edited bv JAMES 0.SCHRECK University of Northern Colorado Greeley. CO 80639 ~~
filtrotes e residues
~~~
~
An Investigative Density Experiment Richard A. Samsa Grove City High School, Grove City, PA 16127 Most laboratom manuals include an exercise involvine the calculation or density In these experiments the ma& of an obiect is measured bv " weiehine it on a balance. and the volu"me of the object is determined by measuring the water dis~lacedwhen the obiect is placed in a filled eraduated cyliider. The students then calculate the densitv of the obiect using the following formula. mass density = volume
- -
Students often accomplish this by following a step by step procedure that allows the determination of the densitv of kregularly shaped objects and objects that are too s m d l to accurately measure (13). Helping Students To Develop Their Own Procedure The purpose of such simple laboratory exercises is to familiarize the student with the skill of recording accurate data and following directions in order to accomplish a goal. One problem with this type of procedure is that the student follows the procedure without consciously considering the purpose. I n the laboratory excercise recommended here, in which a density determination is carried out, students must develop their own procedure. This has proven to be very beneficial because i t challenges students to actively solve problems and evaluate assumptions and techniques based on results. They are also asked to write a detailed procedure that would enable a student from another class to solve this same problem. The objective of the experimental procedure is to calculate the mass of rubber that had been removed from a twoholed stopper when the holes were drilled. We assume that the solid s t o ~ ~ eand r s two-holed sto~oerswere identical before any hbies were made. ~urth&ore, I restrict the students to weighing only one of the stoppers. The following procedure can be used to solve the problem. Experimental Materials two X5 stoppers, one solid and one with two drilled holes two graduated cylinders, 10-mL and 25-mL two beakers. 100-mLand 1-L a balance, Geighingto 0.01 g Steps in Developing the Procedure 1. Determine the mass of the solid stopper to 0.1 g by weighing it on a balance. 2. Determine the volume of the solid stopper using water displacement.
The usual procedure for obtaining this data is to add water to a graduated cylinder and to record the initial vol-
ume. ARer placing the stopper into the water inside the graduated cylinder, record the fmal volume. Subtract the initial volume from the final volume to calculate the volume of the stopper. . students will discover that a #5 stomer At this ~ o i n tthe will not fit inside a 10-mL graduated cylinder. Even i l k e were to use a larger graduated cylinder, the graduations would not show a detectable change in volume. Consequently, the students must change their plan somewhat. Some students turn to mathematics to c&ulate the volume of the stopper using the following formula. volume = %A& 3
+ R,R~+ R;)
where h is the height of the stopper; R1 is the radius of the top of the stopper; and Rz is the radius of the bottom of the stopper. Students then read the following thought-provoking story about Archimedes (4). Archimedes was a Greek scientist with an eye for practical matters. The most famous story about Archimedes is his great bathroom scene. Hieran, the king of Syracuse in Sicily, had a new crown. There was doubt in his mind that it was made of pure gold. The king suspected the goldsmith of cheatinghim by mixing cheaper silver in with the gold. The king asked Archimedes to find out if his crown was pure gold. Archimedes probably talked to himself about this problem. How was he to find out if the crown was purr gold? One day, Archimedes filled his bathtub to the very brim. As be got into the tub, water overflowed onto the floor. The farther he got into the tub, the more water he displaced. If he comnletelv, submereed himself. the overflow would have been the space ur vulum; occupied by his whole body. Then he thought of the crown. i t wns difficult to measure iw volume because it was such an odd shape. If he completely submerged the crown into a full container of water, the ovedow of water would be the volume of the crown. Taking an equal weight of pure gold, he also submerged it in a container full of water. If the volumes were the same, the crown would be pure gold. Archimedes was so excited by this discovery that he ran home naked through the streets shouting 'Eureka, Eureka!'(I have found it! I have found it!). Later he found out that the goldsmith cheated.
.~ ~
Because the crown displaced more water than a n equal mass of pure gold, the crown was found to be made of a material less dense (and less valuable) than gold. The story also suggests a method by which the student can detennine the volume of a stopper that is too big to fit inside a graduated cylinder.
