To balance the chemical equation, we need to ensure that the number of atoms for each element on the reactant side is equal to the number on the product side. The given equation is:
[tex]\[ 2 \, HCl + Na_2O \rightarrow \lambda \, NaCl + H_2O \][/tex]
Let's examine the number of atoms for each element on both sides of the equation.
Reactants:
- [tex]\( 2 \, HCl \)[/tex]:
- H: 2 × 1 = 2 hydrogen atoms
- Cl: 2 × 1 = 2 chlorine atoms
- [tex]\( Na_2O \)[/tex]:
- Na: 1 × 2 = 2 sodium atoms
- O: 1 oxygen atom
Products:
- [tex]\( \lambda \, NaCl \)[/tex]:
- Na: λ sodium atoms
- Cl: λ chlorine atoms
- [tex]\( H_2O \)[/tex]:
- H: 2 hydrogen atoms
- O: 1 oxygen atom
Now, balance the atoms for each element:
1. Hydrogen (H):
- There are 2 hydrogen atoms in [tex]\( 2 \, HCl \)[/tex] and 2 in [tex]\( H_2O \)[/tex]. Hydrogen is balanced.
2. Chlorine (Cl):
- There are 2 chlorine atoms in [tex]\( 2 \, HCl \)[/tex], so we need 2 chlorine atoms on the product side.
- Therefore, [tex]\( \lambda = 2 \)[/tex].
3. Sodium (Na):
- There are 2 sodium atoms in [tex]\( Na_2O \)[/tex], so λ must also be 2 to balance the sodium atoms.
4. Oxygen (O):
- There is 1 oxygen atom in [tex]\( Na_2O \)[/tex] and 1 oxygen atom in [tex]\( H_2O \)[/tex]. Oxygen is balanced.
So, the balanced equation with [tex]\( \lambda = 2 \)[/tex] is:
[tex]\[ 2 \, HCl + Na_2O \rightarrow 2 \, NaCl + H_2O \][/tex]
Thus, the correct value of [tex]\( \lambda \)[/tex] is:
[tex]\[ \boxed{2} \][/tex]
