable contaminant in the a chloranil electrode as the hydrogen ion indicator titration of bases in acetic acid.ld6 With increas- electrode. Since the acetate ion concentration is ing water concentration the magnitude of the first negligible in such a solution, we can write derivative in a potentiometric titration of a base [H+] [H30+] = [Clod-] Pa) and the sharpness of the color change of an indicator in the region of the equivalence point de- From the expressions of the various equilibrium creases. Furthermore3 the potentiometric end- constants we find [ClO,-] = KHC]O~CHCIO~/ [H+] point is found after the equivalence point, and the and [H30+] = KH,OCH,O[H+]/K~. After reartitration error increases with the water content o€ rangement, equation 2a may be written as the acetic acid. Water is a weak base in acetic acid, and it is possible to calculate quantitatively its effect upon titration curves in acetic acid7d and particularly upon the break in potential and the The symbol C refers to the equilibrium concentrasharpness of the color change of an indicator near tion of the species indicated by the subscript and the equivalence point, using the various equilib- K, = [H+][AC-].~ From the stoichiometric conrium constants for acids, bases and salts reported centrations of perchloric acid and water added, in previous papers.'"-' ( C H C I 0 , ) t and ( C H ~ O )respectively, ~, and KfHa0C104 Water reacts with perchloric acid to form hydro- it is possible to calculate equilibrium concentranium perchlorate according to equation 1. The tions of water and perchloric acid. Thus, if CH,O equilibrium constant for the reaction as written, is plotted versus C H C ~ O ~ ~ [aH straight + ] ~ , line of KfI130CIOa slope K s K ~ ~ i ~ , / and K ~ intercept 2 ~ -K,/KH,o should result. Such a plot of the experimental reHzO HClOa J_ HaOC104 (1) sults yielded a straight line, and K H ~ was O calculated from the intercept using the previously deis 34.7b I n order to account quantitatively for the termined value of K , = 3.55 X 10-15.7c KH~OCIO, effect of water over the entire region of a titration could then be calculated from the relationship curve it is necessary to know the over-all dissocia- KfH3OClo4 = K H C ~ O ~ K H ~ O / K ~ K in Hwhich ~OC,O~,~ tion constant of water as a base, KH,o, and the the dissociation constant of hydronium perchlorate over-all dissociation constant of hydronium per- is the only unknown. o ~ . simple way of determinchlorate, K H ~ o c ~ One The Effect of Water on pH over the Entire ing these constants is to study the change in hy- Region of an Acid-Base Titration Curve. Solutions drogen ion concentration of a perchloric acid solu- of Water and a Pure Base.-The pH of a mixture tion as a function of the water concentration, using containing water and another base, B, in acetic acid can be calculated by substituting into the (1) J. B. Conant and N . F.Hall, THISJ O U R N A L , 49, 3047 (1927). ( 2 ) (a) J. S. Fritz, Anal. Chem., 22, 1028 (1950); (b) J. S. Fritz electroneutrality rule equation 3a
+
+
and M. 0. Fulda, ibid., 25, 1837 (1953); ( c ) J. S. Fritz, ibid., 26, 1701 (1054). (3) P. C . Markunas and J. A. Riddick, ibid., 24, 1837 (1952). (4) C. W. Pifer and E. G. Wollish, ibid.,24, 300 (1952). ( 5 ) A. H. Beckett, R. M. C a m p and H . W. Martin, J. €'haunt. a n d Pharmacol., 4, 399 (1952). (6) A. Anastasi, U. Gallo and L. Novacic, ibid., 7,263 (1955). (7) (a) I. M . Kolthoff and S. Brtickenstein, THISJ O U R N A L , 78, 1 (1956); (b) S . Bruckenstein and I. >I. Kolthoff, ibid.,78,10 (1956); (c) 78, 2974 (195C); (d) I. M . Kolthuff and S. Bruckenstein, ibid., 79, 1 (1957).
[H']
+ [BH']
f [H30+]= [.IC-]
(33)
the expressions [BH+] = KnCn[H+I/K,, [H,O+l = KH,OCH,O[H+]/K~ and [=lc-] = K,/[H+] to yield
( 8 ) T h e nomenclature used in t h e present paper is t h e same a s in the preceding papers in this series.
