July, 1955
THERMODYNAMICS OF SODIUM CARBONATE IN SOLUTION
G53
TABLE VI lations were not made for the diborane-diethyl ether system, since the observed lines characterisPOTENTIAL CONSTANTS OF BH3X MODELOF TETRAHYDROtic of the complex in this system were too weak. FURAN-BORINE, X lo6 DYNES CM.-1 We can conclude, therefore, that diethyl ether\[ass Of x f D fd fp fcYb f D a - fDB fa borine is the least stable of the complexes. X = 1G.00 3 . 2 9 3.01 0.300 0.474 0.0415 -0.320 X = 72.10 5 . 4 0 3.01 ,306 ,488 ,0406 - .502 TABLE VI1
Relative Stabilities of Ether-Borine Complexes A quaiititative measure of the apparent equilibrium constants was not attempted, but ail estimate can be made of the relative stabilities of the ether-bovines. The intensity, 1, of a Raman line characteristic of a particular substance is proportional to the concentration of that substance, hence
The ratio of the proportioiiality constants, k l / k z , should depend primarily on the nature of the two species in solution. The intensities of the lines a t 2524, 2284, 2290 and 2289 cm.-l were chosen as indicative of the concentration of diborane, tetrahydrofuran-borine, dimethyl ether-borine and diethyl ether-borine, respectively. If we assume that the ratios k l / k z are almost the same for all the diborane-ether systems investigated, a comparison of the stabilities of the complexes can be obtained. The above assumption appears to be reasonable, since the magnitude of the boron-hydrogen stretching frequency, whose intensity we have chosen to be indicative of the conceiitration of the complex, remains almost unchanged in the three ether-borines. Thus this bond is only slightly affected by the nature of the ether parts of the complexes and similarly the intensities of vibrations characteristic of this bond may be only slightly affected. The solutions for which we were able to calculate “iiitensity ratios” are listed in Table VII. Calcu-
“INTENSITY RATIOS”OF DIBORANE-ETHER SoLuiwNs Solution
B2Hs-CdHsO BsHe-( CH3)zO BzHs( CH3)zO
Initial mole ratio
B~HE/RzO
114 1/6 1/6
Teini)., “C.
1 ~ xI0 is/ ~
-25 -40 -70
IBtlls
S 2 4
The “intensity ratio” of dimethyl ether-boriiie a t -70” is twice as large as its value a t -40”. As anticipated, complex formation is favored by a drop in temperature. Even a t -25” the “iiiteiisity ratio” of the diborane-tetrahydrofuran system is four times as great as the value for the diboranedimethyl ether system a t -40”. It would be hest to compare “intensity ratios” of both solutions a t the same temperature and concentration of diborane. However, if the initial mole ratio of tliborane to tetrahydrofuran was reduced from I/’* to l / B and the temperature decreased from - 2 3 to - l O o , the “intensity ratio” for the diboimetetrahydrofuran system should he still greater than 8. Therefore, we can conclude that the tetrahydrofuran-borine complex is the most stable of tlic ether-borines. Thus the order of stabilities of the ether-l~oriiies is: C4HsOBH3> (CH&0BH3 > (CzH6)20BH3. This is the same order observedll for the snalogous ether-boron trifluoride complexes iii tlie vapor phase. This order emphasizes the predominaiice of steric to inductive effects. (11) H. C. Brown a n d R. M. Adtttiis, J . A m . Clrern. SOL,.,64, 2857 (1942).
THEIiMODYNL4MICS OF SODIUM CARBONATE I N SOLUTIOX’ BY
c. ED\\’4RD
Contribution froin The Institute
TAYLOR 01Paper Chetnistiy, Applcton, Wisconsin
Received Fsbruaty 1.4, 1066
The tlierinoiiynuinics of sodium c:trhon,tte in aqueous solution has been studied from 15 to 05’. From electromotive force measurements of the concentration cells 4 g - 4 g ~ c 0 . Na.C03( 1 0.1 ) NaHg Na2C03(m z )AgzCOa-Ag and determinations of solution vapor pressures, the activity co2Ticie:its have bean calculated over a concantralio:i range of 0.1 t o 1.5 m below 65’ and 0.1 to 2.5 m at 65’ and above. The relative partial inolal enthzlpies hzve been ca1oul:tteJ between 25 and 80”.
