The strength in volumes of a solution containing 30.36 g/L of `H_(2)O_(2)` is (Given volume of 1 mole of gas STP = 22.4 litre)

Options

A. 10 volume
B. 20 volume
C. 5 volume
D. None of these

Answer

To determine the strength in volumes of a solution containing 30.36 g/L of hydrogen peroxide (H₂O₂), we can follow these steps:

### Step 1: Write the decomposition reaction of H₂O₂
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 2: Calculate the molar mass of H₂O₂
The molar mass of H₂O₂ can be calculated as follows:
- Hydrogen (H) has an atomic mass of approximately 1 g/mol, and there are 2 hydrogen atoms.
- Oxygen (O) has an atomic mass of approximately 16 g/mol, and there are 2 oxygen atoms.

Thus, the molar mass of H₂O₂ is:
\[ \text{Molar mass of H}_2\text{O}_2 = (2 \times 1) + (2 \times 16) = 2 + 32 = 34 \text{ g/mol} \]

### Step 3: Determine the number of moles of H₂O₂ in 30.36 g
Using the concentration of the solution (30.36 g/L), we can find the number of moles of H₂O₂:
\[ \text{Number of moles of H}_2\text{O}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{30.36 \text{ g}}{34 \text{ g/mol}} \]

Calculating this gives:
\[ \text{Number of moles of H}_2\text{O}_2 = 0.894 \text{ moles} \]

### Step 4: Calculate the volume of O₂ produced
From the stoichiometry of the reaction, we know that 2 moles of H₂O₂ produce 1 mole of O₂. Therefore, the number of moles of O₂ produced from 0.894 moles of H₂O₂ is:
\[ \text{Number of moles of O}_2 = \frac{0.894 \text{ moles H}_2\text{O}_2}{2} = 0.447 \text{ moles O}_2 \]

### Step 5: Calculate the volume of O₂ at STP
At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 liters. Therefore, the volume of O₂ produced can be calculated as:
\[ \text{Volume of O}_2 = \text{Number of moles of O}_2 \times 22.4 \text{ L/mol} \]
\[ \text{Volume of O}_2 = 0.447 \text{ moles} \times 22.4 \text{ L/mol} \]
Calculating this gives:
\[ \text{Volume of O}_2 = 10.03 \text{ L} \]

### Step 6: Determine the strength in volumes
The strength in volumes of the solution is defined as the volume of O₂ produced by 1 liter of the solution. Since we calculated that 30.36 g of H₂O₂ produces approximately 10.03 L of O₂, we can conclude that the strength in volumes is approximately:
\[ \text{Strength in volumes} \approx 10 \text{ volumes} \]

### Final Answer
The strength in volumes of the solution containing 30.36 g/L of H₂O₂ is approximately **10 volumes**.

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