To balance the chemical equation:
[tex]\[ 2 \text{HCl} + \text{Na}_2\text{O} \rightarrow x \text{NaCl} + \text{H}_2\text{O} \][/tex]
we need to ensure that the number of atoms of each element on the reactant side is equal to the number of atoms of each element on the product side. Let's analyze the atoms on both sides of the equation.
### Step-by-Step Balancing:
1. Count the number of each type of atom on the reactant side:
- For [tex]\(2 \text{HCl}\)[/tex]:
- [tex]\( \text{H} \)[/tex]: [tex]\(2 \times 1 = 2\)[/tex] atoms
- [tex]\( \text{Cl} \)[/tex]: [tex]\(2 \times 1 = 2\)[/tex] atoms
- For [tex]\( \text{Na}_2\text{O} \)[/tex]:
- [tex]\( \text{Na} \)[/tex]: [tex]\(2\)[/tex] atoms
- [tex]\( \text{O} \)[/tex]: [tex]\(1\)[/tex] atom
2. Count the number of each type of atom on the product side:
- For [tex]\(x \text{NaCl}\)[/tex]:
- [tex]\( \text{Na} \)[/tex]: [tex]\(x\)[/tex] atoms
- [tex]\( \text{Cl} \)[/tex]: [tex]\(x\)[/tex] atoms
- For [tex]\( \text{H}_2\text{O} \)[/tex]:
- [tex]\( \text{H} \)[/tex]: [tex]\(2\)[/tex] atoms
- [tex]\( \text{O} \)[/tex]: [tex]\(1\)[/tex] atom
3. Balance the sodium ([tex]\(\text{Na}\)[/tex]) atoms:
[tex]\[
2 \text{Na} \text{ (reactant)} = x \text{Na} \text{ (product)}
\][/tex]
The coefficient [tex]\(x\)[/tex] must be [tex]\(2\)[/tex] to balance the sodium atoms:
[tex]\[
2 = x \implies x = 2
\][/tex]
4. Verify balance of all atoms:
- Hydrogen (H) atoms:
- Reactant side: [tex]\(2\)[/tex] (from [tex]\(2 \text{HCl}\)[/tex])
- Product side: [tex]\(2\)[/tex] (from [tex]\(\text{H}_2\text{O}\)[/tex])
[tex]\[
2 \text{H} \text{ (reactant)} = 2 \text{H} \text{ (product)} \quad \text{(Balanced)}
\][/tex]
- Chlorine (Cl) atoms:
- Reactant side: [tex]\(2\)[/tex] (from [tex]\(2 \text{HCl}\)[/tex])
- Product side: [tex]\(2 \cdot 1 = 2\)[/tex] (from [tex]\(2 \text{NaCl}\)[/tex])
[tex]\[
2 \text{Cl} \text{ (reactant)} = 2 \text{Cl} \text{ (product)} \quad \text{(Balanced)}
\][/tex]
- Oxygen (O) atoms:
- Reactant side: [tex]\(1\)[/tex] (from [tex]\(\text{Na}_2\text{O}\)[/tex])
- Product side: [tex]\(1\)[/tex] (from [tex]\(\text{H}_2\text{O}\)[/tex])
[tex]\[
1 \text{O} \text{ (reactant)} = 1 \text{O} \text{ (product)} \quad \text{(Balanced)}
\][/tex]
Thus, the balanced chemical equation is:
[tex]\[
2 \text{HCl} + \text{Na}_2\text{O} \rightarrow 2 \text{NaCl} + \text{H}_2\text{O}
\][/tex]
The value of [tex]\(x\)[/tex] that balances the equation is [tex]\(2\)[/tex].
