The labeling on a bottle of `H_2 O_2` solution is 20 vol, then the concentration of `H_2 O_2` in percentage strength will be:

Options

A. 0.0303
B. 0.05
C. 0.0455
D. 0.0607

Answer

To find the concentration of `H2O2` in percentage strength from the given volume strength (20 vol), we can follow these steps:

### Step 1: Understand the meaning of volume strength
The labeling of "20 vol" means that 1 liter of the `H2O2` solution can produce 20 liters of oxygen gas (`O2`) at standard temperature and pressure (STP).

### Step 2: Write the balanced chemical equation
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 equation, we see that 2 moles of `H2O2` produce 1 mole of `O2`.

### Step 3: Calculate the moles of `O2` produced
Since 20 liters of `O2` are produced, we can find the number of moles of `O2`:
- At STP, 1 mole of gas occupies 22.4 liters.
- Therefore, the number of moles of `O2` produced from 20 liters is:
\[ \text{Moles of } O_2 = \frac{20 \text{ L}}{22.4 \text{ L/mol}} \approx 0.8929 \text{ moles} \]

### Step 4: Relate moles of `O2` to moles of `H2O2`
From the balanced equation, we know that 2 moles of `H2O2` produce 1 mole of `O2`. Thus, the moles of `H2O2` needed to produce 0.8929 moles of `O2` is:
\[ \text{Moles of } H_2O_2 = 2 \times 0.8929 \approx 1.7858 \text{ moles} \]

### Step 5: Calculate the 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
- Therefore, the molar mass of `H2O2` = 2 + 32 = 34 g/mol.

Now, we can calculate the mass of `H2O2`:
\[ \text{Mass of } H_2O_2 = \text{Moles} \times \text{Molar Mass} = 1.7858 \text{ moles} \times 34 \text{ g/mol} \approx 60.7 \text{ g} \]

### Step 6: Calculate the percentage strength
To find the percentage strength, we need to express the mass of `H2O2` in grams per liter of solution. Since we have calculated that there are 60.7 grams of `H2O2` in 1 liter of solution, we can calculate the percentage strength as follows:
\[ \text{Percentage Strength} = \left( \frac{\text{Mass of } H_2O_2}{\text{Volume of solution in mL}} \right) \times 100 \]
\[ \text{Percentage Strength} = \left( \frac{60.7 \text{ g}}{1000 \text{ mL}} \right) \times 100 \approx 6.07\% \]

### Step 7: Convert to decimal form
To express this percentage as a decimal:
\[ 6.07\% = \frac{6.07}{100} = 0.0607 \]

### Final Answer
The concentration of `H2O2` in percentage strength is **0.0607**.

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