Paul Y. Feng
and Marlene Melzer Marquette University Milwaukee, Wisconsin 55233
II
An Undergraduate Apparatus for Determining Second Viricll Coefficients
T h e second virial coefficient is an important characteristic parameter for real gases from the viewpoints of both practical and theoretical considerations ( 1 , 2 ) ; however, very few convenient apparatus exist for its determination. Existing designs (5-5), as a rule, are based on measurement of the pressure or volume differences which result when a sample gas and a reference gas are both compressed by a fixed ratio, and require closely matched gas bulbs as well as other precision components for their construction. More recently, a simpler student apparatus using only one set of gas bulbs for both the reference and the sample gas has been described, and can be used to determine the second virial coefficient of n-hexane vapor to within *50/0 of its literature value (6). Approximately two days were required, however, to complete one set of experiments. We report herein an apparatus which was constructed in two working days by an experienced amateur glassblower. It does not require closely matchedor precision components, and can be used not only for vapors with relatively large second virial coefficients but also for gases such as carbon dioxide, the Freons, or propane. Experience in our undergraduate physical chemistry laboratory showed that two sets of measurements at room temperature can be easily completed by an average student in a standard 3 4 hr laboratory period.
Figure 1 .
Photograph of the second virial coefficient apparolu~.
Volume 49, Number
5, May 1972 / 375
Description of the Apparatus
A photograph and a schematic diagram of the a p paratus are shown in Figures 1 and 2. The volumes of the gas bulbs B1, B3 and B2, B4 are, respectively, =500 and =MO ml, and are selected to provide both rel* tively large pressure differences upon expansion, and the possibility of a number of successive expansions from one single sample. The differential manometer DM is made from approximately 5-mm 0.d. glass tubing which offers the best compromise between experimental convenience and minimal contribution to the total volume of the system. The reservoir T is used for outgassing and storing the condensed sample gas by the freeze-thaw method (7), and may consist of any suitable vessel. 55 is a stopcock of the Teflon-plug O-ring type. Ordinary high vacuum stopcocks have been used elsewhere in the apparatus although the O-ring stopcocks, which offer the advantage of a grease free system and better control would be, except for the higher cost, undoubtedly preferable. Determination of the second virial coefficient of a sample gas by means of our apparatus is carried out in two principal steps as follows.
DIFFERENTIAL MANOMETER (DM) Figure 2.
MANOMETER
(MI
Sshemotis diagrmm of the second virial coefficient opparotus.
Consequently, the relationship between the pressure of such a gas at two different molar volumes would be
Calibration of the Apparatus Using a Reference Gas
Determination o j the Initial P7essure and the Pressure Differerne (P,)o,M and (AP,h. Stopcocks S5 and S9 are closed, and the entire apparatus (except reservoir T containing the purified sample gas condensed in an appropriate cryoscopic bath) is evacuated and leak tested. A reference gas such as nitrogen is then introduced into the remaining volumes of the vessel to a predetermined pressure ( P , ) O . ~8s indicated by the manometer M. Stopcocks S3 and S7 are subsequently closed, stopcock S5 opened, and any pressure difference (AP,)o between the balancing ( B l ,B2, etc.) and the measuring (R3, 8 4 , etc.) sides of the apparatus is then determined cathetometrically using the differential manometer DM. Determination of the Pressure Differ~nces (AP,),, (AP,),, ete., afler Expansion. Stopcocks S1 and S6 are now closed to isolale the gas bulbs B1 and B3. S5 is closed in turn, and the remainder of the apparatus is evacuated by opening stopcocks 83, S7, and 88. Subsequently, 8 3 and S7 are again closed, S l , S6, and then S5 are opened in turn, and the pressure difference (AP,), between the balancing and measuring sides of the apparatus is measured as described above. (Repetition of the preceding steps will give successively ( A P , ) ~(AP,),, , etc.) Measurement with the Sample Gas
Designating the factor p = &/VI on the balancing and measuring sides of the apparatus, respectively, by p~ and p ~ and , defining (APh = (P),.B - (P)L.M
and (APh = (P)o,B- (P)o,M
(3)
we have, when both sides of the apparatus contain the reference gas with second virial coefficient B,
Similary, if the reference gas since B,
