Measurement Errors: A Lecture Demonstration

Submitted by:

Checked by:

Robert J. Munn University of Maryland College Park , Md 20742

Becky J. Hickey University of Washington

Seattle, Washington 98195

The ideas of measurement errors, significant digits, preci- sion and accuracy are often intruduced early in an intnrduc- torv chemistry course. The followiny lecture demonstration can he used to realistically discuss precision, accuracy, aver- aging, data rejection, and significant digits. The demonstra- tion requires minimal equipment and requires about 5 min t o complete.

The equipment required is several identical 8% X 11-in. pieces of paper (preferably with rounded corners), some file cards t o record individual student results and several meter rules (preferably with protective metal ends). Some time he- fore the demonstration the metal ends of every rule hut one are removed and 1-2 cm sawed off each rule. The metal ends are then replaced as carefully as possible. In addition, each sheet of paper is folded 2 or 3 times in each direction so that it is difficult to flatten effectively.

The demonstration proceeds by selecting students and re- questing that they measure the length of a piece of paper in centimeters and record the result on a card. By using an ap- propriate number of measuring instruments a significant quantity of data can he collected in 5 min without losing the attention of the class. The results are collected and transferred to the board for discussion.

A typical set of results, obtained in the second class meeting of an introductory course, gave the following results: 29.4 cm, 29.4,29.5 cm, 27.5, 29.1 cm and 29.2 cm. A single meter rule (with a scale running in both directions) was used. The "ex- perimental" outcome can he controlled largely by the way the rule is handed to the student.

The first discussion point is devoted to the importance of recording the units of measurement.

The second point concerns the rejection of data. The au- dience is always agreeable to rejecting the "obviously wrong" measurement-27.5 cm. This measurement is crossed out, hut not erased, and the discussion turns to how we determine the "best" value for the length of the paper.

This discussion involves the ideas of certain and uncertain dieits and the average as the "best" value. In calculating the avrrage it is otien instructi\,t. toaska calc~~lntor owner in the audienct. to do the calc~llntion.'I'his will mme often than not yield an average with grossly inflated precision. After a dis- cussion of the relation of significant digits to precision we fi- nally turn to the term accuracy.

Tested Demonstrations is a monthly feature designed to present lecture demonstrations and experiments in a format convenient for classroom use. Readers interested in either submitting or checking demonstrations should contact the column editor. An outline of for- mat requirements was given on page 166 of the March 1976 issue of This Journal.

edited by

GEORGE L. GILBERT Denison University

Granville. Ohio 43023

This segment starts with a unit conversion of the standard paper size in inches to centimeters yielding a length of 27.5 cm. At this point we return to the original data and show that we have eliminated the accurate data and retained the precise data from the original set. Random and systematic errors can he discussed also if appropriate.

Finally, the "secret" of the meter stick is revealed, and a discussion of the proper method of using measuring devices of this type is given.

Formation and Dissolution of Precipitates

N. S. Nogar and W. A. Ja lenak Uniuersity of Nebraska Lincoln, 68588

The concept of limited solubility often proves difficult for first year chemistry students, particularly if they have not had extensive previous experience in the laboratory. An expla- nation of precipitation and dissolution is often more effective if accompanied by a demonstration. In general, however, it is difficult to demonstrate these coocents to a laree lecture class. "

In order to circumvent the problem, we have used light scat- tering to detect the presence of particles suspended in solu- tion.

A low power (0.5-mw) He-Ne laser beam is directed through a beaker containing -100 ml distilled water and a stirring bar. The light passes through the heaker without being scattered, and so cannot he seen from the side. A few ml of -1 M sodium chloride solution is then added to the heaker, followed by dronwise addition of -1 X lo-:' silver nitrate. As the silver ..~ - , ~ ~- ~ ~ ~~~~ ~ ~ ~

chloride begins to precipitate, light is scattered, and the laser heam traces a hrieht track through the solution. This can he seen even from tee rear of a largeUlecture hall if the lights are dimmed. Dissolution of orecinitates hv comolex ion formation . . c;rn he dem,,n.;tr,~trd then h\. the additiun <,I ammunium hy- droxide wlurion: au the ~ r e c i ~ i ~ a t e dissc~loes. the heam track . . becomt:.; dimmer ano dimmer untd it disappears cmpletely. Similar prwnl~lrrs can he used ro t'ollou. the r~rrripitnt~m and dissalutkm of a large number of salts (we have also demon- strated precipitation of silver chromate and lead bromide and the dis&lution of calcium carbooate by nitric acid, for in- stance).

The demonstration can also provide a semiquantative de- termination of solubility product constants. After preparing 100 ml of -5 X 1 0 - W AgN03 solution, a-5 X 1 0 - W NaCl solution is added from a buret until a precipitate is formed, as determined by the appearance of scattered light. Typical titrations yielded a Ksp for AgCl of 6 f 1 X lo-'", with errors due to the "eyeball" determination of scattered light.

CAUTION: hecause of the potential eye damage associated with the use of any laser, care should be taken to terminate the beam after it passes through the beaker, and to direct the reflection from the front surface of the heaker away from t h e class.

Volume 56. Number 4, April 1979 1 267