A bivalent metal has an equivalent mass of 32. The molecular mass of the metal nitrate is

Options

A. 168
B. 192
C. 188
D. 182

Answer

To solve the problem, we need to determine the molecular mass of the metal nitrate given that the bivalent metal has an equivalent mass of 32.

### Step-by-Step Solution:

1. **Identify the Valency of the Metal:**
- The problem states that the metal is bivalent, which means its valency (n) is 2.

2. **Use the Formula for Equivalent Mass:**
- The equivalent mass (E) of a substance is given by the formula:
\[ E = \frac{\text{Atomic Mass (A)}}{\text{Valency (n)}} \]
- We know the equivalent mass is 32 and the valency is 2.

3. **Calculate the Atomic Mass of the Metal:**
- Rearranging the formula to find the atomic mass:
\[ A = E \times n \]
- Substituting the known values:
\[ A = 32 \times 2 = 64 \]
- Therefore, the atomic mass of the metal (M) is 64.

4. **Determine the Formula of the Metal Nitrate:**
- The formula for nitrate is \( \text{NO}_3 \).
- Since the metal is bivalent (valency = 2) and the valency of nitrate is 1, the formula for the metal nitrate will be:
\[ \text{M(NO}_3\text{)}_2 \]
- This indicates that there are two nitrate ions for each metal ion.

5. **Calculate the Molecular Mass of the Metal Nitrate:**
- The molecular mass can be calculated as follows:
- Atomic mass of metal (M) = 64
- Atomic mass of nitrogen (N) = 14 (for 2 nitrogen atoms, it will be \( 14 \times 2 = 28 \))
- Atomic mass of oxygen (O) = 16 (for 6 oxygen atoms, it will be \( 16 \times 6 = 96 \))
- Therefore, the total molecular mass is:
\[ \text{Molecular Mass} = \text{Atomic Mass of M} + 2 \times \text{Atomic Mass of N} + 6 \times \text{Atomic Mass of O} \]
\[ = 64 + 28 + 96 = 188 \]

6. **Conclusion:**
- The molecular mass of the metal nitrate \( \text{M(NO}_3\text{)}_2 \) is 188.

### Final Answer:
The molecular mass of the metal nitrate is **188**.