Is Volume Conserved? A First General Chemistry Experiment John Olmsted, Ill California State University. Fullerton. Fullerton. CA 92634 In freshman general chemistry courses, the designer of initial lahoratory experiments is faced with a dilemma: how to introduce the student to meaningful scientific inquiry while hisher exposure to the fundamental laws of chemistry is just beginning. Many laboratory syllabi deal with this problem by beginning with a largely statistical exercise: weighing pennies, popping popcorn, or the like. While such ex~erimentsreauire little chemistrv and have the virtue of stressing variah~lityin srientifir measurement, they do not immediatelv involve the student in the intrieuine-auestions . of chemicaiscience. Ideally, one would like to have a first e x ~ e r i m e nin t eeneral chemistry that introduced the student t o scientifickethodology, afforded practice in the essential laboratory skills of measurement, and illustrated some fundamental chemical relafionship, all without requiring.any . chemical s o ~ h i s t i cation or expensive materials and equipment. An experiment which meets all of these criteria is an exploration of the change of volume upon mixing two common liquids. Such an experiment, as described below, has been used successfullv for two vears in the Honors General Chemistry h ah oratory a t ~ a l i f b r n i aState University, Fullerton. Students are surprised to discover that volume is not conserved under conditions-mixing of similar liquids -where they intuitively expect it to he, and while the details of the interactions causing volume change on mixing are rather sophisticated, the fundamental notions of molecular size and i&ermolecular forces as determinants of volume are understood by them. ~
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Design OT the Experiment The experiment is designed to he entirely self-contained, except for a single standard: the density of water, which is provided as a graph of density as a function of temperature. Students carry out the following sequence of operations: 1) Calibrate a 10-ml volumetric flask. The flask is weighed dry
and filled to the mark with distilled water of measured temperature. The calibration is done at Least thrice to establish precision. 2) Determine density of a second Liquid. The calibrated flask is filled to the mark with a liquid other than water (acetone, methanol, ethanol, isopropanol, acetonitrile, p-dioxane, dimethyl sulfoxide are all suitable) and weighed to obtain the liquid's density. 3) Calibrate a transfer pipet. A 5-ml transfer pipet is used to deliver five successive aliquots of each of the two Liquids into a small Erlenmeyer flask,which is weighed before and after each transfer. From mass differencesand liquid density, the volume delivered by the pipet is computed. 4) Test for volume conservation. Following the five transfers in step (3,the pure liquid in the Erlenmeyer is used to fill the
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Journal of Chemical Education
calibrated volumetric, which is then weighed. From the resulting density and the total mass transferred to the Erlenmeyer, the volume of liquid in the Erlenmeyer is computed and compared to the volume delivered. 5) Prepare liquid mixtures. Using the calibrated transfer pipet, a series of mixtures of the two liquids of varying composition is prepared. Volume proportions are 15+5, 10+5, 10+10,5+10, and 5+15 ml. 6) Determine density of the mixtures. After thorough mixing and measurement of the temperature, each mixture is used to fill the calibrated volumetric flask to the mark, and it is then weighed. 7) Test for volume conservation. From the~oioet .volume. .~.the~ expected total volume of earh mixture is computed. From the volumes and densities of pure liquids, the total mass of each mixrure is rompured. From these masses and densities of [he mixtures, the actual volumes of the mixtures are computed and compared with the expected volumes. ~~~
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Materials and Equipment Distilled or deionized water: 100-150 mllstudent Acetone for rinsing glassware, optional hut convenient 100 ml of any of the following per student: Ethanol ~ ~ ~ ~ ~ ~ Methanol Isopropanol Acetonitrile Dimethyl sulfoxide p-Dioxane Acetone One per student of the following: 10-mlvolumetric flask 5-ml transfer pipet stoppered 50-ml Erlenmeyer flask 0-100' thermometer pipet bulb Pasteur pipets and rubber bulb graph of density of water versus temperature 0.1-mg-precisionanalytical balance, one for every four students Computations T h e calculations required in this experiment involve either the density equation, p = mlV, or the law of conservation of mass (additivity of masses), mbw = xim,. T h e flask calihration (operation (1))is achieved using known water density and measured masses:
VW = (%M - mrmptJ~Pta
(1)
T h e density of the second liquid (operation (2)) and of the mixtures (operation (6)) is computed from this calihrated volume and measured masses:
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Calibration of the transfer pipet (operation (3)), like flask calibration, is achieved using the known density of the liquid and mass differences. The tests for volume conservation (operations (4) and (7)) involve comparing the expected volume (sum of the pipet volumes added) with the actualvolume as obtained from the density of the final liquid and its total mass:
Here, A and B signify the two pure liquids, VA and Ve are pipet delivery volumes, and n A and ne are the number of aliquots of each pure liquid constituting the mixture. Comparison of Vadud with Verpectedgives the volume change on mixing, which is best reported as a fractional quantity: AV,d'dd
= (V&d - Vex+)/Vadd
(5)
This fractional volume change is then plotted as a function of solution composition, either as volume percent or as mole fraction depending on the level of sophistication of the students. Results A set of typical student results, for the liquid pair water/ acetone, are displayed in Tables 1and 2 and the figure. The stated deviations represent mean deviations observed by the student, a freshman without prior college chemistry laboratory experience. The volume changes observed on adding together aliquot9 of pure liquid are consistent with conservation of volume, within the stated deviations. When water and acetone are mixed, the observed volume changes are more
Table 1.
