A Convenient Device to Demonstrate Statistically Based Sampling Error in a Particulate Mixture Cork or plastic Stopper
Plexiglasatube of length and diameter to accornodate 10 h a d 8
-10
mm high tapered coupling, machined from Plexiglas
- 60
mm long by 36 mm I.D. Plexiglae or Dolyelhylene tube
An undergraduate experiment illustrating this subject has been reported previously.' Here we describe a rapid, inexpensive demonstration suitable for inclusion in a lecture on the topic. The apparatus is shown at Left. The plastic materials used are inexpensive and readily available; only a few minutes' machining is required. Dimensions can he adjusted to fit bead diameter. The main body should be opaque to avoid any hias (conscious or unconscious) in the sampling operation. A 50-50 mixture of two colors of 5-mm beads from a hobby or craft shop provides the particulate population to be sampled. Thenumber of beads can vary but the main body should not be filled to more than two-thirds of its capacity or mixing becomes difficult. Any projections occurring during molding should be removed to promote a freely flowing mixture. The size of the sample is determined by the leneth of the small tube: a 10-bead samole is convenient. By inverting t6e apparatus a sample of beads is taken and "analyzed" visually for compositian. Twelve to 16 trials can be made in 2 min. (Audience participation is recommended.) The mean, standard deviation, and relative standard deviation (RSD) are calculated immediately using an electronic calculator. The derivation of Benedetti-Pichler2 yields the equation ~
~~
Cork or plastic s10pper
where p is the probability of occurence of one type of particle, d l its density,
PI its percent composition in the component of interest, P , the overall average composition, d the average density, and n the tatal number of particles in the sample. For a 50-50 mixture the RSD for a 10-bead sample as calculated by this equation is 32%. (Here PI is taken to be 100,and P2 to be 0.) "Experimental" values of RSD are typicsly within 5%of this. Critical students may contend that such a mixture is unrealistically coarse. Displaying a sample of a mixed-formulation granular fertilizer provides an effective counter argument.
B. Kratochvil University of Alberta Edmonton. Alberta
T6G 202
252
Journal of Chemical Education
R. S. Reid University of Saskatchewan Saskatoon, Sasktachewan S7N OW0
