2.5 g of the carbonate of a metal was treated with 100 ml of 1 N` H_(2)SO_(4)`. After the completion of the reaction, the solution was boiled off to expel `CO_(2)` and was then titrated against 1 N NaOH solution. The volume of alkali that would be consumed, if the equivalent weight of the metal is 20.

Options

A. 50
B. 25
C. 75
D. 100

Explanation

To solve the problem step by step, we will follow the chemical principles involved in the reaction of the metal carbonate with sulfuric acid and the subsequent titration with sodium hydroxide.

### Step-by-Step Solution:

1. **Determine the Equivalent Weight of the Metal Carbonate:**
- The equivalent weight of a compound is calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molar Mass}}{n} \]
- For carbonate (\(CO_3^{2-}\)), the valency factor \(n\) is 2.
- The molar mass of carbonate is calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol (for 3 O atoms, it is \(16 \times 3 = 48\))
- Total molar mass of \(CO_3^{2-} = 12 + 48 = 60\) g/mol
- Therefore, the equivalent weight of carbonate is:
\[ \text{Equivalent Weight of Carbonate} = \frac{60}{2} = 30 \text{ g/equiv} \]

2. **Calculate the Equivalent Weight of the Metal Carbonate:**
- Given that the equivalent weight of the metal is 20 g/equiv, the equivalent weight of the metal carbonate is:
\[ \text{Equivalent Weight of Metal Carbonate} = 20 + 30 = 50 \text{ g/equiv} \]

3. **Calculate the Number of Equivalents of Metal Carbonate:**
- The mass of the metal carbonate used is 2.5 g.
- The number of equivalents of metal carbonate can be calculated as:
\[ \text{Number of Equivalents} = \frac{\text{Mass}}{\text{Equivalent Weight}} = \frac{2.5}{50} = 0.05 \text{ equivalents} \]

4. **Calculate the Number of Equivalents of \(H_2SO_4\) Used:**
- The volume of \(H_2SO_4\) used is 100 mL with a normality of 1 N.
- The number of equivalents of \(H_2SO_4\) is:
\[ \text{Number of Equivalents of } H_2SO_4 = \text{Normality} \times \text{Volume (L)} = 1 \times \frac{100}{1000} = 0.1 \text{ equivalents} \]

5. **Calculate the Number of Equivalents of \(H_2SO_4\) That Remain:**
- The number of equivalents of \(H_2SO_4\) that reacted with the carbonate is 0.05 equivalents.
- Therefore, the number of equivalents of \(H_2SO_4\) that remain unreacted is:
\[ \text{Remaining } H_2SO_4 = 0.1 - 0.05 = 0.05 \text{ equivalents} \]

6. **Determine the Number of Equivalents of NaOH Consumed:**
- The equivalents of NaOH consumed in the titration will equal the equivalents of \(H_2SO_4\) that remain unreacted:
\[ \text{Number of Equivalents of NaOH} = 0.05 \text{ equivalents} \]

7. **Calculate the Volume of NaOH Solution Consumed:**
- Using the formula for equivalents:
\[ \text{Milli equivalents} = \text{Normality} \times \text{Volume (mL)} \]
- Rearranging gives:
\[ \text{Volume (mL)} = \frac{\text{Milli equivalents}}{\text{Normality}} = \frac{0.05 \times 1000}{1} = 50 \text{ mL} \]

### Final Answer:
The volume of NaOH solution consumed is **50 mL**.