1. Treat all complex anions as one group. For example, Nitrate, NO3-, is treated as one group, not as N and O separately.
2. Chemical reactions occur because molecules collide on a molecular scale. It's common for 2 molecules to collide, but it's much less common for 3 and even less common for 4, 5, or 6 molecules to collide. The number that collide is usually the number used in the chemical equation, so look for small numbers to balance equations.
3. Look for the principal atoms (usually metals) to be balanced first. Balance oxygen and hydrogen last. You can often add H+ (or OH-) to balance hydrogen and H2O to balance oxygen if water is involved.
4. Half reactions can be balanced very simply -- by balancing the number of electrons on each side of the equation. Most reactions occur in water solution. If water is involved, you can figure out the half reaction by balancing the hydrogens using H+, and the oxygens using H2O. If it's alkaline solution, use OH- to balance the hydrogen (you can use H+, and then add OH- to each side and combine H+ with OH- to get H2O. Just be sure to cancel out H2Os that appear on both sides).
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