Partial Molal Volumes in Dilute Solution by Injection Dilatometry Richard A. Grieger,' Carol Chaudoir, and Charles A. Eckert2 Department o j Chemistry and Clie?nical Engineering, CTiiversity of Illinois, Urbana. Ill. 61 802
A technique has been developed for the rapid and accurate measurement of partial molal volumes of both liquids and solids in dilute solution, using an injection dilatometer. Results are reported for the reactants and products of two Diels-Alder reactions in a variety of solvents. Solvent effects on the volume change on reaction are discussed in terms of unlike-pair interactions in solution.
24
Ind. Eng. Chem. Fundam., Vol. 10, No. 1 , 1971
RIO('DX \vas piqiared by reactioii of AIAIwith A173 with a trace of hydroquinone :&led to inhibit forniatioii of the copolymer (Stepek, 1964) (m.1). S'i-98"C). So1veiit.s were purified, dried, and distilled according to methods listed by Perrin (1966). The hygroscopic solvent's acetoiiitrile, ethyl acet slid acetone were checked for water content, by Karl cher titration. Ethyl acetate and acetone coiitained less 11 0.00270 water by weight; t'he acetonitrile contained O.Ol7, water. The flask ~ v awl x ~ y . cleaned ; with a Ilot,assium dichromate~ulfuricacid solutioii prior to use. All solvents were degassed by boiling shortly licfore being loaded into the flask. The syi iiige \vas loaded n i t h liquid solute or conceiitrated solute solutioii m i t l coiiiiected to the syringe tubing. 1 small amount of liquid via': expelled through the tubiiig. The flask was filled with solvent and the greased metal stopper \ Y ~ S connected. Any air I~ubhleiremaining in t'he flask could be removed liy tilting the flask aiid addiiig solvent through syringe tiiliing in-;ertcd through the glass capillary tube. 130th the flask aiid syi,iiipc ~ w r eclamped in a holder and placed in the tenil,erat~irc liatli. Temperature equililiri(1m, as indicated liy :I coiistaiit liquid height in the capillary, was attained withiii 20 to 25 miiiutes. The h e i ~ h tof liquid could easily be read ivith a c:ithetonieter to withiii 0.01 c m , which correyionds to :I volunic of 2.5 X 10-5 cc. The liquid height could ea>ilj+be srt by adding or withdran.ing liquid through tu1)iiig iii,*ei?ed through the capillary. lkcausr the iiige niid the flask \vas always a t bnth tenir five volume determiti:itiotib iii rapid wccesem, 11)- cniptyiiig the 0.5-cc sion could lie made oil cnc.li liulb by nicaii-; of iiiserted d o w i the capillary tulw before each iirw meawreinent. T h e volume of thc bull) iii the capillary waq detcriiiiiietl by opcratioii of the app:ir:itu. with the smie liquid iii both the fl:i-k aiid thc syi'ingc. 'Hie volume lietweii tivo refet,eiice nim~ksabove :ind lielon- the bulb w t s measured by setting the liquid lcvrl be lo^ the bulb, iiijectiiig eiiougli liquid from the niicromctcr hyi,inge to bi,iiig the level above the hill^> and corrc.cstiiig the volunic diffcreiice read fwni the niicronietcr syriiige for the differences betiveeli the liquid levels and reference marks. T h e preci-;ion micromrter syriiige could be read with a veriiier to 1 x 10-4 cc, but, the rtnnclarcl dcviatioii for the calilirat'ioiis n-a:, 3 x cc. Several organic liquids u.ed for calibration all gave t'hc same volume for the liulb. liquid Solutes
To nieasiire the partial molal volume of a liquid qolut,e, the same operational procedure was used as for the calibration, but the 11we liquid solnte injected from the For each addition of solntr, t' olurrie added x i ? re the niicromcter mid thc volume change of the .olutioii was calculated from the volunie of the bull) and the change in height of the liquid in the capillary. FOWor five dctelniiliatioiis of thc voluiiie c-hanpe a t iiicreasinp solute coiicciitratioiis were nwde in successioii. The apparent, mold volume, p! n-as calcu1:ited directly from AV P =
Tn
(1)
where A n is the moles of solute added. Within experimeiital error of 1 0 . 1 cc per gram mole, p did not vary over the coiiceiitration range used (0 to 0.2-lf) for .tenis iii thiq work. Thiq is in agreeinelit' with the Iiartial molal volumes nieawred 1))- McCabc et 01. (19TO), who found that the p r t i a l molal volunie in ieveral orgaiiic systems varied about 0.05 cc per grani mole iii this coiicentrntioii range. The volume changes measured in two experiments for 1)yridine ill benzene viere - 1 . O i and - 1.10 cc per gram mole, which agree well with the voluiiie change of - 1.12 i 0.03 cc per gram mole a t infinite dilutioii determined liy AlcCabe. Solid Solutes
The same alqiroach was adapted for the meawrenient of partial rnolal volumes of \elutes \vhich are solids a t the tem-
Precision Bore Capillary Tubing Precision Microrneler Reference
B o f f les Magnetic Stirring Linconel Syringe Tubing
Figure 1. Injection dilatometer for partial molal volume measurements in dilute solutions
peratwe of the determiiiatioii. T o measure the partial molal volume of a qolid solute, a cwiiceiitrated solutio11 (of kiiowii density) in the sanie solveiit \\.a- iiijec+d If pi' i q the a1q)areiit riiolal voluiiie of the solute in the concentrated solution, the total liquid voliune iii the qyriiige mid f l a 4 before injection is
v=
n12'1
+ n+?'
(2)
where r1 i,q the molar volume of pure liquid solvent. Aifter injection, the volume is
V
=
nlnl
+
712p2"
(3)
where p2" is the apparent molal volume iii the dilute solution. The volume change i.; A'[' =
7l2(C"?"
- p2')
(4)
I3ecause p2'' doc-; not vary nieasuixI,ly :it t h r low conceiitratioiis i n thiq study! it iq a good a~qiroxiniatioiifor the liartial niolal volnnie at iiifiiiite diliitioii. The ei'ror for solid solutes dcl~eiidson the coiiceiit~~ntioii of thc ,
