Figure 7 shows the progress of the bands for one set of conditions. This figure was generated by pausing the program during a run and printing the screen. The resulting "chromatogram" simdates the peaks viewed fmm right to left. Conclusion In summary, icon-based programming with graphical display offers a new, exciting, and powerful tool for developing classroom demonstrations. I encourage others to devise virtual instruments for classroom demonstrations and to share them with other LabVIEW users.
The Water Drop Experiment Determining the Surface Tension of a Liquid by Automating the Drop- Weight Method H. Alan Ewart and Kenneth E. Hyde State University of New York College at Oswego Oswego, NY 13126
The measurement of the surface tension of liquids and solutions has a long history (I)and interesting applications. For example, the variation of surface tension may be used to estimate Avogadro's number (2) or the cross-sectional area of a solute (3). The methods most commonly used for the determination of this physical property are the capillary rise, maximum bubble pressure, and DuNoy ring method. A fourth method (41, the drop-weight method, is not included in recent textbooks (5,6). It uses a laboratory balance and involves repetitive mass measurements. It may be used to illustrate the advantages offered by automated data acquisition. Due to the many drop masses obtained, the method serves to illustrate the usefulness of the spreadsheet program in the physical chemistry laboratory, and it complements articles in this Journal (7) and its computer software journal (8).Classical probability calculaiions may be im-piementrd, and a satisfacwry description of the distnbution of the individual drop masses about the mean is obtained The Method W. D. Harkins pioneered (9)and later reviewed (10) the use of the drop-weight method. In the original experiments, drops are collected, and the total mass is divided by the number of drops to obtain the mass of a n average drop. Our automated procedure involves the collection of over 100 drops and allows for the statistical analysis of the data as well as the surface tension of the liquid. The following expression relates surface tension (yl to the mass (m)of a drop of liquid that falls from the end of a tube of radius r.
a
'= 2nrF
where g is the acceleration of gravity, 980.7 d s 2 ; and F is a correction factor that is a function of r W 3 . The volume V may be calculated from the drop mass and liquid density. Tables that list the variation of the correction factor F with r W 3 are available (11). As an example of the calculation, we use the average water drop mass from the room temperature data set pre'Lab Crest Scientific, Fischer and Porter Co., County Line Road, Warminister, PA 18974. 8AIN Plastics Inc., 249 East Sandford Blvd., P.O. Box 151, Mount Vernon, NY 10550.
814
Journal of Chemical Education
u Figure 9. The water drop apparatus. sented in Figure 8. The average mass of a water drop is 0.0868 g when a tube with an inside radius of 0.299 cm is used. The correctionfactor F i s estimated to be 0.6136from the table (11)(rN'" = 0.6853). Thus, the surface tension for water at rwm temperature is calculated as
This is within 2% of the reported value (11)of 72.1 dynelcm a t 20 'C. It is not very temperature-dependent (72.9 a t 25 'C). The Apparatus A diagram of the apparatus is shown in Figure 9. An Erlenmeyer flask is the receiving vessel. The pressureequalizing tube maintains a constant drop rate during the ~ e r i o dof data acauisition (12). . . All other Darts are available Hs components of a commercial chromatography column,7 but a low-cost alternative is a laboratarv buret. The reservoir is directly connected to a throttle valve with a coupling. A tapered threaded teflon tip supplied with the valve may be used if it is cut square. We preferred to fabricate a tip drilled from teflon rods so that the inside radius (0.299 cm) was within the range (0.25-0.35) suggested (10). ~roducingthe most accurate results for all lia;ids and tipmateria&. To use the value of the inside radius of the tube, the drop must form properly a t the inside diameter of the tube. Thus, the liquid must not wet the surface material. We have used teflon tubes with degassed water or ethanolwater mixtures up to a mole fraction of 0.1 to meet this requirement. The Computer Interface An electronicbalance with a n asynchronous serial ASCII interface is used to measure the individual drop masses. The cable required to connect the balance to the serial port of the computer is available from the balance manufacturer. All that is required is a standard crossover serial cable with a DB9F connector a t the balance end and an appropriate connector for the computer a t the PC end. (We used a DB25F connector (131.)
