To balance the chemical equation for the reaction of solid sodium (Na) and solid octasulfur ([tex]$S_8$[/tex]) forming solid sodium sulfide ([tex]$Na_2S$[/tex]), we need to make sure that the number of atoms of each element is the same on both sides of the reaction. Let's go through the steps:
1. Write down the unbalanced equation:
[tex]\[
\text{Na} + S_8 \rightarrow Na_2S
\][/tex]
2. Identify the number of atoms for each element on both sides:
- On the reactant side, we have:
- Sodium (Na): 1 atom
- Sulfur (S): 8 atoms
- On the product side, we have:
- Sodium (Na): 2 atoms in each [tex]$Na_2S$[/tex] molecule
- Sulfur (S): 1 atom in each [tex]$Na_2S$[/tex] molecule
3. Balance the sodium (Na) atoms:
- Since we have 2 sodium atoms in [tex]$Na_2S$[/tex], we need an even number of sodium atoms on the reactant side. Multiply the sodium (Na) by 16 to balance it with the product side:
[tex]\[
16 \text{Na} + S_8 \rightarrow 8 Na_2S
\][/tex]
- Now, we have 16 sodium atoms on the reactant side and 16 sodium atoms on the product side (8 molecules of [tex]$Na_2S$[/tex], each containing 2 sodium atoms).
4. Verify the balance of sulfur (S) atoms:
- On the reactant side, we still have 8 sulfur atoms.
- On the product side, we have 8 sulfur atoms (8 molecules of [tex]$Na_2S$[/tex], each containing 1 sulfur atom).
5. Confirm the balance:
- Sodium (Na): 16 atoms on both sides.
- Sulfur (S): 8 atoms on both sides.
Since the number of atoms for both elements is the same on both the reactant and product sides, the equation is now balanced.
The balanced chemical equation is:
[tex]\[
16 \text{Na} + S_8 \rightarrow 8 Na_2S
\][/tex]
