How many no. of active Hydrogen atoms are present in compound (mol. Mass `90`) `0.45 g` of which when treated with `Na` metal liberates `112m l` of the `H_(2)` gas at `STP`.

Answer

To solve the problem step by step, we will determine the number of active hydrogen atoms present in the compound based on the given data.

### Step 1: Calculate the number of moles of hydrogen gas (H₂) produced.
At STP (Standard Temperature and Pressure), 1 mole of hydrogen gas occupies 22,400 mL. We are given that 112 mL of H₂ gas is produced.

\[ \text{Number of moles of } H_2 = \frac{\text{Volume of } H_2}{\text{Molar volume at STP}} = \frac{112 \, \text{mL}}{22400 \, \text{mL/mol}} = 0.005 \, \text{moles} \]

### Step 2: Determine the number of moles of the compound.
We know the mass of the compound is 0.45 g and its molar mass is 90 g/mol.

\[ \text{Number of moles of compound} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.45 \, \text{g}}{90 \, \text{g/mol}} = 0.005 \, \text{moles} \]

### Step 3: Relate the moles of hydrogen gas to the active hydrogen atoms in the compound.
From the reaction with sodium (Na), we know that each mole of the compound releases hydrogen gas. Since 1 mole of H₂ gas corresponds to 2 moles of active hydrogen atoms (because H₂ contains 2 hydrogen atoms), we can calculate the number of active hydrogen atoms.

\[ \text{Number of active hydrogen atoms} = 2 \times \text{moles of } H_2 = 2 \times 0.005 \, \text{moles} = 0.01 \, \text{moles of active hydrogen atoms} \]

### Step 4: Calculate the total number of active hydrogen atoms.
Since 1 mole of any substance contains \(6.022 \times 10^{23}\) entities (Avogadro's number), we can find the total number of active hydrogen atoms.

\[ \text{Total number of active hydrogen atoms} = 0.01 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} = 6.022 \times 10^{21} \, \text{active hydrogen atoms} \]

### Conclusion
The number of active hydrogen atoms present in the compound is 2.

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