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

Options

A. `3.00%`
B. `4.045 %`
C. `2.509%`
D. `3.035%`

Explanation

To calculate the strength of a 10 volume hydrogen peroxide (H₂O₂) solution, we can follow these steps:

### Step 1: Understand the Concept of Volume Strength
Volume strength of a solution indicates the volume of gas (in liters) produced at NTP (Normal Temperature and Pressure) when 1 liter of the solution decomposes. For hydrogen peroxide, 1 volume strength corresponds to 1 liter of oxygen gas produced from 1 liter of the solution.

### Step 2: Determine the 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 reaction, we see that 2 moles of H₂O₂ produce 1 mole of O₂.

### Step 3: Calculate the Moles of H₂O₂
Given that the solution is 10 volume, it means that 1 liter of this solution will produce 10 liters of oxygen gas at NTP.

Using the ideal gas law, we know that:
1 mole of gas at NTP occupies 22.4 liters.

Thus, the number of moles of O₂ produced from 10 liters is:
\[ \text{Moles of O}_2 = \frac{10 \text{ liters}}{22.4 \text{ liters/mole}} \approx 0.4464 \text{ moles} \]

### Step 4: Relate Moles of O₂ to Moles of H₂O₂
From the balanced equation, we see that 1 mole of O₂ is produced from 2 moles of H₂O₂. Therefore, the moles of H₂O₂ required for 0.4464 moles of O₂ is:
\[ \text{Moles of H}_2\text{O}_2 = 2 \times 0.4464 \approx 0.8928 \text{ moles} \]

### Step 5: Calculate the Mass of H₂O₂
The molar mass of H₂O₂ is approximately 34 g/mol. Therefore, the mass of H₂O₂ in the solution is:
\[ \text{Mass of H}_2\text{O}_2 = 0.8928 \text{ moles} \times 34 \text{ g/mol} \approx 30.35 \text{ grams} \]

### Step 6: Calculate the Strength of the H₂O₂ Solution
The strength of the solution is expressed as a percentage, which can be calculated as follows:
\[ \text{Strength (\%)} = \left( \frac{\text{mass of solute (H}_2\text{O}_2)}{\text{volume of solution (in mL)}} \right) \times 100 \]
Assuming we are considering 1 liter (1000 mL) of the solution:
\[ \text{Strength (\%)} = \left( \frac{30.35 \text{ grams}}{1000 \text{ mL}} \right) \times 100 \approx 3.035\% \]

### Final Answer
The strength of the hydrogen peroxide solution is approximately **3.035%**.

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