25.5 g of `H_(2)O_(2)` solution on decomposition gave 1.68 L of `O_(2)` at STP. The percentage strength by weight of the solution is

Options

A. 30
B. 10
C. 20
D. 25

Answer

To find the percentage strength by weight of the hydrogen peroxide solution, we can follow these steps:

### Step 1: Write the decomposition equation of hydrogen peroxide (H₂O₂).
The balanced equation for the decomposition of hydrogen peroxide is:
\[ 2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2 \]

### Step 2: Calculate the number of moles of oxygen produced.
At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters. Given that 1.68 L of O₂ is produced, we can calculate the number of moles of O₂:
\[ \text{Number of moles of } O_2 = \frac{\text{Volume of } O_2}{\text{Molar volume at STP}} = \frac{1.68 \, \text{L}}{22.4 \, \text{L/mol}} \approx 0.075 \, \text{mol} \]

### Step 3: Determine the number of moles of hydrogen peroxide (H₂O₂).
From the balanced equation, we see that 2 moles of H₂O₂ produce 1 mole of O₂. Therefore, the number of moles of H₂O₂ is:
\[ \text{Number of moles of } H_2O_2 = 2 \times \text{Number of moles of } O_2 = 2 \times 0.075 \, \text{mol} = 0.15 \, \text{mol} \]

### Step 4: Calculate the mass of hydrogen peroxide (H₂O₂).
The molar mass of hydrogen peroxide (H₂O₂) is approximately 34 g/mol. Thus, the mass of H₂O₂ can be calculated as:
\[ \text{Mass of } H_2O_2 = \text{Number of moles} \times \text{Molar mass} = 0.15 \, \text{mol} \times 34 \, \text{g/mol} = 5.1 \, \text{g} \]

### Step 5: Calculate the percentage strength by weight of the solution.
The percentage strength by weight (w/w) is calculated using the formula:
\[ \text{Percentage strength (w/w)} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage strength (w/w)} = \left( \frac{5.1 \, \text{g}}{25.5 \, \text{g}} \right) \times 100 \approx 20\% \]

### Final Answer:
The percentage strength by weight of the hydrogen peroxide solution is **20%**.

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