Balanced Chemical Equations

A chemical equation is a sentence about particles rearranging, not disappearing. Atoms on the reactant side don't vanish or multiply, they just regroup into new substances, so the same count of each element must show up on the product side. Coefficients, the numbers placed in front of formulas, say how many molecules or formula units of each substance take part. You can freely multiply a whole formula by a coefficient because that just means more copies of the same thing. A subscript, by contrast, is baked into what the substance IS: change the 2 in H_2O to a 3 and you no longer have water, you've invented a different, usually nonexistent, molecule. Balancing works by finding the smallest whole-number coefficients that make the atom count of every element match on both sides, usually by inspection, starting with the most complex molecule or the element that appears in the fewest places.

Balancing is just bookkeeping for the law of conservation of mass: atoms rearrange in a reaction but none are created or destroyed, so every atom counted on the left must be accounted for on the right. For aluminum reacting with copper(II) chloride, 2 Al + 3 CuCl₂ → 2 AlCl₃ + 3 Cu, checking each element (2 Al, 3 Cu, 6 Cl on each side) confirms nothing was lost or gained, only regrouped.

Once an equation is balanced, its coefficients become a ratio you can trust for stoichiometry: moles of one substance convert to moles of another using those numbers directly. That ratio is the bridge to the next idea, limiting reactants, because a balanced equation only tells you the proportion needed for a clean, total reaction, not how much of each reactant you actually poured in.