Balanced Equation
A balanced equation has the same number of atoms of each element on both sides, showing that mass is conserved in the chemical reaction.
Definition
A balanced equation has the same number of each kind of atom on both sides of the arrow, because atoms cannot appear or vanish, so the counts must match. It satisfies the law of conservation of mass and is balanced by adjusting coefficients in front of formulas, never by changing subscripts, with the final coefficients reduced to the smallest whole numbers that work; a practical order is to balance elements that appear in only one substance per side first and save hydrogen and oxygen for last. For reactions involving ions a balanced equation also conserves total charge, and for redox reactions it conserves the electrons transferred. Balancing can be done by inspection, by the algebraic method (treating coefficients as unknowns in a system of linear equations), or by the half-reaction method for redox reactions in acidic or basic solution, and the balanced coefficients are the stoichiometric basis for all quantitative predictions of yield.
Example
$H_2 + O_2 \rightarrow H_2O$ is not balanced, with $2$ oxygen atoms on the left and only $1$ on the right, while $2H_2 + O_2 \rightarrow 2H_2O$ is balanced with $4$ hydrogen and $2$ oxygen on each side. To balance $Fe + O_2 \rightarrow Fe_2O_3$, two iron in the product means $2Fe$; three oxygen in the product but two per $O_2$ means a common multiple of six, so $3O_2$ and $2Fe_2O_3$, then $4Fe$, giving $4Fe + 3O_2 \rightarrow 2Fe_2O_3$. Balancing the redox reaction $MnO_4^- + Fe^{2+} \rightarrow Mn^{2+} + Fe^{3+}$ in acid by half-reactions gives $MnO_4^- + 8H^+ + 5Fe^{2+} \rightarrow Mn^{2+} + 5Fe^{3+} + 4H_2O$, where the atoms balance (Mn, O, H, Fe) and the charge balances at $+17$ on each side.
Key Insight
Balancing is like making sure every LEGO brick you started with ends up in the finished model, nothing left over and nothing missing. If you catch yourself writing $H_2O_2$ to balance oxygen, stop, because you just turned water into hydrogen peroxide; only the big numbers in front are yours to change. A balanced equation can be multiplied through by any factor and remain balanced, which is why $\Delta H$ must always be quoted per the equation as written, since doubling every coefficient doubles the enthalpy change.