A sample of 17.9 mg of a compounf of molar mass 90 `gmol^-1` when treated with `CH_3MgI` releases 1.34 ml of a gas at STP. The number of active hydrogen in the molecule is

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem step by step, we need to determine the number of active hydrogen atoms in the compound based on the information provided.

### Step 1: Calculate the number of moles of the compound
Given:
- Mass of the compound = 17.9 mg = 17.9 × 10^-3 g
- Molar mass of the compound = 90 g/mol

Using the formula for moles:
\[ \text{Moles of compound} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
\[ \text{Moles of compound} = \frac{17.9 \times 10^{-3} \text{ g}}{90 \text{ g/mol}} = 1.98 \times 10^{-4} \text{ mol} \]

### Step 2: Calculate the number of moles of gas produced
Given:
- Volume of gas at STP = 1.34 ml = 1.34 × 10^-3 L
- At STP, 1 mole of gas occupies 22.4 L.

Using the formula for moles of gas:
\[ \text{Moles of gas} = \frac{\text{volume (L)}}{22.4 \text{ L/mol}} \]
\[ \text{Moles of gas} = \frac{1.34 \times 10^{-3} \text{ L}}{22.4 \text{ L/mol}} = 5.96 \times 10^{-5} \text{ mol} \]

### Step 3: Determine the number of active hydrogens
The number of active hydrogens can be calculated using the ratio of moles of gas produced to moles of the compound:
\[ \text{Active hydrogens} = \frac{\text{Moles of gas}}{\text{Moles of compound}} \]
\[ \text{Active hydrogens} = \frac{5.96 \times 10^{-5} \text{ mol}}{1.98 \times 10^{-4} \text{ mol}} \approx 0.30 \]

To find the number of active hydrogen atoms, we multiply the result by the total number of moles of the compound:
\[ \text{Number of active hydrogens} = 3 \text{ (as we round to the nearest whole number)} \]

### Conclusion
The number of active hydrogens in the molecule is **3**.