GAUSSIAN DISTRIBUTION SUPERIMPOSED ON ACTUAL DISTRIBUTION
INCREMENT
Figure 10. Experimentaland calculated Gaussian distributionsfor the water drop experiment. Automated Data Acquisition A short QUICKBASIC oroeram was written to acauire the data an> output it to fiie. Once the cable is a t t i h e d and the droo rate is adiusted to 1 dro~l20s, the oromam prompts for'the number of drops to becolle&d. ~ a t cola lection requires about 20 min and produces a spreadsheetreadable file t h a t is written to disk. Copies of t h e QUICKBASIC program and the spreadsheet shown in Figure 8 are available from the authors.
a
Spreadsheet Statistical Analysis The drop-weight data may be used to illustrate the concept of a distribution function. Advantages in experiments that perform this task and the necessary background material have appeared in this Journal (14).Figure 8 shows a spreadsheet page from a n abbreviated (35-point) data set. We call this a work sheet. At the conclusion of the water drop experiment, only the first two columns have data entries.
Column 1 contains the drop number. Column 2 contains the total accumulated weight after a drop has fallen and halanee stabilizationhas occurred. Column 3 calculates the mass of individual drops by subtracting successive mass readings in column 2. The minimum, maximum, average, and standard deviation of the individual drop masses are reported at the hottom ~ ~ -of ~- -column 3. These are calculated usine the soreadsheet's statistical functions. The average drop mas; is all that is reauired to calculate the surface tension of the liauid. The kmaining columns in the work sheet are used foi the statistical analysis of the data. The entries in column 4 are labeled EXPER. RESIDUAL and represent the difference between a single drop mass and the averme &ODmass. If classical ~rohahilitytheory applies, theseresid;als should approximate a daussi& distribution. The umer right three columns (5 through 7) are used to calculaiLthe number ofexperimental residuals that fall in a given value range column 5, FREQUENCY DISTRIBUTION BINS,. The results are displayed in a frequency distribution table tcolumn 6, EXPER. FREQ. 1)ISTKB... Thcsc rcsults are normalized by lvidingeach value hy the residual count (351, and the results arc shown in the column 7 rNORM. EXPI.:I(. PROB. DENSITYJ. ~~
~
The lower three columns on the right-hand side of the work sheet are used to calculate the eaussian distribution of residuals. The cnlculation uses the individual residual (Axi) and the standard deviation of the drop residuals (0).
Aeain. the entries in this column mav be normalized bv diviYdingby the sum of column entries (6.00035) to produck the entries in column 7 (NORM. GAUSSIAN PROB. DENSITY). Figure 10 compares the Gaussian probability densities with the exoerimental ~robabilitvdensities. This experimeni is ideal fordoing a propagation of errors calculation. Based on our micrometer measurements of the diameter of the drill, a reasonable estimate of the error in the diameter was determined to be 0.001 in. Because this error changes the value of the correction factor F by a negligible amount, i t was assumed constant. Using the standard equation for the propagation of errors below gives a value of q 0.34 dyneslcm.
Our value is outside the expected range of experimental error. This result and all of the student data had errors that produced a surface tension that is too high. Harkins (10) suggests that it takes at least 1min to reach thermodynamic equilibrium. Drops that do not attain equilibrium will have drop masses that are too large, leading to an error in the direction we observe.
Simulation of X-Ray Powder Diffraction Qian Pu University of Suzhou Suzhou 215006 People's Republic of China
X-ray powder diffraction is a very important experiment in physical chemistry (1548).Students determine the lattice type and the lattice constants of a cubic crystal from the X-ray diffraction pattern using a powder sample. Then they calculate the size of the unit cell and the density of the material. For lack of funds, many laboratories do not have X-ray equipment available. Each student is given an X-ray powder photograph from which the required measurements mav be carried out. Althoueh there is Dedaeo&dcal value in det&nining crystal structure by th;s met
