To balance the given chemical equation, we need to ensure that the number of atoms of each element on the reactants side is equal to the number of atoms on the products side.
The unbalanced equation is:
[tex]\[ \text{Na} + \text{H}_2\text{O} \rightarrow \text{NaOH} + \text{H}_2 \][/tex]
Step-by-Step Solution:
1. Identify the elements involved: Sodium (Na), Hydrogen (H), and Oxygen (O).
2. Count the number of atoms of each element on both sides:
- Reactants side:
- [tex]\( \text{Na} \)[/tex]: 1 atom
- [tex]\( \text{H} \)[/tex]: 2 atoms (from [tex]\( \text{H}_2\text{O} \)[/tex])
- [tex]\( \text{O} \)[/tex]: 1 atom (from [tex]\( \text{H}_2\text{O} \)[/tex])
- Products side:
- [tex]\( \text{Na} \)[/tex]: 1 atom (from [tex]\( \text{NaOH} \)[/tex])
- [tex]\( \text{H} \)[/tex]: 2 atoms (1 from [tex]\( \text{NaOH} \)[/tex] and 2 from [tex]\( \text{H}_2 \)[/tex])
- [tex]\( \text{O} \)[/tex]: 1 atom (from [tex]\( \text{NaOH} \)[/tex])
3. We see that the hydrogen atoms are not balanced. The reactant side has 2 hydrogen atoms, while the product side has 3 hydrogen atoms (1 from NaOH and 2 from H₂).
4. Adjust the coefficients to balance the hydrogen atoms:
- To balance hydrogen atoms, we need to ensure the total number of hydrogen atoms on both sides is the same. We can start by adding a coefficient to [tex]\( \text{NaOH} \)[/tex].
5. Balance sodium and hydrogen together:
- We can add a coefficient of 2 to both [tex]\( \text{Na} \)[/tex] and [tex]\( \text{H}_2\text{O} \)[/tex] on the reactants side.
- This gives us:
[tex]\[
2\text{Na} + 2\text{H}_2\text{O} \rightarrow 2\text{NaOH} + \text{H}_2
\][/tex]
6. Verify the balanced equation:
- Reactants side:
- [tex]\( \text{Na} \)[/tex]: 2 atoms
- [tex]\( \text{H} \)[/tex]: 4 atoms (2 from each [tex]\( \text{H}_2\text{O} \)[/tex])
- [tex]\( \text{O} \)[/tex]: 2 atoms (1 from each [tex]\( \text{H}_2\text{O} \)[/tex])
- Products side:
- [tex]\( \text{Na} \)[/tex]: 2 atoms (from 2 [tex]\( \text{NaOH} \)[/tex])
- [tex]\( \text{H} \)[/tex]: 4 atoms (2 from 2 [tex]\( \text{NaOH} \)[/tex] and 2 from [tex]\( \text{H}_2 \)[/tex])
- [tex]\( \text{O} \)[/tex]: 2 atoms (from 2 [tex]\( \text{NaOH} \)[/tex])
7. Now the equation is balanced, as the number of atoms of each element on both sides of the equation is the same.
The balanced chemical equation is:
[tex]\[ 2\text{Na} + 2\text{H}_2\text{O} \rightarrow 2\text{NaOH} + \text{H}_2 \][/tex]
Thus, the coefficients are 2, 2, 2, and 1 for Na, H₂O, NaOH, and H₂ respectively.
