Balancing chemical equations — step by step method with 5 examples

Question

Balance the following chemical equations using the hit-and-trial method:

$Fe + O_2 \rightarrow Fe_2O_3$
$H_2 + O_2 \rightarrow H_2O$
$N_2 + H_2 \rightarrow NH_3$
$Al + HCl \rightarrow AlCl_3 + H_2$
$CH_4 + O_2 \rightarrow CO_2 + H_2O$

(NCERT Class 10 — Chemical Reactions and Equations)

Solution — Step by Step

Unbalanced: $Fe + O_2 \rightarrow Fe_2O_3$

Count atoms: Fe (1 vs 2), O (2 vs 3). Balance Fe first by putting 4 on left, then adjust O:

\mathbf{4Fe + 3O_2 \rightarrow 2Fe_2O_3}

Check: Fe (4 = 4), O (6 = 6). Balanced.

Unbalanced: $H_2 + O_2 \rightarrow H_2O$

O is 2 on left, 1 on right. Put 2 before $H_2O$ : $H_2 + O_2 \rightarrow 2H_2O$ . Now H is 2 vs 4. Put 2 before $H_2$ :

\mathbf{2H_2 + O_2 \rightarrow 2H_2O}

Check: H (4 = 4), O (2 = 2). Balanced.

Unbalanced: $N_2 + H_2 \rightarrow NH_3$

N is 2 vs 1. Put 2 before $NH_3$ : $N_2 + H_2 \rightarrow 2NH_3$ . Now H is 2 vs 6. Put 3 before $H_2$ :

\mathbf{N_2 + 3H_2 \rightarrow 2NH_3}

Check: N (2 = 2), H (6 = 6). Balanced.

Unbalanced: $Al + HCl \rightarrow AlCl_3 + H_2$

Cl is 1 vs 3. Put 3 before HCl. Now H is 3 vs 2 — not even. Put 6 before HCl and 3 before $H_2$ , and 2 before Al and $AlCl_3$ :

\mathbf{2Al + 6HCl \rightarrow 2AlCl_3 + 3H_2}

Check: Al (2 = 2), H (6 = 6), Cl (6 = 6). Balanced.

Unbalanced: $CH_4 + O_2 \rightarrow CO_2 + H_2O$

C is already balanced (1 = 1). H is 4 vs 2 — put 2 before $H_2O$ . Now O: right side has $2 + 2 = 4$ , left has 2. Put 2 before $O_2$ :

\mathbf{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O}

Check: C (1 = 1), H (4 = 4), O (4 = 4). Balanced.

Why This Works

Balancing equations follows the Law of Conservation of Mass — atoms are neither created nor destroyed in a chemical reaction. The number of atoms of each element must be the same on both sides.

The hit-and-trial method works by adjusting coefficients (the numbers before formulas) until all atoms balance. We never change the subscripts within a formula — that would change the substance itself ( $H_2O$ is water, but $H_2O_2$ is hydrogen peroxide).

Alternative Method

For complex equations, use the algebraic method: assign variables ( $a, b, c...$ ) to each coefficient, set up equations for each element, and solve. For example 4: $aAl + bHCl \rightarrow cAlCl_3 + dH_2$ . Setting $a = 1$ : Al gives $c = 1$ , Cl gives $b = 3$ , H gives $d = 3/2$ . Multiply all by 2 to get whole numbers.

Start balancing with the element that appears in the fewest compounds, and leave oxygen and hydrogen for last — they usually appear in multiple compounds and adjust more easily at the end.

Common Mistake

Students sometimes “balance” by changing the formula itself — writing $H_3O$ instead of putting a coefficient before $H_2O$ . You can ONLY change coefficients (the big numbers in front). The subscripts (small numbers within the formula) are fixed by the compound’s identity. Changing subscripts means you are talking about a completely different substance.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

Try These Next