1.60 g of a metal was dissolved in `HNO_3` to prepare its nitrate. The nitrate salt on strong heating gave 2g oxide. The equivalent mass of metal is:

Options

A. 16 g
B. 32 g
C. 48 g
D. 12 g

Answer

To find the equivalent mass of the metal, we can follow these steps:

### Step 1: Understand the Reaction
The metal (M) is dissolved in nitric acid (HNO₃) to form its nitrate (M(NO₃)ₙ). Upon strong heating, the nitrate decomposes to form the metal oxide (M₂Oₙ) and nitrogen dioxide (NO₂) along with oxygen (O₂).

### Step 2: Write the Mass Relationships
We know:
- Mass of metal (M) = 1.60 g
- Mass of oxide (M₂Oₙ) = 2 g

### Step 3: Determine the Molar Mass of the Oxide
The molar mass of the oxide can be expressed as:
\[ \text{Molar mass of oxide} = 2M + 16N \]
Where:
- M = Molar mass of the metal
- N = Number of oxygen atoms in the oxide.

### Step 4: Calculate the Number of Moles
The number of moles of the metal and the oxide can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \]

For the metal:
\[ \text{Number of moles of metal} = \frac{1.60}{M} \]

For the oxide:
\[ \text{Number of moles of oxide} = \frac{2}{(2M + 16N)} \]

### Step 5: Establish Stoichiometric Relationships
From the stoichiometry of the reaction, we know:
- 2 moles of metal produce 1 mole of oxide.
Thus, we can set up the relationship:
\[ \frac{1.60}{M} = 2 \times \frac{2}{(2M + 16N)} \]

### Step 6: Cross-Multiply and Simplify
Cross-multiplying gives:
\[ 1.60 \times (2M + 16N) = 4M \]
Expanding this gives:
\[ 3.2M + 25.6N = 4M \]

### Step 7: Rearranging the Equation
Rearranging the equation results in:
\[ 4M - 3.2M = 25.6N \]
\[ 0.8M = 25.6N \]
\[ M = \frac{25.6N}{0.8} \]
\[ M = 32N \]

### Step 8: Determine Equivalent Mass
The equivalent mass of the metal is given by:
\[ \text{Equivalent mass} = \frac{\text{Molar mass}}{\text{n-factor}} \]
Where the n-factor for the metal (M) is equal to N (the number of moles of electrons transferred).

Thus, we have:
\[ \text{Equivalent mass} = \frac{M}{N} = \frac{32N}{N} = 32 \text{ g/equiv} \]

### Conclusion
The equivalent mass of the metal is **32 g/equiv**.

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