Introduction
In our metaphorical STEM toolbox, there are two main compartments: the analytical skills compartment and the personality traits compartment, i.e., compassion, humility, resilience, and perseverance.
We have already discussed one of the analytical skills, translative communication. The next two tools we must sharpen aren’t gadgets or pieces of hardware; they are our own mental processes and insight. I bring these to your attention because I learned of their importance through my personal experiences during my first and second years of college.
For example:
Imagine you’re sitting in a chemistry class, and your teacher asks you to calculate the mass of of water, and you spend several minutes carefully punching numbers into your calculator, only to proudly raise your hand and announce to the class that a volume of water weighs
You don’t question your result. You don’t pause to consider that you’ve just described a volume that has the same mass as 10 1-liter bottles of water or 20 pounds of sugar. Sometimes we trust the “black box” in our hands more than our own common sense. This is the danger of the $130 Calculator: when the battery dies, or a decimal point is misplaced, we’re lost, we’re left without a good answer. How easy it is to forget that the best calculator we have is the one between our ears.
Personal Commentary
I attended high school during the early 1970s, and at the time, calculators did not play the same role in the classroom as they do today. As a matter of fact, throughout my high school years, I never owned one. I either wrote out the calculations on paper or used a slide rule. There was no such thing as a graphing calculator in my high school or college years, so all our graphs were hand-drawn. This gave me a tremendous advantage not only on my ACT exam but also throughout my career.
It was not until my freshman and sophomore chemistry courses that I learned the importance of the following tools for my STEM toolbox. These tools may seem simple, but I guarantee they will save you time and prevent numerous mistakes in your calculations.
Sidebar: Mass vs Weight
In your middle and high school science classes (especially Chemistry and Physics), you spend a lot of time learning that mass and weight are different. It can be confusing because when you place an object on an analytical balance, the result, what we traditionally designate as “weight” of the object, reads in grams or kilograms, the units of mass.
Remember –
Mass is Matter: Mass is the measurement of how many atoms are packed into an object. It is an intrinsic property. If you take a 10-gram sample of copper to the Moon, Mars, or the center of the galaxy, it still has a mass of 10 grams because the “amount of copper” hasn’t changed.
Weight is a Force: Weight is a measure of the gravitational tug-of-war between the Earth and your sample. Because gravity isn’t the same everywhere (it’s slightly weaker on top of a mountain than at sea level), your “weight” actually changes depending on where you are.
How Does an Analytical Balance Work?
An analytical balance is a complex instrument that converts the “weight” of an object, which has the units of Newton’s in the MKS system, to the units of “mass”, grams or kilograms, based upon the strength of the Earth’s gravitational field at that location.
The Golden Ratios
Golden Ratio #1: The Chemist’s “Compass”: “The “1-1-1” Rule.
Before you touch the keypad of your calculator, you should memorize the “The 1:1:1 Rule.” For liquid water at standard conditions, there is a perfect, elegant relationship that serves as a universal “Fact Check”:
If you can visualize this concept, you can calculate with certainty. of water is roughly the size of a standard sugar cube . If you hold that “cube” of water in your hand, it has a mass of exactly . does the 1:1:1 Rule apply to your work? In the lab, the 1-1-1 Rule confirms that your math is correct.
Example 1:
If you calculate that of a dilute aqueous solution is equivalent to , you can refer back to this rule. “If , how can ? You’ve just described a liquid denser than lead.
Example 2:
If you calculate that of distilled water has a mass of , the 1-1-1 Rule screams at you: “Wait! should be about . Something is wrong by a factor of twenty!”
This is more than simply math; it’s spatial reasoning. The 1:1:1 Rule turns abstract numbers back into physical objects. It bridges the gap between the metric prefixes that trip so many students up.
It is the ultimate “Reality Check.”
The Golden Ratio #2: Finding the “Micro” in the “Milli”
To truly understand and master the concept of scale, we have to go smaller, from milliliters down to microliters (1/1000 of a milliliter). The second “Golden Ratio” to understand and then memorize is the Drop:
This ratio should help you realize that isn’t just a number; it’s about 20 drops from a pipette. When you see in a lab procedure or on an exam, you should immediately think “10 drops,” not just a string of zeros. This mental translation turns a cold calculation into a physical action.
Conclusion
The next time you are working in the lab and are asked to determine the mass of water needed to fill a container, try this: first, look at the volume of your container. Estimate the required mass of water using the 1-1-1 Rule. Then, and only then, use the calculator.
If the calculator disagrees with your gut, don’t assume your gut is wrong. Check your decimal points.
