Choose the correct balanced chemical equations to show the reactions of the following:
Caustic soda solution and aluminium oxide.

Options

A. `Al_(2)O_(3) + 2NaOH rarr 2NaAlO_(2) + H_(2)O`
B. `Al_(2)O_(3) + 2NaOH rarr 2NaAlO_(3) + H_(2)O`
C. `Al_(2)O_(3) + 2NaOH rarr 2NaAlO_(2) + H_(2)`
D. `Al_(2)O_(3) + 2NaOH rarr 2NaAlO + H_(2)O`

Explanation

To solve the problem of balancing the chemical reaction between caustic soda (sodium hydroxide, NaOH) and aluminium oxide (Al2O3), we can follow these steps:

### Step 1: Identify the Reactants
The reactants in this reaction are:
- Caustic soda (sodium hydroxide, NaOH)
- Aluminium oxide (Al2O3)

### Step 2: Understand the Nature of the Reactants
- Sodium hydroxide (NaOH) is a strong base.
- Aluminium oxide (Al2O3) is amphoteric, meaning it can react with both acids and bases.

### Step 3: Write the Reaction
When sodium hydroxide reacts with aluminium oxide, it acts as a base and reacts with the amphoteric aluminium oxide. The reaction can be represented as:
\[ \text{Al}_2\text{O}_3 + \text{NaOH} \rightarrow \text{NaAlO}_2 + \text{H}_2\text{O} \]

### Step 4: Balance the Reaction
To balance the reaction, we need to ensure that the number of atoms for each element is the same on both sides of the equation.

1. **Aluminium (Al)**: There are 2 Al in Al2O3, so we need 2 NaAlO2 to balance the aluminium:
\[ \text{Al}_2\text{O}_3 + \text{NaOH} \rightarrow 2 \text{NaAlO}_2 + \text{H}_2\text{O} \]

2. **Sodium (Na)**: Since we have 2 Na in 2 NaAlO2, we need 2 NaOH:
\[ \text{Al}_2\text{O}_3 + 2 \text{NaOH} \rightarrow 2 \text{NaAlO}_2 + \text{H}_2\text{O} \]

3. **Oxygen (O)**: Now we check oxygen. On the left, we have 3 from Al2O3 and 2 from 2 NaOH, totaling 5. On the right, we have 4 from 2 NaAlO2 and 1 from H2O, also totaling 5.

4. **Hydrogen (H)**: We have 2 from 2 NaOH and 2 from H2O, which balances out.

### Final Balanced Equation
The balanced chemical equation is:
\[ \text{Al}_2\text{O}_3 + 2 \text{NaOH} \rightarrow 2 \text{NaAlO}_2 + 3 \text{H}_2\text{O} \]

### Summary
The correct balanced equation showing the reaction of caustic soda solution and aluminium oxide is:
\[ \text{Al}_2\text{O}_3 + 2 \text{NaOH} \rightarrow 2 \text{NaAlO}_2 + 3 \text{H}_2\text{O} \]