There is a smaple of 10 volume of hydrogen peroxide solution . Calculate its strength.

Options

A. `3.00%`
B. `4.045%`
C. `2.59%`
D. `3.035%`

Answer

To calculate the strength of a 10 volume hydrogen peroxide solution, we need to follow these steps:

### Step 1: Understand Volume Strength
Volume strength indicates the volume of oxygen gas (O2) that can be liberated by 1 liter of hydrogen peroxide (H2O2) solution. In this case, a 10 volume solution means that 1 liter of this solution can liberate 10 liters of oxygen gas.

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

### Step 3: Calculate Moles of O2 Produced
Since the volume strength is 10, we know that 10 liters of O2 are produced from 1 liter of H2O2 solution. Using the molar volume of a gas at NTP (22.4 L), we can find the number of moles of O2 produced:
\[ \text{Moles of O}_2 = \frac{10 \text{ L}}{22.4 \text{ L/mol}} = 0.4464 \text{ moles} \]

### Step 4: Calculate Moles of H2O2 Required
From the stoichiometry of the reaction, 2 moles of H2O2 produce 1 mole of O2. Therefore, the moles of H2O2 required to produce 0.4464 moles of O2 can be calculated as:
\[ \text{Moles of H}_2\text{O}_2 = 2 \times 0.4464 = 0.8928 \text{ moles} \]

### Step 5: Calculate Mass of H2O2
The molar mass of hydrogen peroxide (H2O2) is approximately 34 g/mol. Thus, the mass of H2O2 required can be calculated as:
\[ \text{Mass of H}_2\text{O}_2 = 0.8928 \text{ moles} \times 34 \text{ g/mol} = 30.35 \text{ grams} \]

### Step 6: Calculate Percentage Strength
The percentage strength of the solution can be calculated using the formula:
\[ \text{Percentage Strength} = \left( \frac{\text{Weight of solute (g)}}{\text{Volume of solution (mL)}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Strength} = \left( \frac{30.35 \text{ g}}{1000 \text{ mL}} \right) \times 100 = 3.035\% \]

### Conclusion
The strength of the 10 volume hydrogen peroxide solution is **3.035%**.

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