How may moles of `H_(2)O_(2)` must be present in 2L of its solution, such that 100 ml of the solution can liberate 3.2 grams of oxygen at `273^(@)C` and 0.5 atm pressure?

Answer

To solve the problem, we need to determine how many moles of hydrogen peroxide (H₂O₂) are required in a 2L solution such that 100 mL of this solution can liberate 3.2 grams of oxygen (O₂) under the given conditions.

### Step-by-step Solution:

1. **Write the Decomposition Reaction**:
The decomposition of hydrogen peroxide can be represented by the following balanced equation:
\[ 2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2 \]
From this equation, we see that 2 moles of H₂O₂ produce 1 mole of O₂.

2. **Calculate Moles of Oxygen (O₂)**:
We are given that 3.2 grams of O₂ are liberated. To find the number of moles of O₂, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
The molar mass of O₂ (oxygen) is 32 g/mol (since O has an atomic mass of 16 g/mol, and O₂ has two atoms).
\[ \text{Number of moles of O}_2 = \frac{3.2 \text{ g}}{32 \text{ g/mol}} = 0.1 \text{ moles} \]

3. **Determine Moles of H₂O₂ Required**:
From the balanced equation, we know that 2 moles of H₂O₂ produce 1 mole of O₂. Therefore, for 0.1 moles of O₂, the moles of H₂O₂ required will be:
\[ \text{Moles of H}_2\text{O}_2 = 2 \times \text{Moles of O}_2 = 2 \times 0.1 = 0.2 \text{ moles} \]

4. **Calculate Concentration of H₂O₂ in 100 mL**:
We have established that 0.2 moles of H₂O₂ are present in 100 mL of the solution.

5. **Calculate Moles of H₂O₂ in 2L of Solution**:
Since 2L is equivalent to 2000 mL, we can find the number of moles of H₂O₂ in 2000 mL using the ratio:
\[ \text{Moles in 2000 mL} = \left(\frac{0.2 \text{ moles}}{100 \text{ mL}}\right) \times 2000 \text{ mL} = 4 \text{ moles} \]

### Final Answer:
Thus, the number of moles of H₂O₂ that must be present in 2L of its solution is **4 moles**.