STATEMENT-1: For the reaction `NaOH + H_(2)CO_(3) to NaHCO_(3) + H_(2)O` equivalent weight of `H_(2)CO_(3)` is 62.
STATEMENT-2: n factor of `H_(2)CO_(3)` is 1 (in above reaction) and equivalent mass `=("Molecular mass")/("n factor")`

Answer

To solve the problem, we need to analyze the given statements regarding the reaction between sodium hydroxide (NaOH) and carbonic acid (H₂CO₃) to produce sodium bicarbonate (NaHCO₃) and water (H₂O). We will determine the equivalent weight of H₂CO₃ and verify the statements.

### Step-by-Step Solution:

**Step 1: Identify the Reaction**
The reaction given is:
\[ \text{NaOH} + \text{H}_2\text{CO}_3 \rightarrow \text{NaHCO}_3 + \text{H}_2\text{O} \]

**Step 2: Calculate the Molecular Weight of H₂CO₃**
The molecular weight of H₂CO₃ (carbonic acid) can be calculated as follows:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Carbon (C): 12 g/mol × 1 = 12 g/mol
- Oxygen (O): 16 g/mol × 3 = 48 g/mol

Adding these together:
\[ \text{Molecular weight of H}_2\text{CO}_3 = 2 + 12 + 48 = 62 \text{ g/mol} \]

**Step 3: Determine the n-factor of H₂CO₃**
The n-factor is defined as the number of moles of electrons lost or gained per molecule in a redox reaction. In this case, H₂CO₃ acts as an acid and donates one proton (H⁺) to NaOH. Therefore, the n-factor of H₂CO₃ in this reaction is:
\[ n = 1 \]

**Step 4: Calculate the Equivalent Weight of H₂CO₃**
The formula for equivalent weight is:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{\text{n-factor}} \]

Substituting the values we calculated:
\[ \text{Equivalent Weight of H}_2\text{CO}_3 = \frac{62 \text{ g/mol}}{1} = 62 \text{ g/equiv} \]

**Step 5: Analyze the Statements**
- **Statement 1**: The equivalent weight of H₂CO₃ is 62. This is true based on our calculation.
- **Statement 2**: The n-factor of H₂CO₃ is 1 in the above reaction, and the equivalent mass is calculated as molecular mass divided by the n-factor. This is also true as we have shown that the n-factor is indeed 1 and the calculation of equivalent weight is correct.

### Conclusion:
Both statements are true, and Statement 2 correctly explains Statement 1.