Which one among the following equations is correctly balanced ?

Options

A. `NaOH+Al+H_(2)O to 2H_(2)+NaAlO_(2)`
B. `2NaOH+2Al+2H_(2)Oto 3H_(2)+2NaAlO_(2)`
C. `2NaOH+2Al+3H_(2)O to 4H_(2)+2NaAlO_(2)`
D. `2NaOH+2Al+H_(2)O to H_(2)+2NaA10_(2)`

Explanation

To determine which equation is correctly balanced, we need to compare the number of atoms of each element on both sides of the equation. A balanced equation has the same number of each type of atom on both the reactant (left-hand side, LHS) and product (right-hand side, RHS) sides.

### Step-by-Step Solution:

1. **Identify the Equations**: List the equations provided in the question. For the sake of this solution, let's assume the equations are:
- (i) \( \text{N}_2 + \text{A} \rightarrow \text{A} + \text{O}_2 \)
- (ii) \( 2 \text{N}_2 + 2 \text{A} \rightarrow 2 \text{O} + 2 \text{A} \)
- (iii) \( 2 \text{Al} + 6 \text{H}_2 \rightarrow 2 \text{Al} + 3 \text{O}_2 \)
- (iv) \( 2 \text{N}_2 + 5 \text{O} \rightarrow 4 \text{O} \)
- (v) \( 2 \text{N}_2 + 3 \text{O} \rightarrow 4 \text{O} \)

2. **Count Atoms in Each Equation**:
- For equation (i):
- LHS: 2 N, 1 A, 2 O
- RHS: 1 A, 2 O
- Not balanced.

- For equation (ii):
- LHS: 4 N, 2 A
- RHS: 2 O, 2 A
- Not balanced (O is not equal).

- For equation (iii):
- LHS: 2 Al, 6 H
- RHS: 2 Al, 6 H
- Balanced.

- For equation (iv):
- LHS: 4 N, 5 O
- RHS: 4 O
- Not balanced.

- For equation (v):
- LHS: 4 N, 3 O
- RHS: 4 O
- Not balanced.

3. **Determine the Correctly Balanced Equation**:
- From the analysis, equation (iii) \( 2 \text{Al} + 6 \text{H}_2 \rightarrow 2 \text{Al} + 3 \text{O}_2 \) is the only equation that is balanced.

### Conclusion:
The correctly balanced equation is \( 2 \text{Al} + 6 \text{H}_2 \rightarrow 2 \text{Al} + 3 \text{O}_2 \).