To solve this problem, we need to identify the additional product that balances the chemical reaction:
[tex]\[ H_2SO_4 + 2 NaOH \rightarrow Na_2SO_4 + \; ? \][/tex]
First, let's determine the reactants and products involved:
### Reactants
- Sulfuric Acid (H_2SO_4): Generally reacts with bases to form salts and water.
- Sodium Hydroxide (NaOH): A strong base.
### Possible Products
- Sodium Sulfate (Na_2SO_4): Typically formed when sulfuric acid reacts with sodium hydroxide.
- Water (H_2O): Often formed in acid-base neutralization reactions.
Now, let’s break down the balanced chemical equation:
[tex]\[ H_2SO_4 + 2 NaOH \rightarrow Na_2SO_4 + \; ? \][/tex]
1. Balancing Sodium (Na) Atoms: We already have 2 sodium (Na) atoms on both sides of the reaction because one \(Na_2SO_4\) molecule contains 2 sodium atoms, matching the 2 \(Na\) atoms from the 2 \(NaOH\) molecules.
2. Balancing Sulfate (SO4) Groups: We have 1 sulfate (SO4) group on both sides, so these are already balanced.
3. Balancing Hydrogen (H) Atoms:
- There are 2 hydrogen atoms from \(H_2SO_4\) and 2 hydrogen atoms from each of the 2 \(NaOH\) molecules, totaling 4 hydrogen atoms on the reactant side.
- The \(Na_2SO_4\) product does not contain hydrogen, so all 4 hydrogen atoms must appear in the additional product.
4. Balancing Oxygen (O) Atoms:
- There are 4 oxygen atoms in \(H_2SO_4\).
- Each \(NaOH\) has 1 oxygen atom, so 2 \(NaOH\) contribute 2 oxygen atoms.
- This makes a total of 6 oxygen atoms on the reactant side.
- There are 4 oxygen atoms in \(Na_2SO_4\), leaving 2 oxygen atoms to be balanced in the additional product.
Combining the hydrogen and oxygen that needs to be balanced, the additional product must contain 2 hydrogen atoms and 1 oxygen atom per molecule, matching the properties of water, \(H_2O\).
To balance the reaction fully:
[tex]\[ H_2SO_4 + 2 NaOH \rightarrow Na_2SO_4 + 2 H_2O \][/tex]
Thus, the additional product that balances the reaction is:
[tex]\[ \boxed{2 \; H_2O} \][/tex]
