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(ProQuest: ... denotes formulae omitted.)
One of the cautions during Hurricane Irma in 2017 was to avoid using a charcoal grill indoors for heat (https://onsafety.cpsc.gov/blog/2017/09/08/keep-safe-after-hurricane-irma/). The danger is that carbon, present in the charcoal, combined with oxygen in the burning process, can produce carbon monoxide, a poisonous gas that is odourless and deadly. Since burning the carbon transforms it into something different, it is called a "chemical change." In chemistry class, this gets represented in an equation: C (carbon) plus O (oxygen) produces CO (carbon monoxide).
The equation shows the ingredients in this chemical reaction at the molecular level. A molecule of carbon C has one atom, so it could be written as C1 to show this. In general, the subscript 1 is understood and not written. A molecule of oxygen O has two atoms, and the subscript 2 describes this in the representation O2. They combine in burning to produce carbon monoxide, and that molecule is made up of one carbon atom and one oxygen atom. Again, the subscripts of one (C1O1) are assumed, and it is written as CO. Using chemical and mathematical symbols, the equation would be written as C + O2 → CO.
Chemical equations like C + O2 → CO need to be "balanced" so that there are the same number of carbon atoms C and oxygen atoms O on each side of the arrow (the "reactants" and the "product"). As it stands, there is 1 carbon atom on the left side and 1 carbon atom on the right side. That is balanced. For oxygen, there are 2 atoms on the left side and 1 atom on the right side. This is not balanced. To balance the equation, numerical coefficients are used at the beginning of each of the components (elements or compounds) in the equation. If we represent those numbers with lower-case letters-a, b, and c-then we need a balanced equation that will have the form:
a C + b O2 → c CO
The challenge of balancing the equation is to find the values for a, b, and c.
Trial and error (hopefully combined with "educated guessing") is the most common explanation to figure out what those coefficients are. A better approach that...