Balance Chemical Equations
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The balanced equation is 2Al + 3H2SO4 = Al2(SO4)3 + 3H2. Follow these three steps. Step 1 — Balance aluminum (Al): Al2(SO4)3 on the right contains 2 Al atoms, so place the coefficient 2 in front of Al on the left. Step 2 — Treat the sulfate group (SO4) as a single unit: Al2(SO4)3 contains 3 sulfate units, so place 3 in front of H2SO4. Step 3 — Balance hydrogen (H): 3 molecules of H2SO4 supply 3 × 2 = 6 hydrogen atoms, so place 3 in front of H2 on the right. Verification: Al 2 = 2 ✓, S 3 = 3 ✓, O 12 = 12 ✓, H 6 = 6 ✓.
The fundamental rule is the Law of Conservation of Mass: matter cannot be created or destroyed in a chemical reaction, so the total number of atoms of each element must be identical on both sides of the equation. You achieve balance by adjusting the whole-number coefficients in front of each formula — never by altering subscripts — until every element's atom count is equal on both sides.
If a polyatomic ion appears unchanged on both sides of the equation, treat it as a single indivisible unit rather than counting each constituent atom separately. For example, in Ca(OH)2 the hydroxide group (OH) transfers intact, and in 2Al + 3H2SO4 = Al2(SO4)3 + 3H2 the sulfate group (SO4) moves as one unit from acid to product. Counting the ion as a block — rather than tallying O and S individually — makes balancing faster and reduces errors.
Subscripts define the molecular identity of a substance: changing H2O to H3O does not give you more water — it produces an entirely different chemical compound (the hydronium ion, H3O+). Coefficients, by contrast, indicate how many molecules of an existing compound take part in the reaction without altering what that compound is. Modifying a subscript therefore changes the chemical species itself, making the equation describe a different reaction entirely.
Always balance carbon first, hydrogen second, and oxygen last — because oxygen appears in multiple products and is easiest to fix at the end. Step 1 — Carbon: CH4 has 1 C and CO2 has 1 C, so both keep a coefficient of 1. Step 2 — Hydrogen: CH4 has 4 H atoms and each H2O provides 2, so place 2 in front of H2O. Step 3 — Oxygen: the right side now has 2 O (from CO2) + 2 O (from 2 H2O) = 4 O total; place 2 in front of O2 on the left. The balanced equation is CH4 + 2O2 = CO2 + 2H2O.
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Uses Gaussian Elimination to solve for integer coefficients.