Calculate the volume strength of a 3% solution of `H_2 O_2` .

Explanation

To calculate the volume strength of a 3% solution of hydrogen peroxide (H₂O₂), we can follow these steps:

### Step 1: Understand the 3% Solution
A 3% solution of H₂O₂ means that there are 3 grams of H₂O₂ in 100 mL of the solution.

### Step 2: Calculate the Equivalent Weight of H₂O₂
The equivalent weight of a substance is calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{n \text{-factor}} \]
For H₂O₂:
- The molecular weight (M) of H₂O₂ is approximately 34 g/mol.
- The n-factor for H₂O₂ in this reaction (where it decomposes to produce O₂) is 2.

Thus, the equivalent weight of H₂O₂ is:
\[ \text{Equivalent Weight} = \frac{34}{2} = 17 \text{ g/equiv} \]

### Step 3: Calculate Normality
Normality (N) can be calculated using the formula:
\[ N = \frac{\text{Given mass}}{\text{Equivalent weight} \times \text{Volume in liters}} \]
Given mass = 3 g, Equivalent weight = 17 g/equiv, and Volume = 100 mL = 0.1 L.

Substituting the values:
\[ N = \frac{3}{17 \times 0.1} = \frac{3}{1.7} \approx 1.76 \text{ N} \]

### Step 4: Calculate the Volume of O₂ Produced
From the reaction:
\[ 2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2 \]
68 g of H₂O₂ produces 22,400 mL of O₂ at STP.

Using the proportion:
\[ 29.92 \text{ g of H}_2\text{O}_2 \text{ will produce } \frac{22400}{68} \times 29.92 \text{ mL of O}_2 \]

Calculating this:
\[ \text{Volume of O}_2 = \frac{22400}{68} \times 29.92 \approx 9856 \text{ mL} \]

### Step 5: Calculate the Volume Strength
Volume strength is defined as the volume of O₂ produced from 1 liter of H₂O₂ solution. Since we have 9856 mL of O₂ from 1000 mL of H₂O₂ solution, we can express this as:
\[ \text{Volume Strength} = \frac{9856 \text{ mL}}{1000 \text{ mL}} = 9.856 \]

### Final Answer
The volume strength of a 3% solution of H₂O₂ is approximately **9.856**.

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