Chemical Equations

Coefficients are the whole numbers placed in front of chemical formulas (e.g., $2H_2O$) to adjust the number of molecules or atoms. These are the only numbers that can be changed during balancing.

Subscripts (the small numbers within a formula, like the $2$ in $H_2O$) must never be changed, as altering them would change the identity of the chemical substance itself.

A systematic approach involves counting the atoms of one element at a time, starting with the most complex molecule and leaving simple elements (like $O_2$ or $H_2$) for the final step.

If a polyatomic ion (such as $SO_4^{2-}$ or $NO_3^-$) appears unchanged on both sides of the equation, it can be treated as a single unit for easier counting.

Diatomic Check: Always remember that seven non-metal elements exist as diatomic molecules in their elemental state: $H_2, N_2, O_2, F_2, Cl_2, Br_2,$ and $I_2$. Forgetting the '2' is a frequent source of errors.

Final Verification: Once an equation is balanced, perform a final 'atom audit' by listing every element and counting its total atoms on both sides to ensure they match perfectly.

Simplest Ratio: Ensure that the coefficients used are in the lowest possible whole-number ratio. For example, $4H_2 + 2O_2 \rightarrow 4H_2O$ should be simplified to $2H_2 + O_2 \rightarrow 2H_2O$.

State Symbol Precision: Only include state symbols if specifically requested, but ensure they are accurate (e.g., acids are always $(aq)$, and metals are usually $(s)$ except for mercury).

Subscript Tampering: Students often try to balance atoms by changing subscripts (e.g., changing $H_2O$ to $H_2O_2$ to balance oxygen). This is incorrect because it creates an entirely different chemical compound.

Ignoring the Arrow: Treating the arrow like an equals sign is mathematically helpful, but chemically, it represents a directional process of change.

Counting Errors: Forgetting to multiply the coefficient by the subscript is a common calculation mistake (e.g., $2Fe_2O_3$ contains $4$ Iron atoms and $6$ Oxygen atoms).