Ink Tea Stone Leaf

At my tutoring job, I have an opportunity to re-familiarize myself with subjects I have not touched in a while. Certain types of questions tend to come up in waves, as groups of students encounter the same conceptual difficulties at around the same time. By the time a wave crests, I am refreshed enough to offer practical guidance to even the most bewildering problems. At the same time, I can take a little time to appreciate the little steps of logic and skill that form the basis of the sum of human knowledge. Marvelous things!

Today a student brought in a question which had her peer group flummoxed, not only with regard to procedure, but the base level of comprehending-what-the-hell-is going-on. That’s right, folks: high school chemistry, and the balancing of the equations of chemical reactions. Behold the dread thing, in unbalanced form:

H₂SO₄ + NaOH —> Na₂SO4 + H₂O

Now, to your seasoned chemist, this is not even a little bewildering. Not only do they perceive, without even so much as a glance at the periodic table, the significance of all those letters and subscripts; they also find meaning in their particular arrangements. Looking on the left side of the equation, they immediately know the hydroxide ion (OH) and the sulfate ion (SO₄) when they see them. They thoroughly understand the convention of writing the symbols of these negatively charged entities after those for the positively charged hydrogen (H) and sodium (Na) ions that they are bonded to. Glancing to the right side of the equation, they immediately grasp that the sodium ions have ditched their hydroxides and evicted the hydrogens, to take their place alongside the sulfates and form sodium sulfate (Na₂SO₄); meanwhile, the free hydrogens have teamed up with the hydroxides to form water (H₂O), as they are wont to do. Perfectly regular: nothing out of the ordinary here.

But to your chemical novice, your high school sophomore? Gobbledygook. Impenetrable arcana. Gibberish. The very essence of bewilderment.

There are some conceptual hurdles that need to be overcome before one can understand what is going on, let alone accomplish the required balance. There is of course the atomic theory of matter, whereby the student internalizes that (1) atoms are real things that actually exist, (2) all matter is made entirely out of atoms in particular combinations, and (3) those combinations can be changed to transform material substances. Really proving this is beyond the scope of most high school classes; you kind of just have to assert it and wait until it seeps into the various crevices of the brain.

After that, you have the literacy problem; reading the notation of chemicals requires a new, specialized literacy that must often be taught on the spot. Your student needs to know that a chemical element’s symbol consists of either one or two letters, and that if it has two letters the second one will always be lower case, and that if a letter is lowercase it is always the second letter in a two-letter symbol. You’d think that’s simple enough, but it’s a big stumbling block for many kids, who do not always pick up on these patterns without first being alerted to them.

Furthermore, your student has got to know what elements the symbols represent if they’re going to be able to keep them straight. They must know that H is hydrogen, O is oxygen, S is sulfur and definitely not sodium, because sodium is Na and the reason for that is linguistic rather than practical; you don’t need to speak any Latin, but it helps.

Finally, subscripts. Chemistry is probably the first occasion most kids have of encountering a subscript, and they are the lucky ones who know the word for such things by the time they reach high school and can readily distinguish them from coefficients (another word it cannot be assumed they fully understand).

The student who brought us this problem was struggling with much of the vocabulary. Her peers could not fill in the gaps for her. The string of letters and numbers nearly paralyzed their capacity to ask productive questions or employ critical thinking. Intervention was required.

I asked the group to consult the periodic table and determine how many distinct symbols were being used, and what the names were of those elements represented by those symbols. I nearly always ask my groups to do this with chemistry questions, because it’s nearly always helpful, and it’s important to teach students to make effective use of the resources at hand (especially when their teachers have gone out of their way to make those resources available).

Now, I am not a “seasoned chemist.” The description of the chemical reaction I provided above was not immediately obvious to me; I was only able to write it after examining it closely, recalling necessary vocabulary, and working through it with the group. But I knew that consulting the table could help demystify the process for them. This was not a string of random letters, randomly punctuated with numbers and arrows. This was four different kinds of atoms, arranged in molecules of four distinct combinations, with subscripts to indicate their relative proportions in the mix. That is much easier to process.

The student who brought the problem understood that an equation of this type was balanced when the number of atoms of each type was the same on each side. I gave her a push in the right direction: before she could do anything to make this happen, she had to know how many atoms she was looking at already. As complicated as the problem appeared to them, it had to begin with a simple exercise in counting.

After double-checking, the group concluded that on the left side of the equation, the number of atoms of hydrogen, oxygen, sulfur, and sodium were, respectively, 3, 5, 1, and 1. On the right side, the numbers were 2, 5, 1, and 2. Our oxygens and sulfurs were perfectly in sync, but our hydrogens and sodiums were decidedly not. This, I told them, was the knowledge we needed to proceed.

For those of you who haven’t done this for a while, bringing the atoms to parity requires multiplying the amount of a molecule containing the desired atoms. You do this by writing a number in front of the molecule, known as the coefficient. Each of the four molecules in our unbalanced equation has an unwritten coefficient of 1; we can change it to 2 or 3 or any number we like. The trick is, putting a coefficient in front of a molecule multiplies all the atoms in that molecule, not just the one you are trying to increase. They come as a package, and so you really need to be thinking in terms of packages.

The group was still a little shy about tinkering with the packages when so many variables were at play, so I gave them another suggestion: try making very targeted changes to the equation. In this case, O appears in all four molecules and H appears in three, but S and Na both appear in only two, i.e. one molecule on each side of the arrow. The sulfurs were already balanced, but the sodiums were not; there are two Na atoms in Na₂SO4, and only one in NaOH. Whatever else had to be changed, we agreed, there had to be twice as many NaOH molecules as Na₂SO4 molecules for the equation to balance. So we added our first coefficient:

H₂SO₄ + 2NaOH —> Na₂SO4 + H₂O

Then they counted again. The new count of hydrogen, oxygen, sulfur, and sodium on the left was 4, 6, 1, and 2. On the right it was still 2, 5, 1, and 2. Balance had yet to be achieved, and while we had dealt with sodium, we still had hydrogen (and now oxygen) to worry about.

Up to this point I had not written any notes of my own, so I started writing the equation down and figuring where additional coefficients needed to go. This time, however, the group was ahead of me. Before I finished writing, they quickly realized that there was a molecule on the right side that consisted only of the kinds of atoms that needed to be increased: H₂O. The only math left to do was to double the water molecule, and the equation was finished:

H₂SO₄ + 2NaOH —> Na₂SO4 + 2H₂O

Now, both sides finally had 4 hydrogen atoms, 6 oxygen atoms, 1 sulfur atom, and 2 sodium atoms. Balance was achieved; the law of conservation of mass was upheld. The only thing left was to write out the steps and try to remember how to bring the process to bear on the next challenge.

My goal was to help these kids realize that, while chemistry is a challenging subject and could potentially get more confusing the further they pursued it, the task they were now asked to perform was not any different in principle from the skills they had been taught in algebra. Simple chemical reactions like these are governed by simple, predictable rules, none of which are beyond the ability of people their age to understand. The hardest part is to learn how to read the notation, and to recognize the connection between what is written and the way that things in this world actually happen.