Balanced Chemical Equation Calculator

A balanced chemical equation is a statement of conservation. Written as

$\mathrm{Pb(NO_3)_2} + 2\,\mathrm{KI} \longrightarrow \mathrm{PbI_2} + 2\,\mathrm{KNO_3}$

it asserts three things at once:

• Atoms are conserved. Every element has equal counts on both sides.
• Charge is conserved. In an ionic equation the net charge matches as well.
• Mass is conserved. Multiply each formula by its molar mass and the totals on the two sides agree, which is the numerical check that catches a balancing error immediately.

The coefficients are read as moles, not grams. One mole of lead(II) nitrate reacts with two moles of potassium iodide, and the mass ratio that follows from those moles is not 1:2.

Before you can balance, you need correct formulas. For ionic compounds the formula comes from making the charges cancel: $\mathrm{Al^{3+}}$ with $\mathrm{SO_4^{2-}}$ gives $\mathrm{Al_2(SO_4)_3}$. When the formula itself is unknown, it is derived from composition data — percent composition gives the empirical formula, and a measured molar mass turns that into the molecular formula.

Step by step

1. Write correct formulas for every reactant and product, balancing ionic charges to get subscripts.
2. Assign coefficients so each element's atom count matches on both sides, treating intact polyatomic ions as single units.
3. Reduce the coefficients to their lowest whole-number ratio.
4. Verify by mass: $\sum \nu\mathcal{M}$ must be equal on the two sides, to within rounding of the atomic masses.

Empirical formula from percent composition

1. Assume a 100 g sample, so each percentage becomes a mass in grams.
2. Divide each mass by that element's atomic mass to get moles.
3. Divide every result by the smallest of them.
4. If a ratio lands near 1.5, 1.33 or 1.25, multiply all of them by 2, 3 or 4 to reach whole numbers.

Molecular formula

$\text{multiplier} = \frac{\mathcal{M}_{\text{molecular}}}{\mathcal{M}_{\text{empirical}}}$

Round that multiplier to the nearest integer and apply it to every subscript.

Significant figures

Mole ratios must be interpreted, not merely rounded: 1.99 is 2, but 1.50 is genuinely a 3:2 ratio. Percent composition good to four figures makes that judgement safe; data good to two figures does not.

• Balancing before checking the formulas. If a product formula is wrong, no set of coefficients can fix it. Ionic formulas must have charges that cancel.
• Reading coefficients as masses. They count moles. Converting to grams requires a molar mass for each substance.
• Rounding mole ratios too aggressively. Turning 1.50 into 2 destroys the answer; multiply the whole set by 2 instead.
• Forgetting brackets when counting atoms. $\mathrm{Pb(NO_3)_2}$ has 2 N and 6 O.
• Dividing by the wrong value for the empirical ratio. Divide by the smallest mole count, not the largest.
• Mistaking the empirical formula for the molecular one. $\mathrm{CH_2O}$, $\mathrm{C_2H_4O_2}$ and $\mathrm{C_6H_{12}O_6}$ share an empirical formula; only a molar mass distinguishes them.
• Skipping the mass check. Adding up molar masses on each side takes seconds and catches most errors.