3. The students then carefully place a 100-mL beaker filled to the brim inside a larger beaker (1-L). Then the solid stopper is placed in the water, causing the water to overflow. The smaller beaker is carefully lifted out, allowing the drops of water on the bottom of'the beakerto drip into the larger beaker. The water from the larger beaker is Volume 70 Number 2 February 1993
149
Sample Data Mass of solid stopper Volume of water displaced by solid stopper Volume of water displaced by two-holed stopper Volume of rubber removed from two-holed stopper (15.0mL-11.8 mL=3.2 mL) Density of rubber in stopper (16.62 gl15.0 mL = 1.I g/mL) Mass of rubber removed from two-holed stopper (3.2 mLx 1.1 g/mL = 3.5 g)
16.62g 15.0 mL 11.8 mL 3.2 mL
identical neither to each other nor to the solid stoppers before the holes were drilled. Due to this, grading the lab report on the accuracy of the results is not recommended. However, the written procedure used to obtain the results can be evaluated. Conclusion The procedure given above is a somewhat crude way to accom~lishthe stated obiective. The fun art of this labor a t o j i s obsening the &dents prepare apply the density concept to a new situation. This laboratory exercise gives students an opportunity to use higher-level thinking skills in developing a plan to solve a problem.
to
3.5 g
poured into a 25-mL graduated cylinder. The volume of water measured is the volume of the solid stopper. 4. The students can now calculate the density of the solid stopper using the following formula: mass density = volume
5. The students then repeat step 3 with the two-holed stopper and obtain its volume. (Allow the air bubbles attached to the holed stopper to dissipate before recording the volume.) Students can also assume that the holes in the stopper are shaped like a cylinder, calculating the volume of the holes with the following formula: Volume = 2nR2h where R is the radius of one of the holes; and h is the height of the hole. When rulers are used, this mathematical method is not very precise. 6. Subtracting the volume of the two-holed stopper from the volume of the solid stopper, the students then calculate the volume of rubber removed from the two-holed stopper. 7. Finally, the mass of rubber removed from the twoholed stopper can be calculated (see the table): mass of rubber = volume of rubber x density of mbber
Literature Cited 1. Tzimopoulos, N.D.;Metealfe, H. c.;Williams. J. E.:CastIra, J. F.M&m
Erratum: Chromatography of M&MCandies
,I
The last Filtrates and Residues feature, which ap-
3:
the paper by Marjorie Kandel, "Chromatography of M&M Candies" (page 98S989). The table as it should , : have appeared is reproduced below.
!: peared in the December 1992, omitted a table from ;
! i
Colors and Rt Values of the Candy Shells and Dyes Sample
16.62 g- 14.60 g = 2.02 g
Journal of Chemical Education
Colors after development
;j
FA valuesa
Yellow candy Orange candy Red candy Green candy Brown candy
wt of the solid stopper - wt of the two-holed stopper =
150
:14
1,
Discussion The results from this data were checked by comparing the experimental result (3.6 g) with the actual difference between the masses of the two stoppers. This is obtained by weighing both stoppers and then subtracting their masses:
The high percentage error obtained (80%)may be due to the crude procedures used to obtain the volume or the inaccurate assumption that the stoppers were identical before the holes were drilled. Several two-holed stoppers were weighed, and masses of 13.87 g to 14.97 g were obtained. This indicates that the two-holed stoppers were
Chemistry
LzbrotoryExpp?imnt.: Holt.Rioehartaod Wmton:Austin, 199(1:Erperiment3, p 30. 2. Davh, J. E.. Jr;Msnab. W.K.; McCIe1la0,A L.; O'Crmncrmn, P. R.Lzbormo'y M=nuol lor C&mis~:E%ptimnUondPh'mipl~s; D.C. Heath: Icdngtoh MA, 1982;E= penment 4, p 4. 3. Camhehael,L.N.;Haines, D.F;Smoot, R.C.Lzbomt~ryChemiahy;Merrill: Columbus, OH, 1983; b l l m e n t 3, p 25. 4. Bolton, R. P;lemphere. E.Y: Menesine, M.Action Ckrniafry;Holt. Rinehart and Winston: New York, 1979: p 20.
1 1
Yellow 0.43 Orange 0.35 Red 0.21 0.68,0.41 Blue, yellow 0.67.0.46, 0.37?, Blue, yellow, orange?, red 0.16 Tan candy Blue, yellow, 0.67.0.48, 0.30?, orange?, red 0.18 Tartrazine Yellow 0.54 Food color Yellow 0.58 'Except tor the lwd coor, whcn was measurm trom as ngle n n on CnromalaoraDhv mwr. Rt "alms were determsnm tram averaOlno2-3 wns, one'bnkilter'arid1-2 onchromatography paper. Tailing ma& iihard to determine exact spot positions, but the color composition (with the
.: ,
. !
