To balance the chemical equation [tex]\( Na + H_2O \rightarrow NaOH + H_2 \)[/tex], it is essential to follow a systematic approach to ensure the number of atoms of each element is identical on both sides of the equation.
Here's the step-by-step solution to balance the equation:
1. Identify the reactants and the products:
- Reactants: Sodium ([tex]\( Na \)[/tex]) and Water ([tex]\( H_2O \)[/tex]).
- Products: Sodium Hydroxide ([tex]\( NaOH \)[/tex]) and Hydrogen gas ([tex]\( H_2 \)[/tex]).
2. Count the number of atoms for each element in the reactants and the products:
- In the reactants, we have:
- [tex]\( Na \)[/tex]: 1 atom
- [tex]\( H \)[/tex]: 2 atoms (from [tex]\( H_2O \)[/tex])
- [tex]\( O \)[/tex]: 1 atom (from [tex]\( H_2O \)[/tex])
- In the products, we have:
- [tex]\( Na \)[/tex]: 1 atom (from [tex]\( NaOH \)[/tex])
- [tex]\( O \)[/tex]: 1 atom (from [tex]\( NaOH \)[/tex])
- [tex]\( H \)[/tex]: 1 atom (in [tex]\( NaOH \)[/tex]) + 2 atoms (in [tex]\( H_2 \)[/tex]) = 3 atoms
3. Check if the number of atoms for each element matches between reactants and products:
- Sodium ([tex]\( Na \)[/tex]):
- Reactants: 1
- Products: 1
- Oxygen ([tex]\( O \)[/tex]):
- Reactants: 1
- Products: 1
- Hydrogen ([tex]\( H \)[/tex]):
- Reactants: 2
- Products: 3
4. Adjust the coefficients to balance the atoms:
- To balance hydrogen, consider the [tex]\( NaOH \)[/tex] and [tex]\( H_2 \)[/tex] in the products:
- To balance the [tex]\( Na \)[/tex], since [tex]\( Na \)[/tex] is already 1 on both sides, it remains unchanged.
- [tex]\( H \)[/tex] atoms: We need 2 atoms of [tex]\( H \)[/tex] in the reactants to match 3 in the products.
- Since we have 2 hydrogen atoms from water and can form 1 molecule of [tex]\( H_2 \)[/tex]:
[tex]\[ H_2O \rightarrow H_2 + O \][/tex]
- Therefore, adding an additional [tex]\( H_2O \)[/tex] molecule on the reactant side balances out the hydrogen atoms:
[tex]\[ 2Na + 2H_2O \rightarrow 2NaOH + H_2 \][/tex]
5. Verify the equation:
- Reactants: [tex]\( 2Na + 2H_2O \)[/tex]
- Sodium: 2 atoms
- Hydrogen: 4 atoms (2 from each [tex]\( H_2O \)[/tex])
- Oxygen: 2 atoms (1 from each [tex]\( H_2O \)[/tex])
- Products: [tex]\( 2NaOH + H_2 \)[/tex]
- Sodium: 2 atoms
- Hydrogen: 4 atoms (2 from [tex]\( NaOH \)[/tex] and 2 from [tex]\( H_2 \)[/tex])
- Oxygen: 2 atoms (1 from each [tex]\( NaOH \)[/tex])
Now the equation is balanced:
[tex]\[ 2Na + 2H_2O \rightarrow 2NaOH + H_2 \][/tex]
The coefficients that balance the equation are:
- [tex]\( Na \)[/tex]: 1 (however, when exactly balanced, you find 2 [tex]\( Na \)[/tex])
- [tex]\( H_2O \)[/tex]: 2
- [tex]\( NaOH \)[/tex]: 2
- [tex]\( H_2 \)[/tex]: 1
Therefore, the correct answer to find the coefficients that balance the equation is:
- By counting each individual atom and making sure the number of each kind of atom is the same in the reactants and the products.