Repreaentatlve Student Results for Pure Llqulds
than 10 times as large (note error bars in the figure), clearly demonstrating nonconservation of volume for this liquid pair. The 0.1% apparent volume change measured upon mixing water with itself suggests that students should be able to determine reliably volume changes upon mixing in the range of 0.2% or meater. This is verified from student results on mixing acetone and isopropanol, liquids that on mixingshow a small t0.1-0.59 depending on composition) positive volume change. The &dent r<s are consistently positive, falling in the 0.1-0.4% range, in good agreement with literature risults. As indicated in Table 3, numerous liquid pairs exhibit volume changes on mixing sufficient to be suitable for student measurement. Pairs including water show the largest effect. uo to 40 times the uncertainty in the measurement Dlscuoslon The Conservation of Volume experiment described here has pedagogical value a t several levels: it stresses basic laboratory skills, it requires thoughtful data manipulation, it is nearly self-contained, and it yields a challenging, counterintuitive result. Besides giving practice a t the fundamental skills of weighing and volume delivery, the experiment incorporates calihration and techniaues. each in a simple way. (Is ~ ~ reolication ~ ~ the 10-ml fla& exactly 10 mi? Does a 5-ml pipet always deliver the same volume?) Thus, without requiring chemical sophistication, it lays a groundwork of sound experimental technique on which later experiments can build. Although the data collected are absolutely fundamental (masses and temperatures), they lend themselves well to a variety of data-treatment techniques. Graph reading is required in the initial calibration, when the appropriate water density must be read from a density-temperature plot. ~
volume (ml)
10-ml volumewlc flask delivered by 5-ml pipet (water) delivered by 5-ml pipet (acetone) change on adding water to water (fraction) change on adding acetane l o acetone (traction)
Table 2.
RepresentativeStudent Results for Llquld Mixtures
kv
AliqUotS Water
Allquois Acetone
XH#
p,-
1
3 2 2 1 1
0.576 0.671 0.810 0.890 0.924
0.8713 0.8936 0.9283 0.9549 0.9695
1 2 2 3
9.980 5 ,004 4.986 i .005 4.983 i ,004 -1.3 x 1 0 ~ -3.5 X lo-'
Table 3.
AVm
V
-0.696 -0.592 -0.756 -0.422 -0.486
-0.036 -0.041 -0.039 -0.029 -0.025
Maximum Volume Change on Mlxlnga
mixture waterlacetone waterlmethanol waterlethano1 waterlisopropanol waterlaeetoniwlle wsterlpdioxane acetonelmethanol a~etonell~0pr0p~no1
volume change (%)
-4.5 -4.0 -4.0 -3.5 -2.0 -1.8 -0.7 +0.4
.landOit~nPtBln. "N-Ical Data and Functional Relationships in Science and ~ednolwy,"~ a Series, w (Heliwege. K.H.. ~ d l Oovp : iv. vol la, b.
xacetc.m
Change of Mlume (-five percent) on mixlng acetone wl* water, as a function of r o l e percent acetone. Poima and e m r bars reprasem student data. solid line is literaturedata.
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June 1986
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Graph construction is required in order to display the variation of volume change with composition. The density relationship is used in three different ways, to compute volume, density, and mass. Questions of the precision of measurements arise in a natural way as the calibration volume is checked, the pipet delivery volume is replicated, the conservation of volume for a single liquid is tested, and the effect of temperature on the results is considered. One measure of the elegance of an experiment is how nearly i t approaches self-containmenthow much information must be independently supplied. This experiment comes very close to self-containment, requiring only the density of water as supplied information. In our view, the most attractive feature of the experiment is the unexpectedness of the result. Intuitively, students expect to find that liquid volumes are conserved. The finding that, on mixing two apparently similar liquids, there is a definite change of volume presents an immediate challenge. The natural response-why is that?-can be used to turn student's thoughts to intermolecular forces and other determinants of density. At the same time, the counter-intuitiveness of the results calls student attention to the need t o
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Journal of Chemical Education
approach experiments with an open mind, without prejudgment. As described here, the Conservation of Volume experiment requires approximately three standard 2%-hour laboratory periods. In the Fullerton general chemistry laboratory program, which comprises six experiments, each of 2-3 weeks duration. a fourth lab veriod is allocated. durine which students pair up and deteimine the volume change o i mixing the nonaqueous liquids that each was assigned. The experiment can also be compressed, albeit a t some loss of elegance, hv eliminating the calibration stem and usine the nominal voiumes of flask and pipet. As able 1show; the error introduced by doing so is only about 0.2%. A singleperiod laboratory exercise results if the procedure is reduced to determining the densities of two pure liquids, then preparing two or three mixtures and determining their densities. Acknowledgment
The author acknowledges the cooperation of the fall 1983 and fall 1984 students in Honors General Chemistrv at CSUF, who served as the proving ground for the experiment. The re~resentativestudent data were taken bv Stunn Olmsted, afreshman a t MIT.
