Question: Balance the chemical equation below using the smallest possible whole number stoichiometric coefficients.
Na(s) + O_2(g) \rightarrow Na_2O_2(s)
1. **State the problem:** Balance the chemical equation $$\text{Na}(s) + \text{O}_2(g) \rightarrow \text{Na}_2\text{O}_2(s)$$ using the smallest whole number coefficients.
2. **Write the unbalanced equation with coefficients:** $$a\text{Na} + b\text{O}_2 \rightarrow c\text{Na}_2\text{O}_2$$ where $a$, $b$, and $c$ are the stoichiometric coefficients to find.
3. **Balance sodium (Na) atoms:**
- On the left: $a$ Na atoms.
- On the right: $2c$ Na atoms (since each $\text{Na}_2\text{O}_2$ has 2 Na atoms).
Set equal: $$a = 2c$$
4. **Balance oxygen (O) atoms:**
- On the left: $2b$ O atoms (since $\text{O}_2$ molecule has 2 atoms).
- On the right: $2c$ O atoms (each $\text{Na}_2\text{O}_2$ has 2 O atoms).
Set equal: $$2b = 2c \implies b = c$$
5. **Choose the smallest whole number for $c$:**
Let $c = 1$.
Then:
- $a = 2 \times 1 = 2$
- $b = 1$
6. **Write the balanced equation:**
$$2\text{Na} + \text{O}_2 \rightarrow \text{Na}_2\text{O}_2$$
7. **Verify:**
- Sodium atoms: Left $2$, Right $2$.
- Oxygen atoms: Left $2$, Right $2$.
The equation is balanced with coefficients $2$, $1$, and $1$ respectively.