Applied Math in Chem Lab

I just started taking two science classes, Biology and Chemistry, in the evenings. This week I participated in my first chemistry lab since 1988, complete with safety goggles and a Bunsen burner. It was so exciting! In the midst of all this chemistry, the neatest thing for me was helping another student with the math part of the lab—real, applied math.

For our first experiment, we were asked to compare the accuracy and precision of measuring 10 mL of water with a pipet and a graduated cylinder. One of the first steps was to calibrate a thermometer.

Did you know that thermometers are calibrated for a particular atmospheric pressure, and they give inaccurate readings if they’re at a different atmospheric pressure? To avoid inaccuracies, we first had to compare the thermometer reading for ice water to its actual temperature of 0°C, and the thermometer reading for boiling water to its actual boiling temperature of 100.36°C. (What, you say? Water boils at 100°C? Well, not at my atmospheric pressure it doesn’t.)

To determine the boiling point of water in our room, I looked at a barometer and found the pressure of the room, then looked in the CRC Handbook of Chemistry and Physics to find the boiling point of water at that pressure. The book wanted pressure in mBars, and our barometer was in mmHg (millimeters of Mercury), so I had to convert, leading to an atmospheric pressure of 1026.6 mBar. But the handbooks only gave the boiling points at 1025 mBar and 1030 mBar, with nothing between. Interpolation!

Next I found my thermometer reading for freezing water (3.5°C) and boiling water (100.0°C). Then I wrote an equation to convert my thermometer readings to actual temperature.

I’m skipping over some steps here, but you can see that some math is involved. The real intrigue for me was this: I was working next to another woman who also hadn’t done the school thing for a while. She’s been taking prerequisites for veterinary school, including Statistics last semester. At a later point in the lab, we needed to calculate mean and standard deviation of some of our measurements, and she was rock solid at calculating both of these by hand. (Calculating standard deviation by hand is no joke!) But writing a linear equation to convert measured temperature to actual temperature was a real struggle for her, so I helped her through it, with a strong focus on making sense of what we were doing so she could hopefully reason through it again when needed. And I’ll happily keep working with her on the math this semester.

There were many more steps in this lab, including more measurements and calculations. For me, this was a ton of fun! This whole experience made me think about two math topics that weren’t much emphasized when I was a student, but are now emphasized more and more: accuracy and precision, and statistics. I’m just thrilled that these concepts are a focus now, as they’re really relevant and important if you’re doing anything that involves drawing conclusions from measurement—but still, whether you’re in the “real world” or the chemistry lab, good old linear equations hold a place of honor in useful applied math.

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