The backstory of balancing equations
Yasmin Jayathirtha
I was once asked, “How do you teach students to balance equations? The teachers are finding it very difficult.” As I gave a few suggestions, the reason for the difficulty emerged – these students are in the 6th or 7th class, they have not yet learnt atomic structure, bonding, or valency. This means that they do not know why the formulae of substances are what they are. They have to look them up. Why then are they being asked to balance equations? If there has to be chemistry in these classes, surely it can be descriptive chemistry such as teaching the idea of chemical change, outlining the questions that chemists asked, the simple tests that are used to identify common substances, the chemistry of air, water, metals – familiar substances and familiar processes like evaporation, dissolving, corrosion, etc… but of course, this means doing simple experiments and observing changes. At this stage, science has to be integrated.
Most textbooks that I have consulted have covered the ideas of atomic structure, bonding, formulae, and the mole, before coming to the concept of a balanced equation, usually by the 9th class. It just doesn’t make sense to balance equations before learning these concepts. Equations there are, but they are word equations, just describing the reactions that occur. Many subjects have hierarchies, and taken out of context, a concept will just become a matter of rule to follow, rather than adding to the understanding of the subject. No wonder, students find chemistry difficult, being unable to relate what they have learnt to the world they know and being asked to memorize rather complicated formulae and do algebra!
How does one introduce the idea of a balanced equation qualitatively? This is a paradox, since the idea of equations is the start of quantitative chemistry and is linked to the relationship between numbers of particles and their mass – the link between the sub-microscopic world of atoms and the macroscopic world of measurement. Should one even try? I am torn between ‘shouldn’t be done’ and ‘poor kids, how can it be made a little more intelligible?’
Start with reactions – how do we know a reaction has occurred? We can demonstrate various reactions. Add a drop of hydrochloric acid to a piece of magnesium or zinc. Has a change occurred? What do we observe? Bubbles tell us that a gas has formed. After a while, the metal disappears – reaction has taken place. Allow the reacted mixture to dry. There will be white solid substance left behind. So we can write the reaction as;
Magnesium + hydrochloric acid ? a gas + a white solid A curious student may ask – how do we know the white solid is not hydrochloric acid? Ask how we can find that out – just put a drop of the acid to evaporate.
Other reactions that occur visibly are: acid with a carbonate, metal and metal salt (zinc and copper sulfate), precipitation reactions (sodium sulfate+ barium chloride) (lead nitrate + potassium iodide), combustion reactions (a candle or piece of coal burning).
Let us get back to magnesium and hydrochloric acid – it gave off a gas. Compare the reaction with that of calcium carbonate with hydrochloric acid – it also gives off a gas, dissolves and leaves behind a white solid on evaporation. Is it the same reaction? How do we find out?
Take four test tubes: add a piece of magnesium each to two of them and a small amount of calcium carbonate to the other two. Add acid to the magnesium and test the gas given off with a burning splint and by bubbling through limewater. The simplest way of doing this is to use a dropper to pick up the gas. Repeat by adding acid to the carbonate and repeating the tests. This shows quite obviously that the two gases are different. At this point we just need to know that or we can name the gases and say that they can be identified by these tests.
From here we will have to tell the story of chemistry, that people have been doing chemical reactions for a long time. Metals were extracted, glass was made, and limestone was roasted to make ‘chuna’ which was used in the extraction of metals, for mortar and for chewing with tobacco and betel leaves to release the active ingredients in them. People had codified the conditions under which reactions take place and had got an idea of elements, compounds and mixtures, even the measures of reactants though there was no clear theory of why the substances reacted. Though the ideas of atoms were probably around for a long time, it was Dalton’s atomic theory that made the link between particles and masses. This still didn’t answer the question why, that had to wait till the modern theory of atomic structure. Having given this background, we can point out that pure substances have fixed formulae, even though it is complicated, at present, for us to figure out how they were determined.
Students need to know what the formula of any substance tells us.
1. What elements it is made up of.
2. What the proportions of the elements are.
3. And that it gives us an unambiguous way of writing out those proportions.
For example, H2O is the formula for water.
1. It is made up of hydrogen and oxygen
2. Hydrogen and oxygen are in the ratio 2:1 by particles
3. Writing it as H2O but not 2HO or H2O means that there is no confusion between 2H and 1O or 2H and 2O or H and 2O.
We have to point out that formulae of any substance cannot be changed but the component elements can become parts of other substances, i.e., they react. The other thing to stress is that these elements can react and change places, but in the ordinary way, they cannot be created or destroyed.
With this, we are ready to start writing equations and balancing them. We need information and that can come in two forms; a table of substances (elements and compounds) in alphabetical order and the other, a grid as shown below.
HCl | H2SO4 | CuSO4 | O2(air) | |
CaCO3 | CaCl2+CO2+H2O | CaSO4+CO2+H2O | CuCO3+CaSO4 | – |
Mg | MgCl2+H2 | MgSO4+H2 | Cu+MgSO4 | MgO |
Zn | ZnCl2+H2 | ZnSO4+H2 | Cu+ZnSO4 | ZnO |
Cu | – | – | – | CuO |
You can give the word equation and ask the students to turn it into a formula equation using the list
Zinc + Hydrochloric acid ? Zinc Chloride + Hydrogen
Zn + HCl ? ZnCl2 + H2
Looking at the formula equation we realize that there are 2Cl and 2H on the product side and since they have to come from the reactants we can only get the right number if we have 2 HCl, so the equation becomes
Zn + 2 HCl ? ZnCl2 + H2
You can give the reactants and ask them to generate the equation using the grid, CaCO3 + HCl ?
Looking up the table the equation becomes
CaCO32
A symbol or formulae equation gives information that a word equation does not give, that the ratio of the substances matter. If there is not twice as much acid as zinc, in particles, the zinc cannot react fully.
What has been outlined here is not a sequence of rules for balancing equations but a context in which balancing equations makes sense. There is a reaction that we see. There are products formed and they have formulae, though we have not yet learnt how they have been determined. The balanced equation gives us the ratio of the reactants, which will be important when we begin to do reactions to make substances. It is still abstract, still rather like algebra, but with a story and a rootedness in chemistry.
The author works with Centre for Learning, Bengaluru. She can be reached at yasmin.cfl@gmail.com.