Experimental Concentration Cell Measurements.--The equilibriuln c1.nl.f.s of the concentration cells were measured a t 15,25, 5 m and 37.5, 50 and 65’. The reference Sohtion ~ 3 0.1 drawn from a large reservoir of constantIn.composition The solu: The value of Inz \vas varied froln o.2 to tions mere prepared using weighed amounts of reagent grade sodium carbonate twice-distille,j The sodiulll carbonate analyzed 09.8 t o 09.9’% using constant-boiling after heating at 1400 hydrochloric acid diluted to o.5 for an hour. The dissolved oxygen in the solutions was ( 1 ) This communication contains material from a dissertation pres r n t c d t o T h e I n s t i t u t e of Paper Chemistry in partial fulfillment of tlie i,cijuircinents for the degree of Doctor of Philosophy froiii La.vrence College, J u n c , 1954. The work was done under t h e rlireutioii of Roy P. \V til tney.
removed by stripping with nitrogen a t reduced pressure, and the solutions were stored under a positive nitrogen pressure. The reference solution was stored in an 18-liter hottle lined bag to eliminate ntt,ack oll the glaRs by the lvith a solution. ~~~l~~~~ of each solution were run in triplicate using weighed samples and standard hydrochloric mid. The silver-silver carbonate electrodes were similar to the type 2 electrodes of Harned.2 Due t o the higher solubilitJy of silver carbonate, the electrodes were electrolyzed in 0.5 r n sodium bic:trbonate a t 200 nia./cm.a for two hours. It was necessary to form very fine porosity silver on the platinum spirals to obtain equilibrium potentials. These electrodes are apparently less stable than other silver electi,odes, but with care in preparation they were usually reproducible to 0.1 fnv. __(2) H.
S. Harned, J. A m .
Chain. S U C . ,Si, A l i i cl929).
C. EDWARD TAYLOS
654
The 0.2% sodium amalgam was prepared by electrolysis of sodium hydroxide in contact with reagent grade mercury. The prepared amalgam was washed successively with water and acetone and dried by vacuum in the reservoir. The apparatus was adapted with a few modifications From previoua studies and is shown in Fig. 1. All stopcocks were out of the bath for ease in operation a t high temperatures. The amalgam lines leading from the reaervoir to the cells dipped into the bath for about six inches to permit temperature control of the amalgam enteriiig the cells. The water bath was covered by a film of oil to prevent evaporation. By means of a series of mercury-to-platiiiuni thermoregulators, the thermostat was roiltrolled to 0.02" of the desired temperature. NITROGEN
SYSTEM
Vol. 59
a t constant t,emperature and e.m.f. versus hmperature a t constant concentration. The most reliable data were taken from the smooth curves. Vapor Pressure Determinations.-The vapor pressures of solutions \Yere tletei,niined by the dynamic or gas saturation method of conipaiing the vtipor pressure of t,he solutioii with that of wat,er at the mine temperature. I t wits assumed that Dalton's Ian. of pai,tial pressures was applicable for the mixture of nitrogen and water vapor between 05 and 95" a t one atmosphere. The apparatus is showii in Fig. 2. The gas wturatioii cells ~ e r similar e to those used by Peaize and 8now.a The presaturators were 33-iieclc Hasks with mercury seal stirrers which were designed to form many small bubbles and splash the liquid high in the Ausks. The pi,esat,urators were very effective arid caused only it snictll pressure drop. Auhydrous magiiesium perchlorate was used as a desiccant i i i the absorption tubes. Ethylene glycol was used in the bath to reduce heat loss due to evaporation and fiiniplify cleaning of the cells for changes of solution. The therniostat was operated a t 65, 80 and 95" and was coutrolled by niercury-to-l)latiiiuin thermoregulators to 0.02'.
I
%&==
/
I
HEATER CONTROL
I
U'
THERMOSTAT
NITROGEN
ASP I RATOR
Fig. 2.--Vapor
pressure apparatus.
For each of the 14 solutions between 0.1 t n d 2.5 m , four tleterminat,ions were made at 65, 80 and 95 . The results wei~ plotted as a function of concentration, antl the values from tmhesmooth curves are shown in Table 11. The estimated accuracy of the data was 0.2 to 0.5%. Fig. 1.-CoiirentJra.tioii cell :tpparatus.
III the operation of the cells, :I pair of freshly prepared electrodes were put, i i i the apparatus at 25", the cell units were filled, antl t h e e.1a.f. was measured periodically until the equililiriuni value was attained. During the equilibration period, the solutions flowed through t'he cell units at il rate of 0.5 to 1.0 ml./niin. The temperature was changed to 15' and the procedure was repeated. Subsequently the equilibrium values were determined again a t 25" and t,heii at 37.5, 50 and 65'. O w e the electrodes came to equilibrium at 25O, equilibrium was quickly attained when the bath temperature was changed. The silver-silver carbonate electrodes were somewhat unstable a t the highest concentrations at 50 and 65", but the values determined after t.he cells reached temperature equilibrium were reproducible. The results are listed in Tahle I. For each concentration cell, t,wo or three pairs of electrodes were used t o measure the e.m.f. over the ent,ire temperatsure rnngc. The data were averaged by cross-plotting e.m.f. versus concentration TABLE T FORCES OF CELLSA T 15 TO 65'
~ Q L ' l L l B R I L b fELECTIlO\IOTIYE
0.1005 ,3008 ,4009
,6014 8470 1.004T 1.5355
15"
Rrf. -18.7 -37.3 -48 L? -57.5 -ti2 0 -7X3
in inv. 37..i0
iiiin.
950
tiso
(\vatel,) 0 . loo!) , 1.507
187.Ij 186.8
186.4
:m
