Percentage strength of 20 volume `H_2O_2` solution is

Options

A. 0.03
B. `6%`
C. 0.2
D. 0.15

Answer

To determine the percentage strength of a 20 volume H₂O₂ (hydrogen peroxide) solution, follow these steps:

### Step 1: Understand the Concept of Volume Strength
The term "20 volume" means that 1 liter of the H₂O₂ solution can release 20 liters of oxygen gas (O₂) when decomposed.

### Step 2: Write the Decomposition Reaction
The decomposition of hydrogen peroxide can be represented by the following balanced chemical equation:
\[ 2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2 \]

### Step 3: Calculate the Molar Mass of H₂O₂
The molar mass of H₂O₂ is calculated as follows:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Oxygen (O): 16 g/mol × 2 = 32 g/mol
- Total molar mass of H₂O₂ = 2 + 32 = 34 g/mol

### Step 4: Determine the Mass of H₂O₂ Required for 20 Volume
From the definition of volume strength, 20 volumes of O₂ means:
- 20 liters of O₂ at NTP (Normal Temperature and Pressure) can be produced from H₂O₂.

Using the ideal gas law, we know that 1 mole of gas occupies 22.4 liters at NTP. Therefore:
\[ \text{Moles of O₂} = \frac{20 \text{ L}}{22.4 \text{ L/mol}} = 0.8929 \text{ moles} \]

### Step 5: Relate Moles of O₂ to Moles of H₂O₂
From the balanced equation, 1 mole of O₂ is produced from 2 moles of H₂O₂. Thus:
\[ \text{Moles of H₂O₂} = 2 \times \text{Moles of O₂} = 2 \times 0.8929 = 1.7858 \text{ moles} \]

### Step 6: Calculate the Mass of H₂O₂
Now, calculate the mass of H₂O₂ needed:
\[ \text{Mass of H₂O₂} = \text{Moles of H₂O₂} \times \text{Molar Mass of H₂O₂} \]
\[ \text{Mass of H₂O₂} = 1.7858 \text{ moles} \times 34 \text{ g/mol} = 60.71 \text{ g} \]

### Step 7: Calculate the Percentage Strength
The percentage strength is calculated based on the mass of solute (H₂O₂) in 100 mL of solution. Since we have the mass for 1 liter (1000 mL), we can find the mass for 100 mL:
\[ \text{Mass in 100 mL} = \frac{60.71 \text{ g}}{1000 \text{ mL}} \times 100 \text{ mL} = 6.071 \text{ g} \]

Now, the percentage strength can be calculated as:
\[ \text{Percentage Strength} = \left( \frac{\text{Mass of H₂O₂}}{\text{Volume of solution}} \right) \times 100 \]
\[ \text{Percentage Strength} = \left( \frac{6.071 \text{ g}}{100 \text{ mL}} \right) \times 100 = 6.071\% \]

### Final Answer
The percentage strength of the 20 volume H₂O₂ solution is approximately **6%**.

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