It’s that time of year again: labs are gearing up. Drawers are being filled with new glassware, students donning lab coats are beginning to fill the halls…the ol’ machine is revving up to roll again. For me, this time of the semester means emphasizing good practices when working up data and results. I’ve written in past semesters about significant figures and some of the interesting issues that come up when teaching them—it’s about the mindset, not the rules, I swear…!
Take percent yield, a measure that has been reported with false precision by countless numbers of students across the generations. Percent yield is really interesting because the balance is one of the most precise instruments that exist in general chemistry laboratories—depending on the range and precision of the balance, measurements with five, six, and even seven significant figures are possible. Thus, it seems like percent yields (which are really just ratios of masses) should in turn have five, six, or seven significant digits. The measured mass of product points to this level of precision.
Students often struggle to understand that the precision of the balance is irrelevant—inevitable variations between runs of the reaction introduce massive uncertainty into yields. Such variations are gargantuan compared to imprecision in balance measurements and essentially render the precision of the balance meaningless.
Movie times are a nice analogy. Say you’re headed to a 7:30 pm showing of Interstellar. You’ve got your fancy-schmancy phone with you, and it tells you the time down to the millisecond. At the moment the film begins, you note the time down (because you’re in a science-y mood, because you’re watching Interstellar…bear with me here). Later, when someone asks you what time the movie was, are you really going to say 07:31:05.717?! No way! You’re going to tell them 7:30 because obviously, showings scheduled for the same time on other days are not going to start at 07:31:05.717. Variation in the actual start time is large enough that only the “one-minutes” place is significant. (If your cinema is as unreliable as mine, that ones place is barely significant!)
Reaction yields work the same way. The precision of the balance, like the precision of your phone’s clock, is utterly irrelevant to the yield you should report. Although you may never run the reaction again—just as you may never watch Interstellar at 7:30 again—it’s critical to just know that the yield next time will be quite different from the yield this time. Likewise, you just know that the movie will probably start at some time between 7:25 and 7:35, but it will not start at exactly the same time as the showing you saw. The reported yield needs to take into account the extent of variation, just as the published movie time does. Thinking about the “science unseen”—the hypothetical runs of the reaction and their inevitable uncertainty—is critical.
In practice, ±5% variation in yields is common. In some cases, variations can be even higher and reporting only to the tens place (or in increments of 5) is appropriate. Okay, academic chemists often don’t follow this rule…but they should.