Relating Partial Molar Volumes to Molar Refractivities Usually included among the experiments performed in an undergraduate chemistry laboratory are experiments on partial molar volumes and molar refractivity. Although the results from two experiments of this type can be combined conveniently to give insight into the structure of liquid mixtures, we are aware of no laboratory manual that makes full use of any relation between the two sets of results.' An experiment performed in our undergraduate Advanced Techniques Laboratory is essentially the partial molar volume experiment described in Betteheim's text2 with theaddition that an indexof refraction is measured for each solution and its pure components. Aside from the determination of partial molar volumes, the demonstration of the additivity of molar refractivity reveals this quantity to be a useful measure of solution compasition. The procedure and calculations described in Be+lheim lead to the determination of the partial molar volumes (V1 and Vp) as a function of composition in a two component system where
V,=
(F) n l nx
14
,
g \
7 26
0
0.2
0.4
x
0.6
0.8
1.0
Molarrefraaivity,R, and (-) molar volume, V, versus mole fraaion of ethanol, X forthe binary
system. H@ethanol (at 25.0°C). Ideal behavlw far molar volume is also indicated (--).
The total molar volume can be calculated from -
v = X,V, + X2V2
where the !Xi) are the component mole fractions. The Lorentz-Lorenz equation can be written as
for a o w e substance and as
for a mixture.3The (niland n are the indices of refraction for the pure substances and the mixtures, respectively. Equation (3)is valid if the electronic interaction between component molecules is insignificant. Deviations from linearity would indicate appreciable interaction between the electrons of the component molecules and, for the systems investigated in our laboratory, no deviations outside experimental error have been observed. So far we have studied the water-DMSO, water-ethanol, water-methanol, water-acetone, DMSO-acetone and ethanol-acetonekinary systems. For the water-ethanol system, a representative set of data is plotted in the figure. The non-linearity of the V versus X i data indicates non-ideality of this solution over all compositions. On the other hand, the R versus Xi datsdemonstrate linearity aver the entire composition range. As n measure of linearitv. - .the least sauares interceots for R and V were calculated and found - to differ from the exoerimental values hy II8IYonnd :Iq5%, re\perti$rlv. I n n senw the (n2- 1) f n ' T 2) term'corrwu" 1' lor the nun-idenlny of the lunar) mixture. T h ~ndditivity s uf the l.ormtz-l.zoren7 relntlon lusually to well within is,fur n ~ hinnry n ~ solvent sy.tems3, indir ates that N , the m t h r refractivity, is a s y ~ t e mpBT3mPleT that i i an e~ceIIe111 measure uf the cmnpmflon and
