To solve the problem of balancing the chemical equation [tex]\( \text{Na}_{(s)} + \text{H}_2\text{O} \rightarrow \text{NaOH} + \text{H}_2 \)[/tex], follow these steps:
1. Identify the Reactants and Products:
- Reactants: Sodium (Na) and Water ([tex]\(\text{H}_2\text{O}\)[/tex])
- Products: Sodium Hydroxide ([tex]\(\text{NaOH}\)[/tex]) and Hydrogen Gas ([tex]\(\text{H}_2\)[/tex])
2. Write Down the Unbalanced Equation:
[tex]\[
\text{Na} + \text{H}_2\text{O} \rightarrow \text{NaOH} + \text{H}_2
\][/tex]
3. Count the Number of Atoms of Each Element on Both Sides:
- Left side (Reactants):
- Na: 1
- H: 2 (from [tex]\(\text{H}_2\text{O}\)[/tex])
- O: 1 (from [tex]\(\text{H}_2\text{O}\)[/tex])
- Right side (Products):
- Na: 1 (from [tex]\(\text{NaOH}\)[/tex])
- H: 3 (1 from [tex]\(\text{NaOH}\)[/tex] and 2 from [tex]\(\text{H}_2\)[/tex])
- O: 1 (from [tex]\(\text{NaOH}\)[/tex])
4. Adjust the Coefficients to Balance Each Element:
- Sodium (Na) atoms are already balanced (1 on each side).
- Next, balance the Hydrogen (H) atoms.
- There are 2 H atoms on the reactants side (from [tex]\(\text{H}_2\text{O}\)[/tex]) and 3 on the products side (1 from [tex]\(\text{NaOH}\)[/tex] and 2 from [tex]\(\text{H}_2\)[/tex]).
- To balance H atoms, place a coefficient of 2 before both [tex]\(\text{H}_2\text{O}\)[/tex] and [tex]\(\text{NaOH}\)[/tex]:
[tex]\[
\text{Na} + 2 \text{H}_2\text{O} \rightarrow 2 \text{NaOH} + \text{H}_2
\][/tex]
- Finally, balance the Sodium (Na) atoms:
- There is now 1 Na atom on the reactants side, but we need 2 to balance the 2 Na atoms present in [tex]\(\text{NaOH}\)[/tex].
- Place a coefficient of 2 before Na:
[tex]\[
2 \text{Na} + 2 \text{H}_2\text{O} \rightarrow 2 \text{NaOH} + \text{H}_2
\][/tex]
5. Verify the Balance of Each Element:
- Na: 2 atoms on reactants side and 2 atoms on the products side.
- H: 4 atoms on reactants side (from 2 [tex]\(\text{H}_2\text{O}\)[/tex]) and 4 atoms on the products side (2 from 2 [tex]\(\text{NaOH}\)[/tex] and 2 from [tex]\(\text{H}_2\)[/tex]).
- O: 2 atoms on reactants side (from 2 [tex]\(\text{H}_2\text{O}\)[/tex]) and 2 atoms on the products side (from 2 [tex]\(\text{NaOH}\)[/tex]).
6. Write the Final Balanced Chemical Equation:
[tex]\[
\boxed{2 \text{Na} + 2 \text{H}_2\text{O} \rightarrow 2 \text{NaOH} + \text{H}_2}
\][/tex]
