0.2 g of a primary aliphatic amine, on treatment with nitrous acid gave 61.36 ml of `N_2` gas at STP. The molecular mass of the amine will be:

Options

A. 99 g/mole
B. 87 g/mole
C. 73 g/mole
D. 123 g/mole

Answer

To find the molecular mass of the primary aliphatic amine, we can follow these steps:

### Step 1: Understand the Reaction
When a primary aliphatic amine (RNH₂) reacts with nitrous acid (HNO₂), it produces alcohol (ROH) and nitrogen gas (N₂). The balanced reaction can be summarized as:
\[ \text{RNH}_2 + \text{HNO}_2 \rightarrow \text{ROH} + \text{N}_2 \]

### Step 2: Calculate the Moles of Nitrogen Gas (N₂)
We are given that 61.36 mL of N₂ gas is produced at STP (Standard Temperature and Pressure). At STP, 1 mole of any gas occupies 22.4 L (or 22400 mL).

To find the number of moles of N₂ produced, we can use the formula:
\[ \text{Number of moles of } N_2 = \frac{\text{Volume of } N_2 \text{ (in mL)}}{22400 \text{ mL/mol}} \]
Substituting the given volume:
\[ \text{Number of moles of } N_2 = \frac{61.36 \text{ mL}}{22400 \text{ mL/mol}} \]

### Step 3: Perform the Calculation
Calculating the above expression:
\[ \text{Number of moles of } N_2 = \frac{61.36}{22400} \approx 2.743 \times 10^{-3} \text{ moles} \]

### Step 4: Relate Moles of Amine to Moles of N₂
From the reaction, we see that 1 mole of primary aliphatic amine produces 1 mole of N₂. Therefore, the number of moles of the primary aliphatic amine is also:
\[ \text{Number of moles of amine} = 2.743 \times 10^{-3} \text{ moles} \]

### Step 5: Calculate the Molecular Mass of the Amine
The molecular mass (M) of the amine can be calculated using the formula:
\[ M = \frac{\text{Weight of amine (g)}}{\text{Number of moles of amine}} \]
Given that the weight of the amine is 0.2 g:
\[ M = \frac{0.2 \text{ g}}{2.743 \times 10^{-3} \text{ moles}} \]

### Step 6: Perform the Final Calculation
Calculating the molecular mass:
\[ M \approx \frac{0.2}{2.743 \times 10^{-3}} \approx 73.0 \text{ g/mol} \]

### Conclusion
The molecular mass of the primary aliphatic amine is approximately 73 g/mol.

---