Authors:
Rice University
Rice University
Worstell and Worstell, Consultants
Today, many Bachelor of Science Chemical Engineers graduate with little laboratory experience. Thus, they have little or no experience with laboratory-scale equipment. They also graduate with little experience at applying statistics to actual data sets.

In this presentation, we discuss an experiment designed to enlighten future Chemical Engineers about laboratory containers and delivery systems and the use of statistics to choose the appropriate container for making analytic-quality dilutions.

We ask students to fill a variety of laboratory containers to an identified mark on the container, then determine the accuracy and precision of the fill. To determine the accuracy and precision of each fill, they must perform the procedure in triplicate, at least. With the resulting data, they can calculate the mean, <x>, and the standard deviation, s, of the procedure. We also ask them to use a set of pipets to deliver a given volume, which is equal to the target volume used when filling each container.

The students are to identify, using statistics, the precision of each container and delivery system. We also ask the students to determine, statistically, which containers are accurate. The first task requires calculating s/<x>; the smaller this ratio, the more precise the result. The second task requires the use of the one-sample t-test, given as

Â t = |<x> -Â Î¼|/(s/N)

where Î¼ represents the target volume and N is the degrees of freedom for the comparison. This t-value is then compared to the t-value from a table of critical t-values. This comparison determines whether the procedure is accurate or not. We also ask the students to determine whether the containers and delivery systems produce similar or dissimilar fills. The students accomplish this task by individually comparing each data set to all other data sets via the t-test, which requiers using the pooled standard deviation for the test data sets.

Finally, we ask the students to make a 50:50 methanol/water dilution in triplicate and compare the variance of the dilution to the summed variance of each step of the procedure; for example (s2)Dilution = (s2)Scale+ (s2)Pipet + (s2)Container

From this comparison, they are to identify which step requires refinement. This last task generates significant student/instructor interaction, which we will discuss during our presentation.

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