When taking a measurement or performing an experiment, there are many ways in which uncertainty can appear, even if the procedure is performed exactly as indicated. Each experiment and measurement needs to be considered carefully to identify potential limitations or tricky procedural spots.
When considering sources of error for a lab report be sure to consult with your lab manual and/or TA, as each course has different expectations on what types of error or uncertainty sources are expected to be discussed.
Types of Uncertainty or Error
While these are not sources of error, knowing the two main ways we classify uncertainty or error in a measurement may help you when considering your own experiments.
Systematic Error
Systematic errors are those that affect the accuracy of your final value. These can often be greatly reduced or eliminated entirely by adjusting your procedure. These errors usually exist and are often constant for the duration of the experiment – or if changing slightly, like an instrument reading “drifting” with time, they are in a consistent direction (higher or lower than the “true” value).
One example of a systematic error could be using a pH meter that is incorrectly calibrated, so that it reads 6.10 when immersed in a pH 6.00 buffer. Another could be doing calculations using an equilibrium constant derived for a temperature of 25.0° C when the experiment was done at 20.0° C.
Random Error
Random errors are those that primarily affect the precision of your final value. Random error can usually be reduced by adjusting the procedure or increasing skill of the experimenter, but can never be completely eliminated.
You can observe random error when you weigh an object (say, recording a mass of 1.0254 g) and when re-weighing it, you get a slightly different measurement (say 1.0255 g). Another example is the interpolation of the final digit on a scale, as in the example earlier in this section. In a group of people observing the same meniscus you expect to get a range of readings, mostly between 25.5 – 25.7 mL.
Some Common Sources of Error
Every experiment is different, but if you are analyzing your procedure for potential sources of uncertainty, there are a few places you can start:
Assumptions About Physical Status
Every procedure comes with some assumptions. Perhaps you assume that the room temperature is 25.0° C (most UCalgary building HVAC is set to 21 ° C and fluctuates around that). Maybe you assumed a typical ambient air pressure without taking a measurement of the actual value. Perhaps you further assume that physical constants, like equilibrium constants, enthalpies, and others, do not change (much) from 25.0° C to the actual ambient temperature. Perhaps you used a “literature value” rather than measuring that quantity under your own experimental conditions.
You may have also made assumptions about your reaction – that it went to completion, or that you were able to detect a colour change visually that indicated completion (but may have really been 60, 80, or 90% complete). Perhaps there is a “side reaction” that can happen, or your product was not purified or dried thoroughly in this procedure.
There are many places where assumptions (appropriate or not) appear: depending on the difference between assumed and real conditions, this may add a negligible amount of uncertainty, or even a few percent, depending on the measurement.
Limitations on Measurements
As we have seen throughout this section, every measurement has a limit – often expressed through its recorded precision or significant figures. Some equipment can be used more precisely than others: for example, a Mohr (or serological) pipet can at best be used to $\pm$ 0.1 mL precision, while a transfer (or analytical) pipet may be used to $\pm$ 0.01 mL precision.
The less-precise equipment is usually easier and faster to use, but when precision is important, be sure you have chosen the appropriate glassware or equipment for your measurement.
Limitations on Calculations
Generally, laboratory calculations reflect the precision of a measurement, rather than limiting it (or directly affecting the accuracy). However some particular points can be sources of uncertainty.
Use of physical constants can limit your accuracy or precision if you use a rounded version (e.g. $3.00\times 10^{8}$ m/s instead of 299 792 458 m/s. As discussed above, using a value that is determined for a different physical state (temperature, pressure, etc) may also introduce some error.
Creating and reading graphs can be a major source of uncertainty if done sloppily. Remember you can only read your graph as precisely as your gridlines allow: most people can accurately interpolate to 1/10 of a division at best. You may also (manually or by regression) plot a line of best fit: this line is only as good as your data, and your calculations based on it may be limited by the precision at which you have drawn or calculated this line. The video below gives some starting tips for using Excel to create a graph appropriate for a first-year chemistry laboratory report.
Mistakes
“To err is human” … but not all such human error is acceptable in a procedure. Some limitations are unavoidable: for example a colourblind person reading pH from a colour indicator, or a time-dependent procedure step that is tricky to complete quickly and accurately. Often, these can be designed out of a procedure, or corrected by repeating the measurement.
True mistakes along the lines of “I overfilled the volumetric flask” should be corrected in the lab if at all possible. This may be (for example) re-making the solution, or measuring the overfill to determine the true volume used in the flask. There is usually no excuse for allowing a mistake to remain in your experiment, especially if there was time to correct or repeat the measurement. If a mistake happened and you could not correct it, you should include that in your lab report – but know that it may not be enough for a complete “sources of error” discussion.