Knowledgebase

Online Chemistry Laboratories | Experimental Error and Uncertainty

Uncertainty and error in experimental work are unavoidable. By careful technique, such as calibration, purification, and averaging, errors can be minimized. We think one of the most important outcomes of well-thought-out general chemistry labs is when students learn to identify the sources of experimental errors and evaluate their relative significances.

In designing these virtual experiments, we took care to include uncertainties and errors that realistically represent those present in chemistry laboratories. For instance, when the experiment calls for students to weigh out 20 g of a powder and measure the mass precisely on our virtual balance, students will find it extremely difficult to pour exactly 20.000 g of the sample. Instead, as the powder is poured into the weighing pan, the pouring action may result in a resulting mass in a range (depending on the scale chosen) of say, 19 to 21 g. The balance accurately displays the mass to the nearest milligram, however, so the uncertainty is relatively small.

Furthermore, when students read the virtual balance mass display, the displayed value fluctuates in time, just as it does with a real-world balance due to vibrations, wind currents, and electrical noise in the balance electronics. The virtual balance readings will typically vary by 0.2-0.3 mg. These uncertainties can be dealt with by averaging the mass display over time or by making replicate readings and averaging.

How do we generate these random fluctuations in our virtual balance? We've put some thought into this issue. Displayed values include an appropriately scaled error term from a random number generation. It's important that this error term be random and that it has a magnitude and distribution similar to those in real experimental apparatus. For lab balances, display errors of this type tend to follow a Gaussian distribution about the true mass. For instance, the left figure below shows 100 random values for the error term added to the true mass. The vertical axis shows each random value generated sequentially. The terms are scaled to the range of -0.3 mg to +0.3 mg. As seen in the right figure, the error terms are distributed in an approximately Gaussian shape. (When we test these functions by generating large numbers of terms, the distribution is smoother and more Gaussian.)

 Eu1

This may seem like a simple and minor correction to the display values. However, we've found that simulations often fail when virtual data is presented without regard to both the magnitude and distribution of real-world errors. Simple random number generators available in most programming languages or spreadsheets are not suitable for this application, they provide non-physical distributions such as that shown below:

 Eu2

When these non-physical error terms are added to balance displays, large and small errors appear with the same frequency. Within a few seconds, an experienced scientist will detect that the virtual display appears unnatural. Students exposed to this type of display develop a false sense of experimental error, and of course subsequent error analyses are potentially flawed.

Besides the virtual balance, all the virtual instruments used in OnlineChemLabs experiments include random error terms designed to simulate the random errors in real-world instruments.

In addition to the random error terms, our virtual instruments can also generate realistic systematic errors. For instance, in a titration lab, we have students standardize the concentration of an NaOH solution by use of a primary standard calibration reagent. The pipette reproducibly delivers a set volume of solution (nominally 10.00 mL), but the true value might be 95% (or, say, 103%) of the nominal quantity. Students must use the primary standard to work through the calibration to determine the true pipette volume.  Discussion questions probe student comprehension. Students are asked whether such systematic errors generate incorrect results, or whether these errors will cancel in properly designed experiments. In this way, virtual labs help students understand error and help train them for real-world experimentation. For simplicity, most instructors will prefer that the systematic error be identical for all students and all iterations of a particular lab (and this can be a reasonable analog to the real-world situation), however, more complex systematic error scenarios are also possible.