Which of the following solution has normality equal to molarity ?

Options

A. `H_(2) SO_(4)` aqueous solution
B. `H_(3) PO_(4)` aqueous solution
C. `HNO_(3)` aqueous solution
D. `Mg (OH)_(2)` aqueous solution

Answer

To determine which of the following solutions has normality equal to molarity, we need to understand the relationship between normality and molarity. Normality (N) is defined as the number of equivalents of solute per liter of solution, while molarity (M) is defined as the number of moles of solute per liter of solution. The formula connecting them is:

\[ \text{Normality} = n \times \text{Molarity} \]

where \( n \) is the number of equivalents (or the n-factor).

### Step-by-Step Solution:

1. **Identify the Compounds:**
The compounds given in the question are:
- H₂SO₄ (sulfuric acid)
- H₃PO₄ (phosphoric acid)
- HNO₃ (nitric acid)
- Mg(OH)₂ (magnesium hydroxide)

2. **Determine the n-factor for each compound:**
- **H₂SO₄:**
- It can donate 2 H⁺ ions when dissolved in water.
- Therefore, the n-factor = 2.

- **H₃PO₄:**
- It can donate 3 H⁺ ions when dissolved in water.
- Therefore, the n-factor = 3.

- **HNO₃:**
- It can donate 1 H⁺ ion when dissolved in water.
- Therefore, the n-factor = 1.

- **Mg(OH)₂:**
- It can donate 2 OH⁻ ions when dissolved in water.
- Therefore, the n-factor = 2.

3. **Apply the relationship between normality and molarity:**
- For normality to equal molarity, the n-factor must be 1.
- From our calculations:
- H₂SO₄: n-factor = 2
- H₃PO₄: n-factor = 3
- HNO₃: n-factor = 1
- Mg(OH)₂: n-factor = 2

4. **Conclusion:**
- The only compound with an n-factor of 1 is HNO₃.
- Therefore, the solution that has normality equal to molarity is **HNO₃**.

### Final Answer:
**HNO₃ (Nitric acid)** has normality equal to molarity.