Balance coefficients without changing the species
A chemical formula’s subscripts describe the atom proportions within the species. A coefficient multiplies the entire formula. Balancing an equation requires equal counts of each element on the two sides. It does not permit changing the products’ identities until their arithmetic is convenient. Worked symbolic example: let generic element symbols A and B form the species AB. The relation A₂+B₂→2AB has two A atoms and two B atoms on each side. The coefficient 2 belongs to the whole AB unit, so it produces two A atoms and two B atoms. Changing AB to AB₂ would describe another species, not another count of the same species. These are symbolic counting examples, not laboratory preparation directions. For a longer formula, make a table with one row per element. Multiply each subscript by the coefficient, including an unwritten subscript 1. After the counts match, check whether all coefficients share a divisor; the requested smallest whole-number ratio removes such a common factor. In the diagnostic, all formulas are fixed and each proposed coefficient set can be tested directly. Explain a distractor by naming the element whose count fails, rather than saying only that the equation looks unbalanced.
For the symbolic equation P₄+Cl₂→PCl₃, keep all chemical subscripts fixed. Which smallest whole-number coefficients, in the order P₄, Cl₂, PCl₃, balance the equation?
- One P₄ unit supplies 4 P atoms, requiring 4 PCl₃ units. Those products contain 4×3=12 Cl atoms, supplied by 6 Cl₂ units. The coefficients 1, 6, 4 have no common divisor greater than 1. Changing a subscript would change the chemical species.
Compare the other answer choices
Four PCl₃ units contain 12 chlorine atoms, but three Cl₂ units supply only 6.
Four P₄ units supply 16 phosphorus atoms while four PCl₃ units contain only 4.
The left side has 4 P and 12 Cl, while two PCl₃ units have 2 P and 6 Cl.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which evidence or rule supports your decision and why the alternatives do not fit.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Averill/LibreTexts—Chemical Equations